Effective surface viscosities of a particle-laden fluid interface

Phys Rev E Stat Nonlin Soft Matter Phys. 2009 Jul;80(1 Pt 2):016306. doi: 10.1103/PhysRevE.80.016306. Epub 2009 Jul 10.

Abstract

The Einstein formula for the effective shear viscosity of low Reynolds number suspension flows is generalized to the case of flat, low-concentration, particle-laden interfaces separating two immiscible fluids. The effective surface shear and dilational viscosities of this system is found to be eta{s}=5/3(eta{1}+eta{2})R phi and zeta{s}=5(eta_{1}+eta_{2})R phi , correspondingly, where eta{1} and eta{2} are the shear viscosities of two bulk fluids and phi is the surface concentration of spherical particles of radius R . The formula is found to be in excellent agreement with data obtained using multicomponent lattice Boltzmann equation simulation.