Some laminar flow problems at small and moderate Reynolds numbers. Numerical solutions and experiments

Two classes of laminar flows are considered: Stokes or creeping flows, and steady, high Reynolds number separated flows. A method is detailed for solving the Stokes equations for general flow fields and arbitrary geometries that computes the drag, lift, and torque without solving a fully three dimensional problem. Such a method is applied to Stokes flow of an unbounded fluid past a single solid particle surface, thereby rigorously reducing the problem to the solution of a system of linear integral equations of the first kind for the stress force on the particle surface. Next, the method is extended to a situation where the shape of a deformable gas bubble is determined as part of the numerical solution. Finally, torques are computed for ellipsoids rotating about their principle axes and for a benzene molecule rotating normal to its symmetry axis with slip boundary conditions.