Nonequilibrium Interfacial Tensions

When a system contains a soluble surfactant, diffusion, adsorption, and desorption of surfactant may cause interfadal tension to vary with both position and time. If, for instance, a fresh interface is formed on a stagnant pool of a surfactant solution, interfacial tension is found to decrease with time as surfactant diffuses to the interface and adsorbs. 

Let us consider such a situation with a plane interface. If there is no convection, the diffusion equation in the bulk hquid (z 0) is given by 

Initially c has its bulk value c for all z 0. Also, at all times, c - c far from the interface (i.e., as z - oo). Were the solution concentration c(0j) at the interface known, as a function of time. Equation 6.39 could be solved. Instead, it is known from the interfacial mass balance that 

With the additional condition that T(0) = 0, the solution for T(t) is given by 

This equation was first derived by Ward and Tordai (1946) and later by Hansen (1961), who used the method of Laplace transforms. 

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The oil-water dynamic interfacial tensions are measured by the pulsed drop (4) technique. The experimental equipment consists of a syringe pump to pump oil, with the demulsifier dissolved in it, through a capillary tip in a thermostated glass cell containing brine or water. The interfacial tension is calculated by measuring the pressure inside a small oil drop formed at the tip of the capillary. In this technique, the syringe pump is stopped at the maximum bubble pressure and the oil-water interface is allowed to expand rapidly till the oil comes out to form a small drop at the capillary tip. Because of the sudden expansion, the interface is initially at a nonequilibrium state. As it approaches equilibrium, the pressure, AP(t), inside the drop decays. The excess pressure is continuously measured by a sensitive pressure transducer. The dynamic tension at time t, is calculated from the Young-Laplace equation... 

The effect of mutual saturation on the L-V and L-L interfacial tensions is effectively illustrated by considering the spreading coefficient of one liquid on another using both the initial (unsaturated) and equilibrium values of 7. Use the following data to calculate Se/, (equilibrium) and S B/A (nonequilibrium) ... 

Polysaccharides interfaced with water act as adsorbents on which surface accumulations of solute lower the interfacial tension. The polysaccharide-water interface is a dynamic site of competing forces. Water retains heat longer than most other solvents. The rate of accumulation of micromolecules and microions on the solid surface is directly proportional to their solution concentration and inversely proportional to temperature. As adsorbates, micromolecules and microions ordinarily adsorb to an equilibrium concentration in a monolayer (positive adsorption) process they desorb into the outer volume in a negative adsorption process. The adsorption-desorption response to temperature of macromolecules—including polysaccharides —is opposite that of micromolecules and microions. As adsorbate, polysaccharides undergo a nonequilibrium, multilayer accumulation of like macromolecules. 

Here it may be appropriate to note that in the literature the term dynamic interfacial (or surface tension is used in two senses, viz. (i) as the tension obtained by a dynamic method such as scattering or (li) as that obtained under nonequilibrium conditions, l.e. tensions measured at non-zero De, for interfaces that relax during the observation. We shall reserve the term dynamic interfacial tension for the latter case, that is, for Interfaces that are not equilibrated (sec. 1.14). Interfacial tensions derived from scattering are essentially static, although... 

Adsorption. Some substances tend to adsorb onto an interface, thereby lowering the interfacial tension the amount by which it is lowered is called the surface pressure. The Gibbs equation gives the relation between three variables surface pressure, surface excess (i.e., the excess amount of surfactant in the interface per unit area), and concentration—or, more precisely, thermodynamic activity—of the surfactant in solution. This relation only holds for thermodynamic equilibrium, and the interfacial tension in the Gibbs equation is thus an equilibrium property. Nevertheless, also under nonequilibrium conditions, a tension can be measured at a liquid interface. 

In dynamic methods, determination of Vj2 is based on the time evolution of a fluid element shape, from a nonequilibrium to an equiUhrium state. The evolution is driven by the interfacial tension, and depending on the initial shape of the element, it can foUow different dependencies. 

So far, we have treated the interfacial tension as an eqnilibriutn property that can be determined in a system that is relaxed dnring the time of the measurement. However, if the interface is off-eqnilibrinm, that is, dnring the relaxation process toward the equilibrium state, the interfacial tension is time dependent. Such a nonequilibrium, time-dependent interfacial tension is referred to as dynamic interfacial tension. Interpretation of dynamic interfacial tensions is nsnally in terms of surface rearrangements, transport of snrface-active componnds to or from the interface, conformational and orientational changes of adsorbed molecnles, and so on. 

Studied the time evolution of the interfacial tension when polyisobutylene (PIB)-b-PDMS was introduced to PIB/PDMS blend, with the copolymer added to the PIB phase in that study both homopolymers were poly disperse. The time dependence of the interfacial tension was fitted with an expression that allowed the evaluation of the characteristic times of the three components. The characteristic time of the copolymer was the longest, whereas the presence of the additive was found to delay the characteristic times of the blend components from their values in the binary system. The possible complications of slow diffusivities on the attainment of a stationary state of local equilibrium at the interface were thoroughly discussed by Chang et al. [58] within a theoretical model proposed by Morse [279]. Actually, Morse [279] suggested that the optimal system for measuring the equilibrium interfacial tension in the presence of a nearly symmetric diblock copolymer would be one in which the copolymer tracer diffusivity is much higher in the phase to which the copolymer is initially added than in the other phase because of the possibility of a quasi-steady nonequilibrium state in which the interfacial coverage is depleted below its equilibrium value by a continued diffusion into the other phase. 

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