Collision frequency

Physics calculation for collisions From Wikipedia, the free encyclopedia

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^[1]^{[better source needed]} $Z=N_{\text{A}}N_{\text{B}}\sigma _{\text{AB}}{\sqrt {\frac {8k_{\text{B}}T}{\pi \mu _{\text{AB}}}}},$ where

N_{\text{A}}

is the number of A particles in the volume,

N_{\text{B}}

is the number of B particles in the volume,

\sigma _{\text{AB}}

is the collision cross section, the "effective area" seen by two colliding molecules (for hard spheres,

\sigma _{\text{AB}}=\pi (r_{\text{A}}+r_{\text{B}})^{2}

, where

r_{\text{A}}

is the radius of A, and

r_{\text{B}}

is the radius of B),

k_{\text{B}}

is the Boltzmann constant,

T

is the thermodynamic temperature,

\mu _{\text{AB}}={\frac {m_{\text{A}}m_{\text{B}}}{m_{\text{A}}+m_{\text{B}}}}

is the reduced mass of A and B particles.

Collision in diluted solution

In the case of equal-size particles at a concentration $n$ in a solution of viscosity $\eta$ , an expression for collision frequency $Z=V\nu$ , where $V$ is the volume in question, and $\nu$ is the number of collisions per second, can be written as^[2] $\nu ={\frac {8k_{\text{B}}T}{3\eta }}n,$ where

k_{B}

is the Boltzmann constant,

T

is the absolute temperature,

\eta

is the viscosity of the solution,

n

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 $\nu$ .^[2]

References

Related Articles

Wikiwand AI