Kurilko A. Mixing of viscous fluids in microcells

The general method of investigation of viscous incompressible fluid in a rectangular domain in Stokes approximation with moving boundary segments is developed in this thesis. The analytical solutions of the problem of motion of viscous incompressible fluid in a rectangular cavity with moving boundary segments are obtained. An efficient approach for the reduction of infinite systems of algebraic equations is proposed. Selecting an asymptotic behavior of series features made it possible to present the asymptotic solutions with high convergence of series. It is shown that the analytical superposition method to determine the velocity field and numerical algorithm for continuous two-dimensional contour deformation preserves topological properties (connectivity and orientation) for any selected fluid in a rectangular cavity flow.