Flow at Low Reynolds Numbers

Abstract

Newton’s second law of motion requires that the rate of change of momentum of a fluid parcel be balanced by the body force exerted on its volume and the surface force exerted on its boundary. Under certain conditions, the rate of change of momentum is small compared to the body and surface force, and may be neglected without introducing serious error. This occurs, in particular, when the viscosity of the fluid is high, when the density is small, when the velocity changes rapidly over a small distance yielding a sharp spatial gradient, or when the velocity by which a fluid parcel is convected by the flow is sufficiently small. The formal requirement for fluid inertia to be negligible is that a properly defined Reynolds number be sufficiently small. How small it should be, depends on the particular problem under consideration. In this chapter, we consider a family of flows occurring at small Reynolds numbers, and discuss the solution of the simplified system of governing equations that arises by dropping the inertial terms from the equation of motion. This simplification will allow us to address a multitude of physical problems and obtain solutions by a host of analytical and numerical methods.