Английская Википедия:Collision frequency

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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:

<math> Z = N_\text{A} N_\text{B} \sigma_\text{AB} \sqrt\frac{8 k_\text{B} T}{\pi \mu_\text{AB}},</math>

which has units of [volume][time]⁻¹.

Here,

• <math>N_\text{A}</math> is the number of A molecules in the gas,
• <math>N_\text{B}</math> is the number of B molecules in the gas,
• <math> \sigma_\text{AB} </math> is the collision cross section, the "effective area" seen by two colliding molecules, simplified to <math> \sigma_\text{AB} = \pi(r_\text{A}+r_\text{B})^2 </math>, where <math> r_\text{A} </math> the radius of A and <math> r_\text{B} </math> the radius of B.
• <math>k_\text{B}</math> is the Boltzmann constant,
• <math>T</math> is the temperature,
• <math>\mu_\text{AB}</math> is the reduced mass of the reactants A and B, <math> \mu_\text{AB} = \frac{{m_\text{A}}{m_\text{B}}}{{m_\text{A}} + {m_\text{B}}} </math>

Collision in diluted solution

In the case of equal-size particles at a concentration <math>n </math> in a solution of viscosity <math>\eta</math> , an expression for collision frequency <math>Z=V\nu</math> where <math>V</math> is the volume in question, and <math>\nu</math> is the number of collisions per second, can be written as:

<math> \nu = \frac{8 k_\text{B} T}{3 \eta} n, </math>

Where:

• <math>k_B</math> is the Boltzmann constant
• <math>T</math> is the absolute temperature (unit K)
• <math>\eta</math> is the viscosity of the solution (pascal seconds)
• <math>n</math> is the concentration of particles per cm³

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 <math>\nu</math>.