Home » Surface Tension of Water: The surface tension of water is 72 dynes/cm at 25°C . It would take a force of 72 dynes to break a surface film of water 1 cm long. The surface tension of water decreases significantly with temperature as shown in the graph. The surface tension arises from the polar nature of the water molecule.

Surface Tension of Water: The surface tension of water is 72 dynes/cm at 25°C . It would take a force of 72 dynes to break a surface film of water 1 cm long. The surface tension of water decreases significantly with temperature as shown in the graph. The surface tension arises from the polar nature of the water molecule.

June 14, 2024

LESSON 1. SURFACE PHENOMENA

Surface phenomena the special properties of surface layers, that is, the thin layers of a substance at the boundary of contiguous bodies, mediums, or phases. These properties result from the excess free energy of the surface layer and from the special features of the layer’s structure and composition.

Surface phenomena may be purely physical iature, or they may be accompanied by chemical transformations; they occur at liquid (highly mobile) and solid interphase boundaries. Surface phenomena related to surface tension and resulting from the deformation liquid boundary surfaces are also called capillary phenomena. Such phenomena include capillary absorption of liquids into porous bodies, capillary condensation, and the establishment of the equilibrium shape of drops, gas bubbles, and menisci. The properties of a contact surface of two solids or of a solid with a liquid or gaseous medium are determined by such effects as adhesion, wetting, and friction.

The molecular nature and properties of a surface may be radically altered as a result of the formation of surface monomolecular layers or phase (polymolecular) films. Such changes often result from such physical processes as adsorption, surface diffusion, and the spreading of liquids or from the chemical interaction of components of the contiguous phases. Any modification of the surface, or interphase, layer usually leads to an increase or decrease in molecular interaction between the contiguous phases. Physical or chemical transformations in surface layers strongly affect the nature and rate of such heterogeneous phenomena as corrosive, catalytic, and membrane processes.

Surface phenomena also affect the typically volumetric properties of bodies. Thus, a decrease in the free surface energy of solids by an actively adsorptive medium results in a decrease in the strength of these bodies (Rebinder effect). Such surface phenomena as electroadhesive and electrocapillary phenomena and electrode processes, which result from the presence of electric charges in the surface layer, form a special group. Physical or chemical changes in the surface layer of a conductor or semiconductor significantly affect the electron work function. They also affect such surface phenomena in semiconductors as surface states, surface conductivity, and surface recombination; these influences are reflected in the operational characteristics of such semiconductor instruments as solar batteries and photodiodes.

Surface phenomena are found in any heterogeneous system consisting of two or several phases. In essence, the entire physical world, from cosmic bodies to submicroscopic formations, is heterogeneous. Only systems in limited volumes of space may be regarded as homogeneous. Thus, the role of surface phenomena iatural and technological processes is great. Surface phenomena are especially important in disperse (microhetero-geneous) systems, in which the interphase surface is most highly developed. In fact, the conditions facilitating the appearance and prolonged existence of such systems are related to surface phenomena.

The major problems of colloid chemistry reduce to surface phenomena in disperse systems. All the processes that lead to changes in the size of the particles of the highly dispersed phase, including coagulation, coalescence, peptization, and emulsifica-tion, are due to the interaction of Brownian motion and surface phenomena. In coarsely disperse and macroheterogeneous systems, a primary role is played by the tension between surface forces and external mechanical actions. Surface phenomena, by affecting the magnitude of the free surface energy and the structure of the surface layer, control the origin and growth of new-phase particles in supersaturated vapors, solutions, and melts. Surface phenomena also control the interaction of colloidal particles in the formation of various types of disperse structures. Surfactants, which alter the structure and properties of interphase surfaces as a result of adsorption, often fundamentally affect the extent and tendency of processes caused by surface phenomena.

The foundation of the modern thermodynamics of surface phenomena was laid by the American physical chemist J. Gibbs. The Soviet scientists P. A. Rebinder, A. N. Frumkin, B. V. Deriagin, and A. V. Dumanskii developed theoretical concepts of the nature and molecular mechanism of surface phenomena that are of great practical importance.

The utilization of surface phenomena in industry permits the improvement of existing technological processes. Surface phenomena often determine methods for extending the durability of important structural and construction materials; they also determine the efficiency of mining and concentrating minerals and the quality and properties of products of the chemical, textile, food-processing, and pharmaceutical industries. Surface phenomena have great importance in metallurgy and in the production of ceramics, metal ceramics, and such polymer materials as plastics, rubbers, paints, and varnishes. Such surface phenomena as lubrication, abrasion, contact interaction, and structural changes in polycrystalline and composite materials, as well as electrical and electrochemical processes and phenomena occurring on the surfaces of solids, are important in technology.

A knowledge of surface phenomena in biology makes it possible to control biological processes with the aim of increasing agricultural productivity and developing the microbiological industry and the potentialities of medicine and veterinary medicine.

In biology, surface phenomena are important primarily in relation to the cellular, subcellular, and molecular levels of organization of living systems. Various biological membranes separate the cell from its environment and secure its mi-croheterogeneity. Vital processes take place on the membranes of cells and of such intracellular organelles as mitochondria and plastids. These processes include the reception of such exogenous and endogenous biologically active substances as hormones, mediators, antigens and pheromones; enzymatic catalysis (many enzymes exist within membranes, forming mul-tienzymatic catalytic aggregates); the transformation of chemical energy into osmotic action; and oxidative phosphorylation, that is, the linking of oxidation processes with the accumulation of energy in macroergic compounds.

The special properties of surface interactions are responsible for the aggregation of cells and their attachment to living and nonliving substrata; this includes the formation of thrombi when the walls of vessels are injured, as well as the sorption of viruses on cells. The functioning of such important enzymatic systems as the aggregate of respiratory enzymes is an example of heterogeneous catalysis. The adsorption of corresponding physiologically active substances on surfaces is the basis for the identification of innate and foreign macromolecules as well as the basis of narcosis and of the transfer of nervous impulses. As a whole, surface phenomena in living systems differ from those ionliving nature in their far greater chemical specificity and their mutual compatibility over time and in space. For example, the reception of a hormone on the surface of a cell leads to a conformational transition of a series of membrane components. This causes a change in the membrane’s permeability and heterocatalytic activity and in turn leads to numerous physicochemical and biochemical changes in the cell. These changes in the aggregate determine the cell’s reaction to various influences.

With the progress of evolution, surface phenomena have played an increasingly important role in vital activity. Thus glycolysis, the most ancient mechanism for providing cells with energy, is effected by enzymes in the cytoplasm that are only partially attached to structures of the endoplasmic network. The later and more efficient means of obtaining energy— respiration — is achieved by means of heterocatalytic systems. In unicellular organisms, nourishment occurs by means of the ingestion of entire macromolecules and their subsequent breakdown within the cell. In higher organisms, an important role is played by parietal (contact) digestion, in which enzymatic hydrolysis of the food macromolecules occurs on the external surface of the cell and is coordinated with the subsequent transport of the breakdown products to the cell.

Surface tension is a contractive tendency of the surface of a liquid that allows it to resist an external force. It is revealed, for example, in the floating of some objects on the surface of water, even though they are denser than water, and in the ability of some insects (e.g. water striders) to run on the water surface. This property is caused by cohesion of similar molecules, and is responsible for many of the behaviors of liquids.

Surface tension has the dimension of force per unit length, or of energy per unit area. The two are equivalent—but when referring to energy per unit of area, people use the term surface energy—which is a more general term in the sense that it applies also to solids and not just liquids.

In materials science, surface tension is used for either surface stress or surface free energy.

Causes

Diagram of the forces on molecules of a liquid

Surface tension prevents the paper clip from submerging.

The cohesive forces among liquid molecules are responsible for the phenomenon of surface tension. In the bulk of the liquid, each molecule is pulled equally in every direction by neighboring liquid molecules, resulting in a net force of zero. The molecules at the surface do not have other molecules on all sides of them and therefore are pulled inwards. This creates some internal pressure and forces liquid surfaces to contract to the minimal area.

Surface tension is responsible for the shape of liquid droplets. Although easily deformed, droplets of water tend to be pulled into a spherical shape by the cohesive forces of the surface layer. In the absence of other forces, including gravity, drops of virtually all liquids would be perfectly spherical. The spherical shape minimizes the necessary “wall tension” of the surface layer according to Laplace’s law.

Another way to view surface tension is in terms of energy. A molecule in contact with a neighbor is in a lower state of energy than if it were alone (not in contact with a neighbor). The interior molecules have as many neighbors as they can possibly have, but the boundary molecules are missing neighbors (compared to interior molecules) and therefore have a higher energy. For the liquid to minimize its energy state, the number of higher energy boundary molecules must be minimized. The minimized quantity of boundary molecules results in a minimized surface area.^[1]

As a result of surface area minimization, a surface will assume the smoothest shape it can (mathematical proof that “smooth” shapes minimize surface area relies on use of the Euler–Lagrange equation). Since any curvature in the surface shape results in greater area, a higher energy will also result. Consequently the surface will push back against any curvature in much the same way as a ball pushed uphill will push back to minimize its gravitational potential energy.

Effects of surface tension

Water

Several effects of surface tension can be seen with ordinary water:

A. Beading of rain water on a waxy surface, such as a leaf. Water adheres weakly to wax and strongly to itself, so water clusters into drops. Surface tension gives them their near-spherical shape, because a sphere has the smallest possible surface area to volume ratio.

B. Formation of drops occurs when a mass of liquid is stretched. The animation shows water adhering to the faucet gaining mass until it is stretched to a point where the surface tension cao longer bind it to the faucet. It then separates and surface tension forms the drop into a sphere. If a stream of water were running from the faucet, the stream would break up into drops during its fall. Gravity stretches the stream, then surface tension pinches it into spheres.^[2]

C. Flotation of objects denser than water occurs when the object is nonwettable and its weight is small enough to be borne by the forces arising from surface tension.^[1] For example, water striders use surface tension to walk on the surface of a pond. The surface of the water behaves like an elastic film: the insect’s feet cause indentations in the water’s surface, increasing its surface area.^[3]

D. Separation of oil and water (in this case, water and liquid wax) is caused by a tension in the surface between dissimilar liquids. This type of surface tension is called “interface tension”, but its physics are the same.

E. Tears of wine is the formation of drops and rivulets on the side of a glass containing an alcoholic beverage. Its cause is a complex interaction between the differing surface tensions of water and ethanol; it is induced by a combination of surface tension modification of water by ethanol together with ethanol evaporating faster than water.

A. Water beading on a leaf

B. Water dripping from a tap

C. Water striders stay atop the liquid because of surface tension

D. Lava lamp with interaction between dissimilar liquids; water and liquid wax

E. Photo showing the “tears of wine” phenomenon.

Surface Tension of Water: The surface tension of water is 72 dynes/cm at 25°C . It would take a force of 72 dynes to break a surface film of water 1 cm long. The surface tension of water decreases significantly with temperature as shown in the graph. The surface tension arises from the polar nature of the water molecule.

Hot water is a better cleaning agent because the lower surface tension makes it a better “wetting agent” to get into pores and fissures rather than bridging them with surface tension. Soaps and detergents further lower the surface tension.

The cohesive forces between liquid molecules are responsible for the phenomenon known as surface tension. The molecules at the surface do not have other like molecules on all sides of them and consequently they cohere more strongly to those directly associated with them on the surface. This forms a surface “film” which makes it more difficult to move an object through the surface than to move it when it is completely submersed.

Surface tension is typically measured in dynes/cm, the force in dynes required to break a film of length 1 cm. Equivalently, it can be stated as surface energy in ergs per square centimeter. Water at 20°C (Decrease in water surface tension with heating) has a surface tension of 72.8 dynes/cm compared to 22.3 for ethyl alcohol and 465 for mercury.

Cohesion and Surface Tension:The cohesive forces between molecules down into a liquid are shared with all neighboring atoms. Those on the surface have no neighboring atoms above, and exhibit stronger attractive forces upon their nearest neighbors on the surface. This enhancement of the intermolecular attractive forces at the surface is called surface tension.

Cohesion and Adhesion: Molecules liquid state experience strong intermolecular attractive forces. When those forces are between like molecules, they are referred to as cohesive forces. For example, the molecules of a water droplet are held together by cohesive forces, and the especially strong cohesive forces at the surface constitute surface tension.

When the attractive forces are between unlike molecules, they are said to be adhesive forces. The adhesive forces between water molecules and the walls of a glass tube are stronger than the cohesive forces lead to an upward turning meniscus at the walls of the vessel and contribute to capillary action.

The attractive forces between molecules in a liquid can be viewed as residual electrostatic forces and are sometimes called van der Waals forces or van der Waals bonds.

Surface Tension Examples

Walking on water: Small insects such as the water strider can walk on water because their weight is not enough to penetrate the surface.

Floating a needle: If carefully placed on the surface, a small needle can be made to float on the surface of water even though it is several times as dense as water. If the surface is agitated to break up the surface tension, theeedle will quickly sink.

Common tent materials are somewhat rainproof in that the surface tension of water will bridge the pores in the finely woven material. But if you touch the tent material with your finger, you break the surface tension and the rain will drip through.

Soaps and detergents: help the cleaning of clothes by lowering the surface tension of the water so that it more readily soaks into pores and soiled areas.

Clinical test for jaundice:Normal urine has a surface tension of about 66 dynes/cm but if bile is present (a test for jaundice), it drops to about 55. In the Hay test, powdered sulfur is sprinkled on the urine surface. It will float oormal urine, but sink if the S.T. is lowered by the bile.

Washing with cold water: The major reason for using hot water for washing is that its surface tension is lower and it is a better wetting agent. But if the detergent lowers the surface tension, the heating may be unneccessary.

Surface tension disinfectants: Disinfectants are usually solutions of low surface tension. This allow them to spread out on the cell walls of bacteria and disrupt them. One such disinfectant, S.T.37, has a name which points to its low surface tension compared to the 72 dynes/cm for water.

Surface Tension and Bubbles: The surface tension of water provides the necessary wall tension for the formation of bubbles with water. The tendency to minimize that wall tension pulls the bubbles into spherical shapes (LaPlace’s law).

The pressure difference between the inside and outside of a bubble depends upon the surface tension and the radius of the bubble. The relationship can be obtained by visualizing the bubble as two hemispheres and noting that the internal pressure which tends to push the hemispheres apart is counteracted by the surface tension acting around the cirumference of the circle.

For a bubble with two surfaces providing tension tension, the pressure relationship is:

Sessile Drop Method

Optical contact angle measurement to determine the wetting behaviour of solids

Task:Determination of the static and dynamic contact angle and of the surface free energy of solids

Test results: interface-specific parameters and measuring ranges of typical instrument systems

· Measurement of the static contact angle of sessile drops of liquid on a surface as a function of time or temperature

· Measurement of the dynamic contact angle as a function of the dosing rate , as advancing angle or as receding angle

· Measurement of the difference between advancing angle and receding angle (contact angle hysteresis) by metered addition or removal of liquid

· Measurement of the contact angle or until the rolling off of the drop on a plate inclined with the angle (Tilting Plate method)

· Calculation of the critical surface tension and of the surface free energy : determination of the dispersion as well as the non-dispersion parts (e.g. polar parts , acid/base parts , hydrogen bonding parts ) from contact angle measurements with various test liquids

· Typical measuring ranges : 0 … 180°/0,1 mN/m … 1000 mN/m

Pendant Drop Method

Task: Determination of the interface and surface tension of liquids

Test results: interface-specific parameters and measuring ranges of typical instrument systems

· Measurement of the static interfacial or surface tension as a function of time or of temperature

· Measurement of the adsorption/diffusion coefficients of surfactant molecules in vibrating/relaxing drops

· Typical measuring range : : 0,05 … 1000 mN/m

Surface tension measurement is important in quality control and in the development of products and processes with better performances. It is an extremely sensitive indicator providing information on the washability, wetting, emulsification, foaming and other surface related processes. The progress of various chemical reactions and presence of solvents or surfactants in liquid systems can be monitored by surface tension measurement.

There are several methods available to measure surface tension. The best method depends upon the nature of the liquid being measured, the conditions under which its tension is to be measured, and the stability of its surface when it is deformed. The following are some methods:

· Du Noüy Ring method. The traditional and most common way of measuring surface tension. It utilizes a platinum ring with defined geometry that is immersed into the liquid and then carefully pulled out through the liquid surface (Figure). The measurement is performed by a tensiometer, an instrument incorporating a precision micro balance, platinum-iridium ring with defined geometry and a precision mechanism to vertically move sample liquid in a glass beaker

Figure: Illustration of the Du Noüy Ring method to measure surface tension

· Wilhelmy plate method.This method measures the weight of the liquid drawn by a plate when a plate is lifted from or through the surface of liquid. The weight of the liquid is proportional to the surface tension of the liquid.

· Pendant drop method.This method is based on the fact that the shape of a drop of liquid hanging from a syringe tip is determined from the balance of forces which include the surface tension of that liquid. This method has advantages in that it is able to use very small volumes of liquid, measure very low interfacial tensions and can measure molten materials easily.

· Bubble pressure method (Jaeger’s method). This method is useful for determining surface tension at short surface ages. The maximum pressure of each bubble is measured.

· Capillary rise method. In this method, the end of a capillary is immersed into the liquid. The height at which the solution reaches inside the capillary is related to the surface tension.

· Sessile drop method. This method is carried out by placing a drop on a substrate and measuring the contact angle.

· Test ink method. This is a method for measuring surface tension of substrates using test ink.

An application closely related to surface tension measurements is the study of monolayers of insoluble molecules on the surface of water using a Langmuir film balance. The Langmuir film balance can also be used to build multilayer structures commonly named Langmuir-Blodgett or simply LB films.

Measuring surface tension: The starting point for plasma pretreatment

Every material surface has a specific surface tension. Every liquid (such as ink) also has an inherent tension. Reliable adhesion with long-term stability of printing, gluing or coatingrequires that the surface tension of the material is greater than that of the liquid. Plastics, for example, have predominantly low surface tensions (often less than 28 mN/m). If these plastics are to be printed, a surface tension of 40 mN/m for solvent inks or a surface tension of 56 mN/m for UV-curing systems is required. If water-based paint systems are used, the surface tension has to be above 72 mN/m.

For many industrial applications it is crucial that adhesives and/or printing inks and surface properties are optimally aligned. Targeted pretreatment with Openair® atmospheric-pressure plasma achieves a significant increase in surface tension. This gives materials the optimum capabilities for accepting printing ink (wettability) or adhesion.

Good surface wetting

Poor surface wetting

To be able to optimally evaluate the process parameters for surface modification with Openair® plasma, the surface tension of the starting material has to be determined first. Even in ongoing processes, it has to be remeasured again and again for quality assurance purposes. The most important methods for surface determination are the test ink method(test inks), contact angle measurement (drop volume method), and dynamic measurement with the Surface Analyst™ goniometer.

Plasmatreat test inks: Measuring surface tension

A simple method to measure the surface tension of various materials, such as plastic, glass, and recycled or composite materials, is the determination using test inks. Plasmatreat test inks are an excellent tool for surface determination, quality assurance during ongoing production, and determination of accurate parameters for plasma treatment.

All Plasmatreat test inks are manufactured according to DIN Draft 53364 or ISO 8296.

The simple application of Plasmatreat test inks

The test ink is applied quickly to the surface using the integrated brush of the bottle. Start with an ink with a high surface tension (such as 72 mN/m) directly after the pretreatment. If the brush stroke edges are stable for two seconds, the surface is easily wettable. Then, the surface tension of the substrate is at least equal to the value of the test ink. If the brush strokes of the test ink contract, the next lower test ink should be used. This way, you are gradually approaching the surface tension value of your material. The surface tension of the material is equal to the value of the test ink last used that showed good wetting for at least 2 seconds.

Good surface wetting

Poor surface wetting

The following test inks are available:

1. Ethanol test inks (C Series) Suitable for all common surfaces. Non-toxic, non-harmful. Available from 28 to 72 mN/m (in increments of 2 mN/m)

2. Formamide test inks (A Series) Especially suited for warmer surfaces, but not for PVC. Longer reading time. Toxic. Teratogenic. Available from 30 to 72 mN/m (in increments of 2 mN/m)

3. Methanol test inks (B Series) Suitable for all common surfaces. Toxic. Available from 28 to 72 mN/m (in increments of 2 mN/m)

Note:
The maximum measurement error is 2 mN/m. For test series with multiple measurements, the error tolerances are reduced accordingly. As with any measurement process, the determination of surface tension using test inks also requires a critical approach to the measurement results. The measurement values obtained with the test ink method for measuring surface tension are relative values and have limited comparability with other methods. The calculated surface tension can only be a measure of the current state of the substrate because, according to experience, surface tension decreases with storage time.

SURFACTANTS. SURFACE ACTIVE AGENTS

A surface active agent (= surfactant) is a substance which lowers the surface tension of the medium in which it is dissolved, and/or the interfacial tension with other phases, and, accordingly, is positively adsorbed at the liquid/vapour and/or at other interfaces. The term surfactant is also applied correctly to sparingly soluble substances, which lower the surface tension of a liquid by spreading spontaneously over its surface.

A soap is a salt of a fatty acid, saturated or unsaturated, containing at least eight carbon atoms or a mixture of such salts.

A detergent is a surfactant (or a mixture containing one or more surfactants) having cleaning properties in dilute solution (soaps are surfactants and detergents).

A syndet is a synthetic detergent; a detergent other than soap.

An emulsifier is a surfactant which when present in small amounts facilitates the formation of an emulsion, or enhances its colloidal stability by decreasing either or both of the rates of aggregation and coalescence.

A foaming agent is a surfactant which when present in small amounts facilitates the formation of a foam, or enhances its colloidal stability by inhibiting the coalescence of bubbles.

The property of surface activity is usually due to the fact that the molecules of the substance are amphipathic or amphiphilic, meaning that each contains both a hydrophilic and a hydrophobic (lipophilic) group.

Surfactants in solution are often association colloids, that is, they tend to form micelles, meaning aggregates of colloidal dimensions existing in equilibrium with the molecules or ions from which they are formed.

If the surfactant ionizes, it is important to indicate whether the micelle is supposed to include none, some, or all of the counterions. For example, degree of association refers to the number of surfactant ions in the micelle and does not say anything about the location of the counterions: charge of the micelle is usually understood to include the net charge of the surfactant ions and the counterions bound to the micelle: micellar mass and micellar weight usually refer to a neutral micelle and therefore include an equivalent amount of counterions with the surfactant ions.

I. At the Interface:

Unlike forces between molecules in the bulk of a liquid phase, cohesive force formed by a molecule at an interface are between adjacent molecules and molecules in the bulk. Any cohesive forces between a molecule at an interface and molecules in the other phase are likely to be weak. The net effect is the formation of an overall inward force which tends to shrink the surface. This shrinkage of the surface can be regarded as an attempt to reduce or eliminate contact with the other phase. On the other hand, as the degree of interaction between molecules of one phase with molecules of another phase increases, the tendency to reduce contact decreases. In the case of the two liquid phases, reductions in shrinkage, i.e. increasing cohesive forces, may result in miscibility of the liquids.

A class of compounds known as surface active agents or surfactants contain both hydrophilic and lipophilic regions has an affinity for interfaces. They are molecules and ions that are adsorbed at interfaces. An alternative expression is amphilphile which suggests that the molecule or ion has a certain affinity for both polar and nonpolar solvents. Refer to figure 1, glyceryl monstearate, for an example of a surface active agent. Such a compound is an amphiphile which

is soluble in at least one phase of the system
forms monolayers at an interface
exhibits equilibrium concentrations at interfaces higher than the concentrations in the bulk solution and forms micelles at specific concentrations.
exhibits one or more of the following characteristics: detergency, foaming, wetting, emulsifying, solubilizing, dispersing.

Depending on the number and nature of the polar and nonpolar groups present, the amphiphile may be predominantly hydrophilic (water-loving), lipophilic (oil-loving), or reasonably well balanced between these two extremes.

Eg, straight-chain alcohols, amines, and acids are amphiphiles that change from being predominantly hydrophilic to lipophilic as the number of carbon atoms in the alkyl chains is increased. Ethyl alcohol is miscible with water in all proportions. In comparison, the aqueous solubility of amyl alcohol is much reduced, while cetyl alcohol may be said to be strongly lipophilic and insoluble in water.

Glyceryl monostearate

In order for the amphiphile to be concentrated at the interface, it must be balanced with the proper amount of water- and oil- soluble groups. If the molecule is too hydrophilic, it remains within the body of the aqueous phase and exerts no effect at the interface. Likewise, if it is too lipophilic, it dissolves completely in the oil phase and little appears at the interface.

Surfactant classification according to the composition of their head: nonionic, anionic, cationic, amphoteric.

II. Chemical Classification of Surface Active Agents

Surfactants may be viewed as providing a link between phases of markedly different polarities. Furthermore, the relationship of hydrophilic and lipophilic portions of the molecules will determine the overall characteristics of the compounds. This relationship has beeumerically defined using the HLB (Hydrophile/lipophile balance). This provides a relative ranking of affiniites of amphiphiles towards aqueous and lipid solvent phases.

III. Systems of Hydrophile-Lipophile Classification

The Hydrophilic-Lipophilic balance (HLB) establishes a range of optimum efficiency for each class of surfactant. The higher the HLB of an agent, the more hydrophilic it is. The Spans, sorbitan esters are lipophilic (low HLB values ranging from 1.8 – 8.6); the Tweens, polyoxyethylene derivatives of the Spans, are hydrophilic and have high HLB values, ranging from 9.6 – 16.7.

If the molecule is too hydrophilic, it remains within the aqueous phase and exerts no effect at the interface. Likewise, if it is too lipophilic it dissolves completely in the oil phase and little appears at the interface.
Depending on the number and nature of the polar and nonpolar groups present, the amphiphile may be predominantly hydrophilic to lipophilic as the number of carbon atoms in the alkyl chains is increased.

ANIONIC

Sulfate, sulfonate, and phosphate esters

Anionic surfactants contain anionic functional groups at their head, such as sulfate, sulfonate, phosphate, andcarboxylates. Prominent alkyl sulfates include ammonium lauryl sulfate, sodium lauryl sulfate (SDS, sodium dodecyl sulfate, another name for the compound) and the related alkyl-ether sulfates sodium laureth sulfate, also known as sodium lauryl ether sulfate (SLES), and sodium myreth sulfate.

Docusates: dioctyl sodium sulfosuccinate, perfluorooctanesulfonate (PFOS), perfluorobutanesulfonate, linear alkylbenzene sulfonates(LABs). These include alkyl-aryl ether phosphates and the alkyl ether phosphate

Carboxylates

These are the most common surfactants and comprise the alkyl carboxylates (soaps), such as sodium stearate. More specialized species include sodium lauroyl sarcosinate and carboxylate-based fluorosurfactants such as perfluorononanoate, perfluorooctanoate(PFOA or PFO).

Cationic head groups

· pH-dependent primary, secondary, or tertiary amines: Primary and secondary amines become positively charged at pH < 10:

· Octenidine dihydrochloride;

· Permanently charged quaternary ammonium cation:

· Alkyltrimethylammonium salts: cetyl trimethylammonium bromide (CTAB) a.k.a. hexadecyl trimethyl ammonium bromide, cetyl trimethylammonium chloride (CTAC)

· Cetylpyridinium chloride (CPC)

· Benzalkonium chloride (BAC)

· Benzethonium chloride (BZT)

· 5-Bromo-5-nitro-1,3-dioxane

· Dimethyldioctadecylammonium chloride

· Cetrimonium bromide

· Dioctadecyldimethylammonium bromide (DODAB)

Zwitterionic surfactants

Zwitterionic (amphoteric) surfactants have both cationic and anionic centers attached to the same molecule. The cationic part is based on primary, secondary, or tertiary amines or quaternary ammonium cations. The anionic part can be more variable and include sulfonates, as in CHAPS (3-[(3-Cholamidopropyl)dimethylammonio]-1-propanesulfonate). Other anionic groups are sultaines illustrated by cocamidopropyl hydroxysultaine. Betaines, e.g., cocamidopropyl betaine. Phosphates: lecithin

Nonionic surfactant

Many long chain alcohols exhibit some surfactant properties. Prominent among these are the fatty alcohols, cetyl alcohol, stearyl alcohol, and cetostearyl alcohol (consisting predominantly of cetyl and stearyl alcohols), and oleyl alcohol.

· Polyoxyethylene glycol alkyl ethers (Brij): CH₃–(CH₂)_10–16–(O-C₂H₄)_1–25–OH:

· Octaethylene glycol monododecyl ether

· Pentaethylene glycol monododecyl ether

· Polyoxypropylene glycol alkyl ethers: CH₃–(CH₂)_10–16–(O-C₃H₆)_1–25–OH

· Glucoside alkyl ethers: CH₃–(CH₂)_10–16–(O-Glucoside)_1–3–OH:

· Decyl glucoside,

· Lauryl glucoside

· Octyl glucoside

· Polyoxyethylene glycol octylphenol ethers: C₈H₁₇–(C₆H₄)–(O-C₂H₄)_1–25–OH:

· Triton X-100

· Polyoxyethylene glycol alkylphenol ethers: C₉H₁₉–(C₆H₄)–(O-C₂H₄)_1–25–OH:

· Nonoxynol-9

· Glycerol alkyl esters:

· Glyceryl laurate

· Polyoxyethylene glycol sorbitan alkyl esters: Polysorbate

· Sorbitan alkyl esters: Spans

· Cocamide MEA, cocamide DEA

· Dodecyldimethylamine oxide

· Block copolymers of polyethylene glycol and polypropylene glycol: Poloxamers

· Polyethoxylated tallow amine (POEA).

According to the composition of their counter-ion

In the case of ionic surfactants, the counter-ion can be:

· Monatomic / Inorganic:

· Cations: metals : alkali metal, alkaline earth metal, transition metal

· Anions: halides: chloride (Cl⁻), bromide (Br⁻), iodide (I⁻)

· Polyatomic / Organic:

· Cations: ammonium, pyridinium, triethanolamine (TEA)

· Anions: tosyls, trifluoromethanesulfonates, methylsulfate

Biosurfactants are surface-active substances synthesised by living cells. Interest in microbial surfactants has been steadily increasing in recent years due to their diversity, environmentally friendly nature, possibility of large-scale production, selectivity, performance under extreme conditions, and potential applications in environmental protection.Few of the popular examples of microbial biosurfactants includes Emulsan produced by Acinetobacter calcoaceticus, Sophorolipids produced by several yeasts belonging tocandida and starmerella clade, and Rhamnolipid produced by Pseudomonas aeruginosa etc.

Biosurfactants enhance the emulsification of hydrocarbons, have the potential to solubilise hydrocarbon contaminants and increase their availability for microbial degradation. The use of chemicals for the treatment of a hydrocarbon polluted site may contaminate the environment with their by-products, whereas biological treatment may efficiently destroy pollutants, while being biodegradable themselves. Hence, biosurfactant-producing microorganisms may play an important role in the accelerated bioremediation of hydrocarbon-contaminated sites. These compounds can also be used in enhanced oil recovery and may be considered for other potential applications in environmental protection. Other applications include herbicides and pesticides formulations, detergents, healthcare and cosmetics, pulp and paper, coal, textiles, ceramic processing and food industries, uranium ore-processing, and mechanical dewatering of peat.

· Several microorganisms are known to synthesise surface-active agents; most of them are bacteria and yeasts. When grown on hydrocarbon substrate as the carbon source, these microorganisms synthesise a wide range of chemicals with surface activity, such as glycolipid, phospholipid, and others.These chemicals are synthesised to emulsify the hydrocarbon substrate and facilitate its transport into the cells. In some bacterial species such as Pseudomonas aeruginosa, biosurfactants are also involved in a group motility behavior called swarming motility.

IV. Purity of SAA

Commercial SAAs are not single pure compounds, but contain a mixture of homologues of differing alkyl chain length because of

1. Nature of raw starting materials e.g. petroleum fractions or natural fats

2. Deliberate choice to achieve definite objectives
e.g. cationic SAA: long chain compounds – bactericidal action; short chain homologues – solubilize the long chain molecules.

V. Pharmaceutical uses of SAA

1. SAA used in emulsions as an emulsifying agent

2. SAA used in suspensions as a flocculating agent

3. SAA as a wetting agent

4. SAA as a bactericidal agent

5. SAA as a solubilizing agent

6. To modify the properties of membranes

o Enhancement of percutaneous absorption

o Enhancement of transport across mucosal membranes (rectal, vaginal, ophthalmic, nasal)

SAA as a foaming agent

Many solutions containing surface active materials produce stable foams when mixed intimately with air. A foam is a relatively stable structure consisting of air pockets enclosed within thin films of liquid, the gas-in-liquid dispersion being stabilized by a foaming agent. The foam dissipates as the liquid drains away from the area surrounding the air globules, and the film finally collapses. Antifoaming agents such as alcohol, ether, castor oil, and some surfactants may be used to break the foam. Foams are sometimes useful in pharmacy but are usually a nuisance and are prevented or destroyed when possible. The undesirable foaming of solubilized liquid preparations poses a problem in formulation.

The relative molecular mass () of a micelle is called the relative micellar mass or micellar weight and is defined as the mass of a mole of micelles divided by the mass of $\frac{1}{12}$ mole of $^{12}$ C.

There is a relatively small range of concentrations separating the limit below which virtually no micelles are detected and the limit above which virtually all-additional surfactant forms micelles. Many properties of surfactant solutions, if plotted against the concentration appear to change at a different rate above and below this range. By extrapolating the loci of such a property above and below this range until they intersect, a value may be obtained known as the critical micellization concentration (critical micelle concentration), symbol , abbreviation c.m.c. As values obtained using different properties are not quite identical, the method by which the c.m.c. is determined should be clearly stated.

Solubilization. In a system formed by a solvent, an association colloid and at least one other component (the solubilizate), the incorporation of this other component into or on the micelles is called micellar solubilization, or, briefly solubilization. If this other component is sparingly soluble in the solvent alone, solubilization can lead to a marked increase in its solubility due to the presence of the association colloid. More generally, the term solubilization has been applied to any case in which the activity of one solute is materially decreased by the presence of another solute.

Concentrated systems of surfactants often form liquid crystalline phases, or mesomorphic phases. Mesomorphic phases are states of matter in which anisometric molecules (or particles) are regularly arranged in one (nematic state) or two (smectic state) directions, but randomly arranged in the remaining direction(s).

Examples of mesomorphic phases are: neat soap, a lamellar structure containing much (e.g. 0.75%) soap and little (e.g. 0.25%) water; middle soap, containing a hexagonal array of cylinders, less concentrated (e.g. 0.50%), but also less fluid thaeat soap.

A soap curd is not a mesomorphic phase, but a gel-like mixture of fibrous soap-crystals (`curd-fibers’) and their saturated solution.

Myelin cylinders are birefringent cylinders which form spontaneously from lipoid-containing material in contact with water.

Krafft point, symbol (Celsius or other customary temperature), , (thermodynamic temperature) is the temperature (more precisely, narrow temperature range) above which the solubility of a surfactant rises sharply. At this temperature the solubility of the surfactant becomes equal to the c.m.c. It is best determined by locating the abrupt change in slope of a graph of the logarithm of the solubility against or .

Surface tension is visible in other common phenomena, especially when surfactants are used to decrease it:

Soap bubbles have very large surface areas with very little mass. Bubbles in pure water are unstable. The addition of surfactants, however, can have a stabilizing effect on the bubbles (see Marangoni effect). Notice that surfactants actually reduce the surface tension of water by a factor of three or more.

Emulsions are a type of solution in which surface tension plays a role. Tiny fragments of oil suspended in pure water will spontaneously assemble themselves into much larger masses. But the presence of a surfactant provides a decrease in surface tension, which permits stability of minute droplets of oil in the bulk of water (or vice versa).

Basic physics

Two definitions

Diagram shows, in cross-section, a needle floating on the surface of water. Its weight, F_w, depresses the surface, and is balanced by the surface tension forces on either side, F_s, which are each parallel to the water’s surface at the points where it contacts the needle. Notice that the horizontal components of the two F_s arrows point in opposite directions, so they cancel each other, but the vertical components point in the same direction and therefore add up to balance F_w.

Surface tension, represented by the symbol γ is defined as the force along a line of unit length, where the force is parallel to the surface but perpendicular to the line. One way to picture this is to imagine a flat soap film bounded on one side by a taut thread of length, L. The thread will be pulled toward the interior of the film by a force equal to 2 $\scriptstyle\gamma$ L (the factor of 2 is because the soap film has two sides, hence two surfaces). Surface tension is therefore measured in forces per unit length. Its SI unit is newton per meter but the cgs unit of dyne per cm is also used.^[5] One dyn/cm corresponds to 0.001 N/m.

An equivalent definition, one that is useful in thermodynamics, is work done per unit area. As such, in order to increase the surface area of a mass of liquid by an amount, δA, a quantity of work, $\scriptstyle\gamma$ δA, is needed.^[4] This work is stored as potential energy. Consequently surface tension can be also measured in SI system as joules per square meter and in the cgs system as ergs per cm². Since mechanical systems try to find a state of minimum potential energy, a free droplet of liquid naturally assumes a spherical shape, which has the minimum surface area for a given volume.

The equivalence of measurement of energy per unit area to force per unit length can be proven by dimensional analysis.

Surface curvature and pressure

Surface tension forces acting on a tiny (differential) patch of surface. δθ_x and δθ_y indicate the amount of bend over the dimensions of the patch. Balancing the tension forces with pressure leads to the Young–Laplace equation

If no force acts normal to a tensioned surface, the surface must remain flat. But if the pressure on one side of the surface differs from pressure on the other side, the pressure difference times surface area results in a normal force. In order for the surface tension forces to cancel the force due to pressure, the surface must be curved. The diagram shows how surface curvature of a tiny patch of surface leads to a net component of surface tension forces acting normal to the center of the patch. When all the forces are balanced, the resulting equation is known as the Young–Laplace equation:

$\Delta p\ =\ \gamma \left( \frac{1}{R_x} + \frac{1}{R_y} \right)$

where:

· Δp is the pressure difference.

· $\scriptstyle\gamma$ is surface tension.

· R_x and R_y are radii of curvature in each of the axes that are parallel to the surface.

The quantity in parentheses on the right hand side is in fact (twice) the mean curvature of the surface (depending on normalisation).

Solutions to this equation determine the shape of water drops, puddles, menisci, soap bubbles, and all other shapes determined by surface tension (such as the shape of the impressions that a water strider’s feet make on the surface of a pond).

The table below shows how the internal pressure of a water droplet increases with decreasing radius. For not very small drops the effect is subtle, but the pressure difference becomes enormous when the drop sizes approach the molecular size. (In the limit of a single molecule the concept becomes meaningless.)

Δp for water drops of different radii at STP

Droplet radius

1 mm

0.1 mm

1 μm

10 nm

Δp (atm)

0.0014

0.0144

1.436

143.6

Liquid surface

Minimal surface

To find the shape of the minimal surface bounded by some arbitrary shaped frame using strictly mathematical means can be a daunting task. Yet by fashioning the frame out of wire and dipping it in soap-solution, a locally minimal surface will appear in the resulting soap-film within seconds.^[4]^[7]

The reason for this is that the pressure difference across a fluid interface is proportional to the mean curvature, as seen in the Young-Laplace equation. For an open soap film, the pressure difference is zero, hence the mean curvature is zero, and minimal surfaces have the property of zero mean curvature.

Contact angles

The surface of any liquid is an interface between that liquid and some other medium. The top surface of a pond, for example, is an interface between the pond water and the air. Surface tension, then, is not a property of the liquid alone, but a property of the liquid’s interface with another medium. If a liquid is in a container, then besides the liquid/air interface at its top surface, there is also an interface between the liquid and the walls of the container. The surface tension between the liquid and air is usually different (greater than) its surface tension with the walls of a container. And where the two surfaces meet, their geometry must be such that all forces balance.^[4]^[6]

Forces at contact point shown for contact angle greater than 90° (left) and less than 90° (right)

Where the two surfaces meet, they form a contact angle, $\scriptstyle \theta$ , which is the angle the tangent to the surface makes with the solid surface. The diagram to the right shows two examples. Tension forces are shown for the liquid-air interface, the liquid-solid interface, and the solid-air interface. The example on the left is where the difference between the liquid-solid and solid-air surface tension, $\scriptstyle \gamma_{\mathrm{ls}} - \gamma_{\mathrm{sa}}$ , is less than the liquid-air surface tension, $\scriptstyle \gamma_{\mathrm{la}}$ , but is nevertheless positive, that is

$\gamma_{\mathrm{la}}\ >\ \gamma_{\mathrm{ls}} - \gamma_{\mathrm{sa}}\ >\ 0$

In the diagram, both the vertical and horizontal forces must cancel exactly at the contact point, known as equilibrium. The horizontal component of $\scriptstyle f_\mathrm{la}$ is canceled by the adhesive force, $\scriptstyle f_\mathrm{A}$ .

$f_\mathrm{A}\ =\ f_\mathrm{la} \sin \theta$

The more telling balance of forces, though, is in the vertical direction. The vertical component of $\scriptstyle f_\mathrm{la}$ must exactly cancel the force, $\scriptstyle f_\mathrm{ls}$ .^[4]

$f_\mathrm{ls} - f_\mathrm{sa}\ =\ -f_\mathrm{la} \cos \theta$

Liquid

Solid

Contact angle

water

soda-lime glass

lead glass

fused quartz

0°

paraffin wax

107°

silver

90°

methyl iodide

soda-lime glass

29°

lead glass

30°

fused quartz

33°

mercury

soda-lime glass

140°

Some liquid-solid contact angles^[4]

Since the forces are in direct proportion to their respective surface tensions, we also have:

$\gamma_\mathrm{ls} - \gamma_\mathrm{sa}\ =\ -\gamma_\mathrm{la} \cos \theta$

where

· $\scriptstyle \gamma_\mathrm{ls}$ is the liquid-solid surface tension,

· $\scriptstyle \gamma_\mathrm{la}$ is the liquid-air surface tension,

· $\scriptstyle \gamma_\mathrm{sa}$ is the solid-air surface tension,

· $\scriptstyle \theta$ is the contact angle, where a concave meniscus has contact angle less than 90° and a convex meniscus has contact angle of greater than 90°.

This means that although the difference between the liquid-solid and solid-air surface tension, $\scriptstyle \gamma_\mathrm{ls} - \gamma_\mathrm{sa}$ , is difficult to measure directly, it can be inferred from the liquid-air surface tension, $\scriptstyle \gamma_\mathrm{la}$ , and the equilibrium contact angle, $\scriptstyle \theta$ , which is a function of the easily measurable advancing and receding contact angles (see main article contact angle).

This same relationship exists in the diagram on the right. But in this case we see that because the contact angle is less than 90°, the liquid-solid/solid-air surface tension difference must be negative:

$\gamma_\mathrm{la}\ >\ 0\ >\ \gamma_\mathrm{ls} - \gamma_\mathrm{sa}$

Special contact angles

Observe that in the special case of a water-silver interface where the contact angle is equal to 90°, the liquid-solid/solid-air surface tension difference is exactly zero.

Another special case is where the contact angle is exactly 180°. Water with specially prepared Teflon approaches this.^[6] Contact angle of 180° occurs when the liquid-solid surface tension is exactly equal to the liquid-air surface tension.

$\gamma_{\mathrm{la}}\ =\ \gamma_{\mathrm{ls}} - \gamma_\mathrm{sa}\ >\ 0\qquad \theta\ =\ 180^\circ$

Methods of measurement

Surface tension can be measured using the pendant drop method on a goniometer.

Because surface tension manifests itself in various effects, it offers a number of paths to its measurement. Which method is optimal depends upon the nature of the liquid being measured, the conditions under which its tension is to be measured, and the stability of its surface when it is deformed.

Du Noüy Ring method: The traditional method used to measure surface or interfacial tension. Wetting properties of the surface or interface have little influence on this measuring technique. Maximum pull exerted on the ring by the surface is measured.

Du Noüy-Padday method: A minimized version of Du Noüy method uses a small diameter metal needle instead of a ring, in combination with a high sensitivity microbalance to record maximum pull. The advantage of this method is that very small sample volumes (down to few tens of microliters) can be measured with very high precision, without the need to correct for buoyancy (for a needle or rather, rod, with proper geometry). Further, the measurement can be performed very quickly, minimally in about 20 seconds. First commercial multichannel tensiometers [CMCeeker] were recently built based on this principle.

Wilhelmy plate method: A universal method especially suited to check surface tension over long time intervals. A vertical plate of known perimeter is attached to a balance, and the force due to wetting is measured.

Spinning drop method: This technique is ideal for measuring low interfacial tensions. The diameter of a drop within a heavy phase is measured while both are rotated.

Pendant drop method: Surface and interfacial tension can be measured by this technique, even at elevated temperatures and pressures. Geometry of a drop is analyzed optically. For details, see Drop.

Bubble pressure method (Jaeger’s method): A measurement technique for determining surface tension at short surface ages. Maximum pressure of each bubble is measured.

Drop volume method: A method for determining interfacial tension as a function of interface age. Liquid of one density is pumped into a second liquid of a different density and time between drops produced is measured.

Capillary rise method: The end of a capillary is immersed into the solution. The height at which the solution reaches inside the capillary is related to the surface tension by the equation discussed below.

Stalagmometric method: A method of weighting and reading a drop of liquid.

Sessile drop method: A method for determining surface tension and density by placing a drop on a substrate and measuring the contact angle (see Sessile drop technique).

Vibrational frequency of levitated drops: The natural frequency of vibrational oscillations of magnetically levitated drops has been used to measure the surface tension of superfluid ⁴He. This value is estimated to be 0.375 dyn/cm at T = 0 K.

Effects

Liquid in a vertical tube

Diagram of a mercury barometer

An old style mercury barometer consists of a vertical glass tube about 1 cm in diameter partially filled with mercury, and with a vacuum (called Torricelli‘s vacuum) in the unfilled volume (see diagram to the right). Notice that the mercury level at the center of the tube is higher than at the edges, making the upper surface of the mercury dome-shaped. The center of mass of the entire column of mercury would be slightly lower if the top surface of the mercury were flat over the entire crossection of the tube. But the dome-shaped top gives slightly less surface area to the entire mass of mercury. Again the two effects combine to minimize the total potential energy. Such a surface shape is known as a convex meniscus.

The reason we consider the surface area of the entire mass of mercury, including the part of the surface that is in contact with the glass, is because mercury does not adhere at all to glass. So the surface tension of the mercury acts over its entire surface area, including where it is in contact with the glass. If instead of glass, the tube were made out of copper, the situation would be very different. Mercury aggressively adheres to copper. So in a copper tube, the level of mercury at the center of the tube will be lower than at the edges (that is, it would be a concave meniscus). In a situation where the liquid adheres to the walls of its container, we consider the part of the fluid’s surface area that is in contact with the container to have negative surface tension. The fluid then works to maximize the contact surface area. So in this case increasing the area in contact with the container decreases rather than increases the potential energy. That decrease is enough to compensate for the increased potential energy associated with lifting the fluid near the walls of the container.

Illustration of capillary rise and fall. Red=contact angle less than 90°; blue=contact angle greater than 90°

If a tube is sufficiently narrow and the liquid adhesion to its walls is sufficiently strong, surface tension can draw liquid up the tube in a phenomenon known as capillary action. The height the column is lifted to is given by:

$h\ =\ \frac {2\gamma_\mathrm{la} \cos\theta}{\rho g r}$

where

· $\scriptstyle h$ is the height the liquid is lifted,

· $\scriptstyle \gamma_\mathrm{la}$ is the liquid-air surface tension,

· $\scriptstyle \rho$ is the density of the liquid,

· $\scriptstyle r$ is the radius of the capillary,

· $\scriptstyle g$ is the acceleration due to gravity,

· $\scriptstyle \theta$ is the angle of contact described above. If $\scriptstyle \theta$ is greater than 90°, as with mercury in a glass container, the liquid will be depressed rather than lifted.

Puddles on a surface

Profile curve of the edge of a puddle where the contact angle is 180°. The curve is given by the formula: $\scriptstyle x - x_0 \ = \ \frac {1} {2} H \cosh^{-1}\left(\frac {H}{h}\right) - H \sqrt{1 - \frac{h^2} {H^2}}$ where $\scriptstyle H \ = \ 2 \sqrt{\frac {\gamma} {g \rho}}$

Small puddles of water on a smooth clean surface have perceptible thickness.

Pouring mercury onto a horizontal flat sheet of glass results in a puddle that has a perceptible thickness. The puddle will spread out only to the point where it is a little under half a centimeter thick, and no thinner. Again this is due to the action of mercury’s strong surface tension. The liquid mass flattens out because that brings as much of the mercury to as low a level as possible, but the surface tension, at the same time, is acting to reduce the total surface area. The result is the compromise of a puddle of a nearly fixed thickness.

The same surface tension demonstration can be done with water, lime water or even saline, but only on a surface made of a substance that the water does not adhere to. Wax is such a substance. Water poured onto a smooth, flat, horizontal wax surface, say a waxed sheet of glass, will behave similarly to the mercury poured onto glass.

The thickness of a puddle of liquid on a surface whose contact angle is 180° is given by:

$h\ =\ 2 \sqrt{\frac{\gamma} {g\rho}}$

where

$\scriptstyle h$ is the depth of the puddle in centimeters or meters.

$\scriptstyle \gamma$ is the surface tension of the liquid in dynes per centimeter or newtons per meter.

$\scriptstyle g$ is the acceleration due to gravity and is equal to 980 cm/s² or 9.8 m/s²

$\scriptstyle \rho$ is the density of the liquid in grams per cubic centimeter or kilograms per cubic meter

Illustration of how lower contact angle leads to reduction of puddle depth

In reality, the thicknesses of the puddles will be slightly less than what is predicted by the above formula because very few surfaces have a contact angle of 180° with any liquid. When the contact angle is less than 180°, the thickness is given by:

$h\ =\ \sqrt{\frac{2\gamma_\mathrm{la}\left( 1 - \cos \theta \right)} {g\rho}}.$

For mercury on glass, γ_Hg = 487 dyn/cm, ρ_Hg = 13.5 g/cm³ and θ = 140°, which gives h_Hg = 0.36 cm. For water on paraffin at 25 °C, γ = 72 dyn/cm, ρ = 1.0 g/cm³, and θ = 107° which gives h_H2O = 0.44 cm.

The formula also predicts that when the contact angle is 0°, the liquid will spread out into a micro-thin layer over the surface. Such a surface is said to be fully wettable by the liquid.

The breakup of streams into drops

Intermediate stage of a jet breaking into drops. Radii of curvature in the axial direction are shown. Equation for the radius of the stream is $\scriptstyle R\left( z \right) = R_0 + A_k \cos \left( kz \right)$ , where $\scriptstyle R_0$ is the radius of the unperturbed stream, $\scriptstyle A_k$ is the amplitude of the perturbation, $\scriptstyle z$ is distance along the axis of the stream, and $\scriptstyle k$ is the wave number

Main article: Plateau–Rayleigh instability

In day-to-day life we all observe that a stream of water emerging from a faucet will break up into droplets, no matter how smoothly the stream is emitted from the faucet. This is due to a phenomenon called the Plateau–Rayleigh instability, which is entirely a consequence of the effects of surface tension.

The explanation of this instability begins with the existence of tiny perturbations in the stream. These are always present, no matter how smooth the stream is. If the perturbations are resolved into sinusoidal components, we find that some components grow with time while others decay with time. Among those that grow with time, some grow at faster rates than others. Whether a component decays or grows, and how fast it grows is entirely a function of its wave number (a measure of how many peaks and troughs per centimeter) and the radii of the original cylindrical stream.

Thermodynamics

As stated above, the mechanical work needed to increase a surface is $\scriptstyle dW \ = \ \gamma dA$ . Hence at constant temperature and pressure, surface tension equals Gibbs free energy per surface area:

$\gamma = \left( \frac{\partial G}{\partial A} \right)_{T,P,n}$

where $\scriptstyle G$ is Gibbs free energy and $\scriptstyle A$ is the area.

Thermodynamics requires that all spontaneous changes of state are accompanied by a decrease in Gibbs free energy.

From this it is easy to understand why decreasing the surface area of a mass of liquid is always spontaneous ( $\scriptstyle \Delta G \ < \ 0$ ), provided it is not coupled to any other energy changes. It follows that in order to increase surface area, a certain amount of energy must be added.

Gibbs free energy is defined by the equation,^[14] $\scriptstyle G \ = \ H \ - \ TS$ , where $\scriptstyle H$ is enthalpy and $\scriptstyle S$ is entropy. Based upon this and the fact that surface tension is Gibbs free energy per unit area, it is possible to obtain the following expression for entropy per unit area:

$\left( \frac{\partial \gamma}{\partial T} \right)_{A,P}=-S^{A}$

Kelvin’s Equation for surfaces arises by rearranging the previous equations. It states that surface enthalpy or surface energy (different from surface free energy) depends both on surface tension and its derivative with temperature at constant pressure by the relationship.^[15]

$H^A\ =\ \gamma - T \left( \frac {\partial \gamma}{\partial T} \right)_P$

Thermodynamics of soap bubbles

The pressure inside an ideal (one surface) soap bubble can be derived from thermodynamic free energy considerations. At constant temperature and particle number, , the differential Helmholtz energy is given by

$dF\ = -PdV\ + \gamma dA$

where is the difference in pressure inside and outside of the bubble, and $\gamma$ is the surface tension. In equilibrium, , and so,

$PdV\ = \gamma dA$ .

For a spherical bubble, the volume and surface area are given simply by

$V = \frac{4}{3}\pi R^3 \rightarrow dV \approx 4\pi R^2 dR$ ,

and

$A = 4\pi R^2 \rightarrow dA \approx 8\pi R dR$ .

Substituting these relations into the previous expression, we find

$P = \frac{2}{R}\gamma$ ,

which is equivalent to the Young–Laplace equation when R_x = R_y. For real soap bubbles, the pressure is doubled due to the presence of two interfaces, one inside and one outside.

Influence of temperature

Temperature dependence of the surface tension of pure water

Temperature dependency of the surface tension of benzene

Surface tension is dependent on temperature. For that reason, when a value is given for the surface tension of an interface, temperature must be explicitly stated. The general trend is that surface tension decreases with the increase of temperature, reaching a value of 0 at the critical temperature. For further details see Eötvös rule. There are only empirical equations to relate surface tension and temperature:

$\gamma V^{2/3}=k(T_C-T)\,\!$

Here V is the molar volume of a substance, T_C is the critical temperature and k is a constant valid for almost all substances. A typical value is k = 2.1 x 10⁻⁷ [J K⁻¹ mol^−2/3]. For water one can further use V = 18 ml/mol and T_C = 374°C.

A variant on Eötvös is described by Ramay and Shields:

$\gamma V^{2/3} = k\left(T_C - T - 6\right)$

where the temperature offset of 6 kelvins provides the formula with a better fit to reality at lower temperatures.

Guggenheim-Katayama:

$\gamma = \gamma^o \left( 1-\frac{T}{T_C} \right)^n$

$\scriptstyle \gamma^o$ is a constant for each liquid andis an empirical factor, whose value is 11/9 for organic liquids. This equation was also proposed by van der Waals, who further proposed that $\scriptstyle \gamma^0$ could be given by the expression, $\scriptstyle K_2 T^{\frac {1}{3}}_c P^{\frac {2}{3}}_c$ , where $\scriptstyle K_2$ is a universal constant for all liquids, and $\scriptstyle P_c$ is the critical pressure of the liquid (although later experiments found $\scriptstyle K_2$ to vary to some degree from one liquid to another).

Both Guggenheim-Katayama and Eötvös take into account the fact that surface tension reaches 0 at the critical temperature, whereas Ramay and Shields fails to match reality at this endpoint.

Influence of solute concentration

Solutes can have different effects on surface tension depending on their structure:

Little or no effect, for example sugar
Increase surface tension, inorganic salts
Decrease surface tension progressively, alcohols
Decrease surface tension and, once a minimum is reached, no more effect: surfactants

What complicates the effect is that a solute can exist in a different concentration at the surface of a solvent than in its bulk. This difference varies from one solute/solvent combination to another.

Gibbs isotherm states that: $\Gamma\ =\ - \frac{1}{RT} \left( \frac{\partial \gamma}{\partial \ln C} \right)_{T,P}$

$\scriptstyle \Gamma$ is known as surface concentration, it represents excess of solute per unit area of the surface over what would be present if the bulk concentration prevailed all the way to the surface. It has units of mol/m²

$\scriptstyle C$ is the concentration of the substance in the bulk solution.

$\scriptstyle R$ is the gas constant and $\scriptstyle T$ the temperature

Certain assumptions are taken in its deduction, therefore Gibbs isotherm can only be applied to ideal (very dilute) solutions with two components.

Influence of particle size on vapor pressure

The Clausius–Clapeyron relation leads to another equation also attributed to Kelvin, as the Kelvin equation. It explains why, because of surface tension, the vapor pressure for small droplets of liquid in suspension is greater than standard vapor pressure of that same liquid when the interface is flat. That is to say that when a liquid is forming small droplets, the equilibrium concentration of its vapor in its surroundings is greater. This arises because the pressure inside the droplet is greater than outside.

$P_v^{fog}=P_v^o e^{\frac{V 2\gamma}{RT r_k}}$

Molecules on the surface of a tiny droplet (left) have, on average, fewer neighbors than those on a flat surface (right). Hence they are bound more weakly to the droplet than are flat-surface molecules.

· $\scriptstyle P_v^o$ is the standard vapor pressure for that liquid at that temperature and pressure.

· $\scriptstyle V$ is the molar volume.

· $\scriptstyle R$ is the gas constant

is the Kelvin radius, the radius of the droplets.

The effect explains supersaturation of vapors. In the absence of nucleation sites, tiny droplets must form before they can evolve into larger droplets. This requires a vapor pressure many times the vapor pressure at the phase transition point.

This equation is also used in catalyst chemistry to assess mesoporosity for solids.^[17]

The effect can be viewed in terms of the average number of molecular neighbors of surface molecules (see diagram).

The table shows some calculated values of this effect for water at different drop sizes:

P/P₀ for water drops of different radii at STP^[15]

Droplet radius (nm)

1000

100

P/P₀

1.001

1.011

1.114

2.95

The effect becomes clear for very small drop sizes, as a drop of 1 nm radius has about 100 molecules inside, which is a quantity small enough to require a quantum mechanics analysis.

Data table

Surface tension of various liquids in dyn/cm against air^[18] Mixture compositions denoted “%” are by mass dyn/cm is equivalent to the SI units of mN/m (millinewton per meter)
Acetic acid	20	27.60
Acetic acid (40.1%) + Water	30	40.68
Acetic acid (10.0%) + Water	30	54.56
Acetone	20	23.70
Diethyl ether	20	17.00
Ethanol	20	22.27
Ethanol (40%) + Water	25	29.63
Ethanol (11.1%) + Water	25	46.03
Glycerol	20	63.00
n-Hexane	20	18.40
Hydrochloric acid 17.7M aqueous solution	20	65.95
Isopropanol	20	21.70
Liquid helium II	-273	^[19]0.37
Liquid nitrogen	-196	8.85
Mercury	15	487.00
Methanol	20	22.60
n-Octane	20	21.80
Sodium chloride 6.0M aqueous solution	20	82.55
Sucrose (55%) + water	20	76.45
Water	0	75.64
Water	25	71.97
Water	50	67.91
Water	100	58.85
Toluene	25	27.73

Surface tension of various liquids in dyn/cm against air^[18]
Mixture compositions denoted “%” are by mass
dyn/cm is equivalent to the SI units of mN/m (millinewton per meter)

Liquid

Temperature °C

Surface tension, γ

Acetic acid

27.60

Acetic acid (40.1%) + Water

40.68

Acetic acid (10.0%) + Water

54.56

Acetone

23.70

Diethyl ether

17.00

Ethanol

22.27

Ethanol (40%) + Water

29.63

Ethanol (11.1%) + Water

46.03

Glycerol

63.00

n-Hexane

18.40

Hydrochloric acid 17.7M aqueous solution

65.95

Isopropanol

21.70

Liquid helium II

-273

^[19]0.37

Liquid nitrogen

-196

8.85

Mercury

487.00

Methanol

22.60

n-Octane

21.80

Sodium chloride 6.0M aqueous solution

82.55

Sucrose (55%) + water

76.45

Water

75.64

Water

71.97

Water

67.91

Water

100

58.85

Toluene

27.73

In physics, the Young–Laplace equation is a nonlinear partial differential equation that describes the capillary pressure difference sustained across the interface between two static fluids, such as water and air, due to the phenomenon of surface tension or wall tension, although usage on the latter is only applicable if assuming that the wall is very thin. The Young–Laplace equation relates the pressure difference to the shape of the surface or wall and it is fundamentally important in the study of static capillary surfaces. It is a statement of normal stress balance for static fluids meeting at an interface, where the interface is treated as a surface (zero thickness):

$\begin{align} \Delta p &= -\gamma abla \cdot \hat\\ &= 2 \gamma H \\ &= \gamma \left(\frac{1}{R_1} + \frac{1}{R_2}\right) \end{align}$

where $\Delta p$ is the pressure difference across the fluid interface, γ is the surface tension (or wall tension), $\hat n$ is the unit normal pointing out of the surface, is the mean curvature, and and are the principal radii of curvature. (Some authorsrefer inappropriately to the factor as the total curvature.) Note that only normal stress is considered, this is because it can be shown that a static interface is possible only in the absence of tangential stress.

The equation is named after Thomas Young, who developed the qualitative theory of surface tension in 1805, and Pierre-Simon Laplace who completed the mathematical description in the following year. It is sometimes also called the Young–Laplace–Gauss equation, as Gauss unified the work of Young and Laplace in 1830, deriving both the differential equation and boundary conditions using Johann Bernoulli‘s virtual work principles.

Soap films

If the pressure difference is zero, as in a soap film without gravity, the interface will assume the shape of a minimal surface.

Emulsions

The equation also explains the energy required to create an emulsion. To form the small, highly curved droplets of an emulsion, extra energy is required to overcome the large pressure that results from their small radius.

Capillary pressure in a tube

Spherical meniscus with wetting angle less than 90°

In a sufficiently narrow (i.e., low Bond number) tube of circular cross-section (radius a), the interface between two fluids forms a meniscus that is a portion of the surface of a sphere with radius R. The pressure jump across this surface is:

$\Delta p = \frac{2 \gamma}{R}.$

This may be shown by writing the Young–Laplace equation in spherical form with a contact angle boundary condition and also a prescribed height boundary condition at, say, the bottom of the meniscus. The solution is a portion of a sphere, and the solution will exist only for the pressure difference shown above. This is significant because there isn’t another equation or law to specify the pressure difference; existence of solution for one specific value of the pressure difference prescribes it.

The radius of the sphere will be a function only of the contact angle, θ, which in turn depends on the exact properties of the fluids and the solids in which they are in contact:

$R = \frac{a}{\cos \theta}$

so that the pressure difference may be written as:

$\Delta p = \frac{2 \gamma \cos \theta}{a}.$

Illustration of capillary rise. Red=contact angle less than 90°; blue=contact angle greater than 90°

In order to maintain hydrostatic equilibrium, the induced capillary pressure is balanced by a change in height, h, which can be positive or negative, depending on whether the wetting angle is less than or greater than 90°. For a fluid of density ρ:

$h = \frac{2 \gamma \cos \theta}{\rho g a}.$ .

— where g is the gravitational acceleration. This is sometimes known as the Jurin rule or Jurin height after James Jurin who studied the effect in 1718.

For a water-filled glass tube in air at sea level:

γ = 0.0728 J/m² at 20 °C

θ = 20° (0.35 rad)

ρ = 1000 kg/m³

g = 9.8 m/s²

— and so the height of the water column is given by:

$h\approx {{1.4 \times 10^{-5}}\over a}$ m.

Thus for a 2 mm wide (1 mm radius) tube, the water would rise 14 mm. However, for a capillary tube with radius 0.1 mm, the water would rise 14 cm (about 6 inches).

Capillary action in general

In the general case, for a free surface and where there is an applied “over-pressure”, Δp, at the interface in equilibrium, there is a balance between the applied pressure, the hydrostatic pressure and the effects of surface tension. The Young–Laplace equation becomes:

$\Delta p = \rho g h - \gamma \left( \frac{1}{R_1} + \frac{1}{R_2}\right)$

The equation can be non-dimensionalised in terms of its characteristic length-scale, the capillary length:

$L_{c} = \sqrt{\frac{\gamma}{\rho g}},$

— and characteristic pressure:

$p_{c} = \frac {\gamma} {L_{c}} = \sqrt{ \gamma \rho g}.$

For clean water at standard temperature and pressure, the capillary length is ~2 mm.

The non-dimensional equation then becomes:

$h^*- \Delta p^*= \left( \frac{1}{{R_1}^{*}} + \frac{1}{{R_2}^{*}}\right).$

Thus, the surface shape is determined by only one parameter, the over pressure of the fluid, Δp^* and the scale of the surface is given by the capillary length. The solution of the equation requires an initial condition for position, and the gradient of the surface at the start point.

A pendant drop is produced for an over pressure of Δp^*=3 and initial condition r₀=10⁻⁴, z₀=0, dz/dr=0

A liquid bridge is produced for an over pressure of Δp^*=3.5 and initial condition r₀=0.25⁻⁴, z₀=0, dz/dr=0

Axisymmetric equations

The (nondimensional) shape, r(z) of an axisymmetric surface can be found by substituting general expressions for curvature to give the hydrostatic Young–Laplace equations:

$\frac{r''}{(1+r'^2)^{\frac{3}{2}}} - \frac{1}{r(z) \sqrt{1+r'^2} } = z - \Delta p^*$

$\frac{z''}{(1+z'^2)^{\frac{3}{2}}} + \frac{z'}{r (1+z'^2)^{\frac{1}{2}} } = \Delta p^*- z(r).$

Application in medicine

In medicine it is often referred to as the Law of Laplace, used in the context of cardiovascular physiology, and also respiratory physiology. Arteries may be viewed as cylinders, and the left ventricle of the heart can be viewed as part cylinder, part hemisphere (a bullet shape), modeled by the Law of Laplace as T=p x r / (2 x t), where T=wall tension, p=pressure, r=radius, t=wall thickness. For a given pressure, increased radius requires increased wall thickness to accommodate a stable wall tension; also, increased pressure requires increased thickness to maintain a stable wall tension. The latter is used to explain thickening of arteries and thickening of the left ventricle to accommodate high blood pressure. However, the thickened left ventricle is stiffer than when the thickness is normal, so it requires elevated pressures to fill, a condition known as diastolic heart failure. Note that trucks carrying pressurized gas often have multiple tubes of small radius, so that the wall tension T will be low to reduce need for thick walls to prevent pipes from bursting. The lung contains small spherical gas-exchange chambers called alveoli, where a single alveolus can be modeled as being a perfect sphere. The Law of Laplace explains why alveoli of the lung need small radius to accommodate their thin walls for gas exchange at atmospheric pressure. Numerous small radius alveoli also achieves high surface area

Applying the Law of Laplace to alveoli of the lung, the pressure differential nets a force pushing on the surface of the alveolus, tending to decrease size during exhalation. The Law of Laplace states that pressure is inversely proportional to alveolar radius, and directly proportional to surface tension. It follows from this that if the surface tensions are equal, a small alveolus will experience a greater inward pressure than a large alveolus. In that case, if both alveoli are connected to the same airway, the small alveolus will be more likely to collapse, expelling its contents into the large alveolus.

This explains why the presence of surfactant lining the alveoli is of vital importance. Surfactant reduces the surface tension on all alveoli, but its effect is greater on small alveoli than on large alveoli. Thus, surfactant compensates for the size differences between alveoli, and ensures that smaller alveoli do not collapse.^[6] You can mimic this issue by connecting two inflated balloons to either ends of a plastic straw or a stiffer tube (you may need rubber bands to secure them). If the balloons are equal in thickness and radius then they can stay equally inflated, but if you squeeze one a bit to reduce its radius, the condition will be unstable, and in accord with the Law of Laplace, the smaller one will empty itself into the larger one.

The Law of Laplace also explains various phenomena encountered in the pathology of vascular or gastrointestinal walls. The wall tension in this case represents the muscular tension on the wall of the vessel. For example, if an aneurysm forms in a blood vessel wall, the radius of the vessel has increased. This means that the inward force on the vessel decreases, and therefore the aneurysm will continue to expand until it ruptures. A similar logic applies to the formation of diverticuli in the gut.^[7]

The Law of Laplace can also be used to model transmural pressure in the heart and the rest of the circulatory system.

The stalagmometric method is one of the most common methods for measuring surface tension. The principle is to measure the weight of the drops of the fluid falling from the capillary glass tube, and then calculate the surface tension of the specific fluid which we are interested in. We know the weight of each drop of the liquid by counting the number of the drops falling out. From this we can determine the surface tension

Stalagmometer

A stalagmometer, straight form.

A stalagmometer is a device for investigating surface tension using the stalagmometric method. It is also called a stactometer or stalogometer. The device is based on a capillary glass tube whose middle section is widened. In terms of the volume of the drop, it could be calibrated to the same size based on the design of the stalagmometer. The part of the bottom of the device is narrowed down to let the fluid fall out from the tube in a shape of drop.^[2]^[3] In the experiments, the drops of the specific fluid are flowing slowly from the tube in a vertical direction. The drops hanging on the bottom of the tube start to fall when the volume of the drop reaches the maximum value which is dependent on the characteristic of the solution. In this moment, the weight of the drops is in an equilibrium state with the surface tension. Based on the Tate’s law:

$\ mg=2\pi r \sigma$

The drop is falling when the weight (mg) is equal to the circumference (2πr) multiplied by the surface tension (σ). The surface tension can be calculated when we know the radius of the tube (r) and the mass of the fluid droplet (m). On the other hand, on account the surface tension proportional to the weight of the drop, we can use a reference fluid (mostly using water as a reference) to compare with the fluid which we are interested in.

$\frac {m_1}{\sigma_1}=\frac {m_2}{\sigma_2}$

In the equation, m₁ and σ₁ can be the mass and surface tension of the reference fluid, and m₂ and σ₂ can be the mass and surface tension of the fluid we want to investigate. If we take water as a reference fluid, then:

$\sigma=\sigma_{H_2O}\times\frac {m}{m_{H_2O}}$

If the surface tension of water is known, we can calculate the surface tension of the specific fluid from the equation. The weight of more drops we measure, the more precise we calculate the surface tension from the equation.^[2] One thing we need to notice is that keeping the stalagmometer clean is really important so as to get meaningful reading. There are commercial tubes for stalagmometric method in three kinds of size: 2.5, 3.5, and 5.0 (ml). The size of 2,5 (ml) is suitable for small volume and low viscosity, of 3.5 (ml) for relatively high viscous fluid, of 5.0 (ml) for large volume and low viscosity, 2,5 (ml) for small volume and high viscosity and are flexible for different size of most of the fluids.^[5] “Survismeter” produces ultra accurate results of surface tension along with viscosity, interfacial tension, wetting coefficient and density data. The survismeter is most accurate and safer for volatile, inflammable and carcinogenic liquids.

Modified method

During the experiment, we may sizes of the drops each time, thus reduce the precision of value of the surface tension. The stalagmometric method was currently improved by S. V. Chichkanov and his colleagues that they modify the experiment to measure the weight of the drops in a fixed number rather than directly measure the number of the drops. The modified method to determine the surface tension based on the weight of the drops in a fixed number can be more precise than the original method based on the number of drops, especially for the fluid which surface is highly active. The advantage of the modified method is that it actually get more precise value of the surface tension and reduce the duration of experiments.

References:

1.The abstract of the lecture.

2. intranet.tdmu.edu.ua/auth.php

3. Atkins P.W. Physical chemistry. – New York. – 1994. – P.299-307.

4. Cotton, F. A., Chemical Applications of Group Theory, John Wiley & Sons: New York, 1990

5.Girolami, G. S.; Rauchfuss, T. B. and Angelici, R. J., Synthesis and Technique in Inorganic Chemistry, University Science Books: Mill Valley, CA, 1999

6.John B.Russell. General chemistry. New York.1992. – P. 550-599

7. Lawrence D. Didona. Analytical chemistry. – 1992: New York. – P. 218 – 224.

8. en.wikipedia.org/wiki

Prepared by PhD Falfushynska H.