Boundary-element analysis of planar drop deformation in confined flow. Part 1. Newtonian fluids

A boundary element formulation is presented for the general two-dimensional simulation of confined two-phase incompressible creeping Newtonian flow (visco-elastic elaids will be considered in a second part). The method requires the solution of two simultaneous integral equations on the interface between the two fluids and the confining solid boundary. The method is illustrated through the simulation of the deformation of a drop as it is driven by the ambient flow inside a convergent channel. The accuracy and convergence of the method are assessed by varying the time increment for a given number of boundary elements. The influences of the degree of channel convergence and viscosity ratio are investigated. Circular as well as elliptic initial drops are also considered.