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A second kind integral equation formulation for the interaction between a solid particle and a compound drop at low Reynolds number

Kohr M.

Applied Mechanics and Engineering

2000

Vol. 5, no 3

557-577

In this paper, we determine a boundary integral formulation for the motion and deformation of a compound drop due to its interaction with a solid particle. The problem is reduced to a system of Fredholm integral equations of the second kind. We prove that this system has a unique continous solution when the boundaries of the flow are Lyapunov surfaces and the boundary data are continous.

An integral method for two-dimensional stokes flows past rigid obstacles in the half-plane

Kohr M.

Applied Mechanics and Engineering

1998

Vol. 3, no 1

5-24

The problem of determining the slow viscous flow of a fluid past a cylinder with an arbitrary cross section, in a domain with boundary limited by a plane wall, is formulated as a system of Fredholm linear integral equations of the second kind. We next complete the double-layer potentials of the system with some terms having singularities located inside the obstacle and which satisfy the nonslip boundary condition on the wall. We next prove that this system of integral equations has a unique continuous solution when the boundary of the particle is a Lyapunov curve. Also, the numerical results are given for the case of a fixed circular obstacle. For the numerical solution we use a standard boundary element technique.