THE COMPLETED DOUBLE-LAYER BOUNDARY INTEGRAL-EQUATION METHOD FOR THE STOKES-FLOW OF A MICROPOLAR FLUID

The problem of determining the slow flow of an unbounded micropolar fl uid past a solid particle of arbitrary shape, is formulated as a syste m of linear Fredholm integral equations of the second kind. These inte gral equations are found when the velocity and microrotation vector fi elds are represented by a double layer micropolar potential with unkno wn density, plus a pair of singular solutions of the Stokes' micropola r equations, corresponding to a concentrated force and concentrated co uple, located in the interior of the particle, these singularities giv e rise to force and torque, including the effect of the couple stress, with magnitude depending linearly upon the unknown density of the dou ble layer. It is shown that this system of integral equations possess a unique continuous solution, when the particle boundary is a Lyapunov surface and the boundary data on the particle surface is continuous. In comparison with previous works, where it was necessary to include i n the formulation certain unknown eigenfunctions, to guarantee uniquen ess of solution, the method proposed here, without recourse to the eig enfunctions, is constructive and can be used as a basis for a numerica l solution.