Passage of a liquid drop through a bifurcation

Numerical simulations of the motion of a viscous liquid drop through a two-dimensional bifurcating channel are conducted using a boundary-element method for Stokes flow. The drop viscosity is assumed to be equal to the ambient fluid viscosity and the drop interface is assumed to exhibit uniform surface tension. The mean fluid pressures are prescribed at the channel inlet and two outlets, and the corresponding flow rates are computed as part of the solution. Preliminary simulations show that the shape of a two-dimensional drop moving through a channel with parallel walls is similar to that of an axisymmetric drop moving along the centerline of a circular tube. The ability of a drop to remain intact as it passes through the bifurcation is determined by the drop size and capillary number expressing the significance of surface tension. For a given drop size and channel inlet and outlet pressures, there is a critical capillary number above which a drop splits into two pieces connected by a thinning bridge. The presence of the drop has a weak effect on the inlet and outlet flow rates throughout its passage. Simulations based on a boundary-element method for a rigid particle with circular or elliptical shape reveal a significantly stronger effect due to the absence of interfacial mobility.