Shear effects in interfacial rheology and their implications on oscillating pendant drop experiments

Adsorbed molecules that associate or entangle with one another at the fluid interface will give rise to shearing resistance (i.e., resistance to shape change at constant area) on the continuum scale. Where these shear effects occur, familiar theoretical constructs, such as the Young-Laplace equation or the complex dilational modulus, are rendered invalid. In this work, we report numerical simulations of an oscillating pendant drop with a surface that is a shear-resisting film. Specifically, the drop surface is treated as a Boussinesq fluid (i.e., one that possesses independent viscous coefficients for dilation and shearing). We show that the frequency response of the apparent dilational modulus (based on tensions determined from the Young-Laplace equation) is remarkably consistent with the Maxwell model of viscoelasticity. It is argued, however, that usage of the Maxwell model, in the context of dilational rheology, is unphysical; as such, the apparent "Maxwellian behavior" is likely due to shear resistance within the Boussinesq material (i.e., the interface may not be undergoing any internal relaxation at all). Our results also predict an apparent "softening" of the adsorbed layer as the interfacial structure becomes more developed.