Affiliation:
1. Department of Civil Engineering
and Engineering Mechanics, Columbia University, 610 Seeley W. Mudd Building, 500 West 120th Street, New York, NY 10027
Abstract
The equivalent inclusion method is presented to derive the Stokes flow of multiple drops moving in a viscous fluid at a small Reynolds number. The drops are replaced by inclusions with the same viscosity as the fluid, but an eigenstrain rate field that is a fictitious nonmechanical strain rate field is introduced to represent the viscosity mismatch between each drop and the matrix fluid. The velocity and pressure fields can be solved by considering the body force and eigenstrain rate on the inclusions with the Green's function technique. When one spherical drop is considered, the solution recovers the closed-form classic solution. This method is versatile and can be used in the simulation of a many-body system with different drop size, elongation ratio, and viscosity. Numerical examples demonstrate the capability and accuracy of the proposed formulation and illustrate particles' rotation and motion caused by particle interactions.
Subject
Mechanical Engineering,Mechanics of Materials,Condensed Matter Physics
Cited by
14 articles.
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