When a microorganism moves in a viscous fluid, inertia (fluid density) has a negligible influence on the organism’s drag force. These are called creeping flows. The only important parameters are velocity U, viscosity μ, and body length scale L.
(a) Write this relationship in dimensionless form.
(b) The drag coefficient CD = F/(1/2 ρU2A) is not appropriate for such flows. Define a more appropriate drag coefficient and call is Cc (for creeping flow).
(c) For a spherical organism, the drag force can be calculated exactly from creeping-flow theory: F = 3πμUd. Evaluate both forms of the drag coefficient for creeping flow past a sphere.