The Interfacial Tension of Liquids

When one considers that a molecule at an interface or surface has fewer nearest neighbors than a molecule in the bulk of the solution, it is easy to understand that the interfacial molecule has different thermodynamic properties. If one wishes to increase the area of a liquid, one must bring molecules from the bulk to the surface, thereby breaking intermolecular bonds and doing work. The work done to increase the surface area by unit amount is the interfacial or surface tension. Mathematically, the reversible work dw is given by 

The interfacial tension is obviously an important property of a liquid because it gives a direct indication of the magnitude of intermolecular forces. As a result of interfacial tension a liquid which is not in contact with another condensed phase, such as a water droplet in air, assumes the shape which has minimum area. It turns out that this shape is a sphere. As a result, there are no elliptical or square water droplets By maintaining a spherical shape, the area-to-volume ratio, and the number of molecules at the surface are their lowest possible values. One is not surprised by this fact on the basis of experience. 

consider again a spherical liquid drop. Because of the curvature of the interface, there is a pressure difference between the inside and outside of the drop. This difference exists because of the interfacial tension, which tends to reduce the area of the liquid system, so that equilibrium is maintained with a higher pressure inside the drop than the atmospheric pressure outside. If the radius of the drop is r, its surface area is 4nr. The incremental work dvrs done in increasing the radius by dr is 

This is counterbalanced by mechanical work dwj done on the basis of the volume change which occurs under a pressure difference, — Patnu where P is the internal pressure in the drop and Patm is the external atmospheric pressure. Thus, 

This is the Young-Laplace equation applied to a spherical surface. A more general form of this equation is used when the curvature of the interface is not spherical [Gl]. 

---

The ratio (p/G) has the units of time and is known as the elastic time constant, te, of the material. Little information exists in the published literature on the rheomechanical parameters, p, and G for biomaterials. An exception is red blood cells for which the shear modulus of elasticity and viscosity have been measured by using micro-pipette techniques 166,68,70,72]. The shear modulus of elasticity data is usually given in units of N m and is sometimes compared with the interfacial tension of liquids. However, these properties are not the same. Interfacial tension originates from an imbalance of surface forces whereas the shear modulus of elasticity is an interaction force closely related to the slope of the force-distance plot (Fig. 3). Typical reported values of the shear modulus of elasticity and viscosity of red blood cells are 6 x 10 N m and 10 Pa s respectively 1701. Red blood cells typically have a mean length scale of the order of 7 pm, thus G is of the order of 10 N m and the elastic time constant (p/G) is of the order of 10 s. 

Hartridge and Peters (Froo. Roy. Soc. A, Cl. 348, 1922) have measured the interfacial tension of liquid fatty acids and their solutions in benzene against aqueous borate, phthalate and phosphate buffer solutions of varying concentration and Ph. 

Wilhelmy (1863) suggested that the interfacial tension of liquids could be determined by measuring the maximum force required to pull a glass plate vertically from the interface. In his experiment, he was careful to ensure that the glass plate was extremely clean so that the angle of contact ((p) was relatively small or close to zero. The force, F, exerted on the plate raises the meniscus of the fluid above the level of the flat surface as shown in Figure D3.6.7. The mass of the liquid that is elevated above the fluid interface increases to some maximum value as F increases. Once the meniscus is fully formed, the force acting on the plate is equal to... 

When the powder particle melts, it wets the substrate (Figure 10-12). The liquid is pulled over the surface by a line tension a. This depends on the interfacial tensions of liquid, solid and gas it is lower than the surface tension. This tension is counteracted by forces due to the viscosity r]. The flattening will also depend on the initial size Rq of the drop. Finally you would expect the drop to become flatter with increasing time t. 

In defining the interfacial tension of liquids in section 8.2, the discussion was kept general in terms of two fluids a and p. When one of these fluids is air, then the interfacial tension has the values which are given in table 8.1 for a collection of polar liquids. A relationship between the interfacial tension between two immiscible liquids a and p, and that at the liquid air interface for each pure liquid can also be defined. These quantities are connected by the work of adhesion Wo,p, which is the work required to separate the two phases so that an air interface is formed at both a and p. Thus, if y p is the interfacial tension at the a P interface, that is, the work required to increase the area of this interface by unit amount, then... 

They lower the interfacial tension of liquid interfaces, thereby facilitating bending of the interface, hence deformation and breakup of drops and bubbles. 

This technique is one of oldest methods for the measurement of surface and interfacial tensions between two fluids. The precursor of this method is the so-called stalagmometer method. Essentially, it consists of counting the number of drops formed from a definite amount of liquid detaching from a capillary. This drop number is then compared with values obtained for liquids of known interfacial tension. The stalagmometer method is still used in many laboratories for a first estimation of the interfacial tension of liquids. 

Among the methods for measuring the interfacial tension of liquid interfaces the drop and bubble shape tensiometry is known for a long time [1]. However, it became applicable with an acceptable accuracy only about 15 years ago with the availability of a video technique that can be directly linked to a high performance computer [2]. The first set-ups were run with expensive work stations, while today typically PCs are used as their performance is much higher now than the work stations of the first instruments. The development of this experimental technique was extremely fast and quite a number of commercial instruments are at present available on the market. 

This rule is approximately obeyed by a large number of systems, although there are many exceptions see Refs. 15-18. The rule can be understood in terms of a simple physical picture. There should be an adsorbed film of substance B on the surface of liquid A. If we regard this film to be thick enough to have the properties of bulk liquid B, then 7a(B) is effectively the interfacial tension of a duplex surface and should be equal to 7ab + VB(A)- Equation IV-6 then follows. See also Refs. 14 and 18. 

Single-Bubble Regime Bubbles are produced one at a time, their size being determined primarily by the orifice diameter d, the interfacial tension of the gasdiquid film C, the densities of the liquid Pl and gas Pc, and the gravitational acceleration g according to the relation... 

Since the interfacial tension between two liquids can always be expressed as the difference between two surface tensions, interfacial tensions in general must necessarily be smaller than surface tensions, and may be very small indeed. As a rule, especially with a closely related series of compounds, the interfacial tension increases as the solubility in the second liquid diminishes. Thus at 20° the interfacial tension of alcohols against water are... 

In the case of the interfacial tension of two pure liquids we have had to deal with the superficial system in equilibrium with a two phase two component system of three dimensions. If we add to this system a third component the problem becomes still more complicated. The simplest case is that in which the added substance is soluble in one phase and completely insoluble in the other, the original liquids being themselves mutually insoluble. The change of interfacial tension should then run parallel to the change of surface tension of the liquid in which the third component dissolves. 

Apart from anomalous situations where surfactant interacts with the organic phase, the stability of HIPEs is linked to the interfacial tension of the system. Ruckenstein and coworkers [109] showed that the maximum volume of hydrocarbon which could be incorporated in an o/w HIPE increased with increasing surfactant concentration, presumably due to a concomitant decrease in the interfacial tension. Solans et al. [9] claimed that the interfacial tension between the aqueous phase and the liquid-crystalline surfactant layer in their highly... 

If the interfacial tension of the bare solid surface is higher than that of the solid-liquid interface (7s > Isl), the right hand side of Young s equation is positive. Then cos has to be positive and the contact angle is smaller than 90° the liquid partially wets the solid. If the solid-liquid... 

Viscosity and density of the component phases can be measured with confidence by conventional methods, as can the interfacial tension between a pure liquid and a gas. The interfacial tension of a system involving a solution or micellar dispersion becomes less satisfactory, because the interfacial free energy depends on the concentration of solute at the interface. Dynamic methods and even some of the so-called static methods involve the creation of new surfaces. Since the establishment of equilibrium between this surface and the solute in the body of the solution requires a finite amount of time, the value measured will be in error if the measurement is made more rapidly than the solute can diffuse to the fresh surface. Eckenfelder and Barnhart (Am. Inst. Chem. Engrs., 42d national meeting, Repr. 30, Atlanta, 1960) found that measurements of the surface tension of sodium lauryl sulfate solutions by maximum bubble pressure were higher than those by DuNuoy tensiometer by 40 to 90 percent, the larger factor corresponding to a concentration of about 100 ppm, and the smaller to a concentration of 2500 ppm of sulfate. 

The quantity y is usually called the surface tension for liquid-gas interfaces and the interfacial tension for liquid-liquid interfaces. We see from Equation (13.2) that y da is the differential quantity of work that must be done reversibly on the system to increase the area of the system by the differential amount da at constant entropy, volume, and mole numbers. 

The movement of droplets is based on an electrostatic method which changes the interfacial tension of the droplets by voltage, which is known as electrowetting (see Figure 1.33) [97, 98]. The nature of the liquid to be moved has to be polarizable and/or conductive. Application of an electric field on only one side of the droplet creates an imbalance of interfacial tension which can drive bulk flow of the droplet. 

The work of dispersion, Wd, involved in wetting a unit area of the solid substrate is given by the difference between the interfacial tension of the solid/liquid interface, ysL, and that of the solid/vapor interface, ySv,... 

A number of methods are available for the measurement of surface and interfacial tension of liquid systems. Surface tension of liquids is determined by static and dynamic surface tension methods. Static surface tension characterises the surface tension of the liquid in equilibrium and the commonly used measurement methods are Du Notiy ring, Wilhelmy plate, spinning drop and pendant drop. Dynamic surface tension determines the surface tension as a function of time and the bubble pressure method is the most common method used for its determination. 

With liquid contents beyond the capillary state, liquid completely envelopes the particles (Fig. 2.3D). Only the interfacial tension of the convex surface of a continuous liquid drop tends to hold the particles captive. 

A more complete procedure to compute the average thicknesses of the water and oil layers will be presented below. It is based on eq 3c, mass balances of components, and phase equilibrium equations. The calculations indicated that the interfacial tension of lamellar liquid crystals is very low, of the order of 10 5 N/m. It will be shown that y = 0 is always an excellent approximation of eq 3 c. 

The term ysv is the interfacial tension of the solid material in equilibrium with a fluid vapor yLV is the surface tension of the fluid material in equilibrium with its vapor and ySL is the interfacial tension between the solid and liquid materials. Complete, spontaneous wetting occurs when 9 = 0° or when the material spreads uniformly over a substrate to form a thin sheet. A contact angle of 0° occurs with pure water droplet on a clean, glass shde. Therefore, for complete spontaneous wetting, cos 9 > 1.0 or when... 

Adhesion between two liquids. The attraction exerted by one liquid across the interface on the other requires that work must be done to separate them. It may easily be shown that this work, called the adhesional work9 between the liquids, is equal to the sum of the surface tensions of the liquids singly, less the interfacial tension of the liquid-liquid interface. Suppose A and B (Fig. 1) are the liquids in a column one square centimetre in cross-section then when they are in contact the energy of the interface is yAB when they have been separated by a direct... 

---