Stretching of a capillary bridge featuring a particle-laden interface: particle sedimentation in the interface

Abstract

Colloidal particles adsorbed at fluid interfaces can be subject to external forces, for instance of magnetic, electrical, or gravitational origin. To develop a tool that will enable to study the effect of these forces on interfacial particle transport, we derive a transport equation for the surface particle concentration using the method of volume averaging. This equation is specialised to the problem of particle sedimentation induced by external forces on an axisymmetric capillary bridge stretched with assigned constant velocity between two circular plates. The equation for the interfacial concentration is one-way coupled to the unsteady Stokes equation in the capillary bridge, and solved in the thin-thread approximation, in the limit of small capillary and Bond numbers and for moderate area fractions. We find that owing to the competition between particle settling in one direction, and fluid velocity in the opposite direction, a concentration peak develops between the neck region and the moving plate. Hydrodynamic interactions, modelled through a concentration-dependent hindrance function, have the effect of steepening the shock-like concentration gradients that develop in the interface.