Stokes Velocity -- from Eric Weisstein's World of Physics

Stokes Velocity

The Stokes velocity is the terminal velocity v at which a sphere of density will sink (or rise) in a medium of density . For a solid sphere with , in equilibrium, the gravitational force is balanced by the sum of the buoyancy and drag forces ,

(1)

Plugging in

(2)

(3)

(4)

where is the dynamic viscosity and the drag force is known from Stokes flow, gives

(5)

Rearranging,

(6)

so solving for the speed v finally gives

(7)

(Lamb 1945, p. 599).

Bubble, Drop, Rayleigh Number, Stokes Flow--Sphere, Terminal Velocity

References

Lamb, S. H. Hydrodynamics, 6th ed. New York: Dover, p. 599, 1945.

Stokes, G. G. "On the Effect of the Internal Friction of Fluids on the Motion of Pendulums." Cambridge Philos. Trans. 9, 8-106, 1851. Reprinted in Mathematical and Physical Papers, 2nd ed., Vol. 3. New York: Johnson Reprint Corp., p. 1, 1966.