In 1851,
George Gabriel Stokes derived an expression, now known as
Stokes' law, for the frictional force – also called
drag force – exerted on
spherical objects with very small
Reynolds numbers (i.e. very small particles) in a
viscous fluid. Stokes' law is derived by solving the
Stokes flow limit for small Reynolds numbers of the
Navier–Stokes equations:
Statement of the law
The force of viscosity on a small sphere moving through a viscous fluid is given by:
where
Fd is the frictional force – known as
Stokes' drag – acting on the interface between the fluid and the particle,
µ is the
dynamic viscosity,
R is the radius of the spherical object, and
V is the
flow velocity relative to the object. In
SI units,
Fd is given in
Newtons,
µ in Pa·s,
R in meters, and
V in m/s.