Stokes' law

In 1851, George Gabriel Stokes derived an expression for the frictional force exerted on spherical objects with very small Reynolds numbers (e.g., very small particles) in a viscous fluid by solving the generally unsolvable Navier-Stokes equations:

<math>F = 6 \pi r \eta </math>

where:

F is the frictional force

r is the particle radius

η is the fluid viscosity, and

v is the particles speed

If the particles are falling in the viscous fluid by their own weight, then we can derive their settling velocity by equating this frictional force with the gravitational force:

<math>V_s = \frac{2}{9}\frac{r^2 g (\rho_p - \rho_f)}{\eta}</math>

where:

V_s is the particles settling velocity,

g is the acceleration of gravity,

ρ_p is the density of the particles, and

ρ_f is the density of the fluid

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See also:

Navier-Stokes equations

Stokes' theorem