Dynamic measurements with the bicone interfacial shear rheometer: The effects of the numerical implementation of the interfacial boundary condition

Abstract

The increasing popularity of flow field-based data analysis (FFBDA) techniques has a paradigmatic example in the routines already developed for the rotational oscillating bicone bob interfacial shear rheometer. Such routines use a second order centered finite difference (SOCFD) discretization scheme, in both the vertical and radial coordinates, for the velocity field in the bulk fluid subphase and a first order forward finite difference (FOFFD) scheme in the vertical coordinate for the velocity field at the air/water interface. Such a mixture of schemes causes non-smooth flow fields at the interface that can be tackled by appropriately devising a SOCFD scheme for the vertical coordinate at the interface using a line of “phantom” nodes that merely serve to adequately merge the Navier-Stokes equations and the Boussinesq-Scriven boundary condition at the interface. Here we report on a detailed analysis of the quantitative improvements of such a scheme over the previous one by comparing the structure of the flow fields at and close to the interface, the differences in the interfacial and bulk drag torques on the bicone bob, and the differences in the torque/displacement complex amplitude ratio.