Creeping flows in and around a compound multiphase droplet

Exact analytical solutions for steady-state axisymmetric creeping flow of a viscous incompressible fluid in the presence of a compound multiphase droplet are derived. The two spherical surfaces constituting a vapor-liquid compound droplet are assumed to overlap with a contact angle /2. It is further assumed that the surface tension forces are sufficiently large so that the interfaces have uniform curvature. The singularity solutions for the flow induced by a stokeslet in the presence of a compound droplet are obtained by the method of reflections. The flow patterns are discussed in the case of a flow induced by a pair of opposite stokeslets. Toroidal eddy patterns are observerd in the continous phase for some fixed value of the viscosity ratio. The eddy changes its size and shape if the locations of the initial stokeslets are altered. These observations may be useful hi the study of hydrodynamic interactions of droplets with other objects in a viscous fluid. We also provide a brief discussion of our results in connection with the computation of mobility functions. The exact results presented here can be useful in validating numerical algorithms and codes on multiphase flow and fluid-droplet interactions.

Creeping flows in and around a compound multiphase droplet Conference Paper