OVERVIEW

Flow at low Reynolds numbers is distinguished by the fact that the nonlinear convective term ? u ? u makes a small contribution to the equation of motion, and may thus be neglected. Consequently, the flow is governed by the continuity equation and one of the linear equations of steady, quasisteady, or unsteady Stokes flow discussed earlier in Section 3.7. The linear nature of the governing equations allows us to build an extensive theoretical framework regarding the mathematical properties of the solution and physical structure of the flow and, furthermore, derive solutions to a broad range of problems using a variety of analytical and numerical methods, many of them in closed form. Examples include methods based on separation of variables, singularity representations, and boundary integral formulations.

In the present chapter we shall discuss the general properties and illustrate methods of computing steady and unsteady flows at low Reynolds numbers, with reference to specific applications. Classes of flows to be considered include a family of flows near boundary corners, flows of liquid films, lubrication-type flows in confined geometries, flows past or due to the motion of rigid bodies and liquid drops, and oscillatory or transient flows due to particle motions.

The study of uniform flow past a stationary body or flow due to the translation of a body will lead us to examine the structure of the flow far from the body where the assumption of Stokes flow is no longer appropriate. Fortunately, in the far...