Mean free time explained

Molecules in a fluid constantly collide with each other. The mean free time for a molecule in a fluid is the average time between collisions. The mean free path of the molecule is the product of the average speed and the mean free time.[1] These concepts are used in the kinetic theory of gases to compute transport coefficients such as the viscosity.[2]

In a gas the mean free path may be much larger than the average distance between molecules. In a liquid these two lengths may be very similar.

Scattering is a random process. It is often modeled as a Poisson process, in which the probability of a collision in a small time interval

dt

is

dt/\tau

. For a Poisson process like this, the average time since the last collision, the average time until the next collision and the average time between collisions are all equal to

\tau

.

Notes and References

  1. Web site: The Feynman Lectures on Physics Vol. I Ch. 43: Diffusion. 2021-02-04. feynmanlectures.caltech.edu.
  2. Web site: The Kinetic Theory of Gases . Department of Physics & Astronomy Hunter College . 16 May 2024.