Collision frequency

Collision frequency describes the rate of collisions between two atomic or molecular species in a given volume, per unit time. In an ideal gas, assuming that the species behave like hard spheres, the collision frequency between entities of species A and species B is

where

is the number of A particles in the volume,

is the number of B particles in the volume,

is the collision cross section, the "effective area" seen by two colliding molecules (for hard spheres, , where is the radius of A, and is the radius of B),

is the Boltzmann constant,

is the thermodynamic temperature,

is the reduced mass of A and B particles.

Collision in diluted solution

In the case of equal-size particles at a concentration in a solution of viscosity , an expression for collision frequency , where is the volume in question, and is the number of collisions per second, can be written as

where

is the Boltzmann constant,

is the absolute temperature,

is the viscosity of the solution,

is the number density.

Here the frequency is independent of particle size, a result noted as counter-intuitive. For particles of different size, more elaborate expressions can be derived for estimating .

References