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In fluid dynamics, Stokes' law gives the frictional force – also called drag force – exerted on spherical objects moving at very small Reynolds numbers in a viscous fluid. [1] It was derived by George Gabriel Stokes in 1851 by solving the Stokes flow limit for small Reynolds numbers of the Navier–Stokes equations. [2]
If a moving fluid meets an object, it exerts a force on the object. Suppose that the fluid is a liquid, and the variables involved – under some conditions – are the: speed u, fluid density ρ, kinematic viscosity ν of the fluid, size of the body, expressed in terms of its wetted area A, and; drag force F d.
For example, consider a small sphere with radius = 0.5 micrometre (diameter = 1.0 μm) moving through water at a velocity of 10 μm/s. Using 10 −3 Pa·s as the dynamic viscosity of water in SI units, we find a drag force of 0.09 pN. This is about the drag force that a bacterium experiences as it swims through water.
Laminar flow over a body occurs when layers of the fluid move smoothly past each other in parallel lines. In nature, this kind of flow is rare. As the fluid flows over an object, it applies frictional forces to the surface of the object which works to impede forward movement of the object; the result is called skin friction drag.
The mobility of non-spherical aerosol particles can be described by the hydrodynamic radius. In the continuum limit, where the mean free path of the particle is negligible compared to a characteristic length scale of the particle, the hydrodynamic radius is defined as the radius that gives the same magnitude of the frictional force, as that of a sphere with that radius, i.e.
The normal force and the frictional force are ultimately determined using vector analysis, usually via a free body diagram. In general, process for solving any statics problem with friction is to treat contacting surfaces tentatively as immovable so that the corresponding tangential reaction force between them can be calculated.
A smaller ion with stronger hydration, for example, may have a greater Stokes radius than a larger ion with weaker hydration. This is because the smaller ion drags a greater number of water molecules with it as it moves through the solution. [1] Stokes radius is sometimes used synonymously with effective hydrated radius in solution. [2]
The force acting on the particle is written as a sum of a viscous force proportional to the particle's velocity (Stokes' law), and a noise term representing the effect of the collisions with the molecules of the fluid. The force () has a Gaussian probability distribution with correlation function (′) =, (′), where is the Boltzmann constant ...