Mesoscopic Thermodynamics in Smooth and Curved Interfaces in Asymmetric Fluids
Abstract
Phase separation has a significant impact on many chemical engineering applications, and since the phase transition of asymmetric one–component fluid or mixture interfaces can be gradual, or smooth, further analysis is warranted for fluid separation on the mesoscale. Complete scaling is applied to account for fluctuations in the critical region and to model the interfacial profiles of one–component and dilute binary mixtures, as well as calculate the curvature correction to the surface of tension (or Tolman length). Well–established symmetric profiles were selected for the order parameter and thermal scaling densities for use in complete scaling to model these asymmetric fluids. Real fluid asymmetry was applied to these profiles though the scaling coefficients of one–component fluids. Scaling coefficients for mixtures were introduced through the experimental critical parameters of the specific mixture; characteristics accounted for included consideration of the difference in molar volume between solvent and solute, changes in critical temperature and pressure with concentration as well as the Krichevskii parameter. Flory theory was used to approximate the scaling coefficients in dilute polymer solutions to determine the Tolman length. These results indicated that the Tolman length diverges near the critical point of separation and with an increasing degree of polymerization. As an infinite degree of polymerization is approached, the Tolman length becomes half of the width of the interface. Since fluid behavior near the critical point of separation is universal, many of the theoretical expressions shown in this work can be applied to other asymmetric systems. The results of this analysis showed that a large difference in molecular volume led to a higher degree of fluid asymmetry in polymer solutions. The concentration of added solute, specifically in dilute <italic>n</italic>–heptane–ethane solutions resulted in increased fluid asymmetry in density profiles, as well as a shift toward the density of the added solute. When considering dilute mixtures of aqueous <italic>n</italic>–hexane and <italic>n</italic>–heptane–ethane solutions, a slight increase in concentration of solute, coupled with an increasing temperature distance to the critical point of separation, yielded the greatest increase in fluid asymmetry in concentration profiles.