Interfacial Tension

Interfacial tension measurements provide a direct means of probing the interaction between fluids. This property is crucial in an industrial context for controlling the size and phase stability of mechanically dispersed droplets and other transient structures formed in the course of phase separation. In principle, the interfacial tension, $\sigma$, provides a conceptually simple means of determining the reduced temperature variable $\tau=(T-T_c)/T_c$ = (T - T_c) / T_c needed to characterize the phase stability of fluid mixtures, but experimental complications [82,83] (e.g., high viscosity in polymeric systems) have limited somewhat the application of this method to the critical phenomena of fluid mixtures. Part of the difficulty is the need for a more predictive theory of interfacial tension on which reliable thermodynamic interaction ($\chi$ or G) measurements can be based. Recently, there has been great effort in modeling the interfacial tension of polymeric blends by Monte Carlo simulation methods as a guide to improving analytic theory in this important area of technological application [69,70].

We calculate the LB interfacial tension $\sigma$ through an integration of the interfacial composition profile,

$$\sigma= \int (P_{zz}-\frac{1}{2}[P_{xx}+P_{yy}]) dz$$ (27)

where P_zz and ½ [P_xx + P_yy] are the normal and tangential parts of the pressure tensor, respectively. The numerical values of the interfacial tension for the symmetric LB fluid mixture, shown in Fig. 10, are consistent with a power law,

$$\sigma= \sigma_o \tau^{1.5}_G, \sigma_0 \approx 4.2$$ (28)

over a broad temperature range. The exponent 1.5 is an established result for the interfacial tension in mean-field theory [12,70], and is found to agree reasonably well with observations outside the critical region [84,85,86]. Fluctuation effects modify the exponent to a value $\approx 1.25$ 1.25 [87]. This fluctuation modified exponent is often found to be quite accurate near the critical point for phase separation [77,78]. The amplitude of the interfacial tension, $\sigma_0$₀, is a non-universal quantity that depends on the interparticle potential range, interparticle spacing, and molar volume of the liquid. Further discussion of the origin of interfacial tension in the LB model is given in Appendix A.

  

Figure 10: Interfacial tension versus quench depth, $\tau _G$_G.