An Indirect Boundary Integral Equation For
Confined Stokes Flow Of Drops
Author(s)
G. Zhu, A.A. Mammoli & H. Power
Abstract
An indirect boundary integral formulation is used to model the viscous flow of
drops in a container. The indirect formulation results in well-conditioned linear
systems, suitable for solution using iterative methods. The formulation is tested
using several benchmarks. The tests allow the determination of the range of viscosity
ratio and capillary number which can be treated accurately using the formulation.
The convergence behavior is also tested, and it is shown that it is relatively
independent of the systems size, and that the method is suitable for treating systems
with large numbers of drops. Finally, the method is applied to a typical problem,
that of the flow of one or more drops through a contraction. The outcome of the
passage through the contraction is highly dependent on the viscosity ratio and the
capillary number.
1 Introduction
Multiphase flow in porous media is currently one of the more challenging topics
in fluid mechanics. In many cases (gas sequestration in aquifers, oil recovery, filtration),
one continuous phase carries drops and particles of different phases. The
interaction of the multiphase fluid with the porous formation at the scale of the
droplet size or pore size determines the macroscopic characteristics of the flow.
An experimental treatment of the phenomenon presents considerable difficulties
due to the small scales involved, on the order of a few microns. As a consequence,
Insight into the interaction may be obtained using simulation. Boundary integral
techniques appear suitable for this type of problem, characterized by very complex,
evolving geometries. Recently, several types of acceleration methods have
Keywords
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