Session MB - Drops I. Emulsions & Drops.
MIXED session, Tuesday afternoon, November 23
Grand II, Westin Seattle
Mixing inside a 2D circular drop driven by non-uniform surface tension along its boundary is studied numerically. The internal flow undergoes substantial change as the surface tension gradient on the boundary is switched periodically. Under Stokes flow conditions relevant to microfluidics, the stream-function of the flow can be obtained analytically, leading to a nonlinear system of ordinary differential equations for the pathlines of passive tracers in the drop. This system exhibits chaotic mixing for certain ranges of the switching period. In addition, the type and order of switching phenomena are seen to be effective parameters for controlling the mixing. Poincaré maps for different switching periods are presented, demonstrating fixed points, attractors and basins of attraction inside the drop. Also, the center of mass and first and second moments of a swarm of passive particles, initially concentrated in a small region in the drop, are calculated to quantify the degree and quality of mixing. A threshold is found for the switching period, above which mixing is nearly complete.