A MICROMECHANICAL MODEL OF LINEAR SURFACE RHEOLOGICAL BEHAVIOR

A rheological theory of a fluid-fluid interface adsorbed by surfactant material is developed, based largely upon the suspension rheological theory of Adler and Brenner [Int. J. Multiphase Flow 11, 361-385, 387-417 (1985)]. "Ghost particle layers" are employed in the bulk phases, exhibiting no hydrodynamic interaction with the interfacial monolayer itself, and thus possessing no physical reality. These serve as a mathematical aid in the construction of a spatially periodic theory. Surfactant particles assume the role of suspended particles which are adsorbed preferentially to an interface within an instantaneous, spatially periodic monolayer arrangement. By focusing upon rigid, neutrally-buoyant spherical and cylindrical particles, a linear constitutive expression for the instantaneous surface excess stress tensor is developed in terms of three surface rheological coefficients. The coefficients corresponding to pure strain and simple shearing motions are expected to combine and yield a single time averaged surface shear viscosity (analogous to that which is observed with bulk phase spatially periodic suspensions), whereas the third coefficient is the instantaneous surface dilatational viscosity. Numerical calculations of the three surface rheological coefficients are obtained employing a finite element numerical method. As bulk particle-surface particle interactions are not accounted for in this model, the calculations are most applicable to real systems below the critical micelle concentration. The model might be generalized to account for more realistic surfactant particle shapes and physico-chemical interactions, resulting in a more general non-Newtonian surface rheological behavior.