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Gaseous diffusion as a correlated random walk.

Santos Bravo Yuste1, Rubén Gómez González1, Vicente Garzó1

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Summary
This summary is machine-generated.

This study introduces a new method to calculate molecular diffusion using the mean-square free path and mean persistence ratio. The improved diffusion formula shows excellent agreement with simulations, especially for lighter molecules.

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Area of Science:

  • Statistical Mechanics
  • Kinetic Theory of Gases

Background:

  • Calculating molecular diffusion is crucial for understanding gas behavior.
  • Existing methods like Sonine approximations have limitations, particularly with varying molecular masses.

Purpose of the Study:

  • To develop a more accurate method for determining the diffusion coefficient.
  • To simplify the calculation of mean-square displacement per collision.

Main Methods:

  • Deriving a series expansion for mean-square displacement per collision.
  • Utilizing the mean persistence ratio as a key parameter.
  • Comparing theoretical results with direct simulation Monte Carlo (DSMC) solutions of the Boltzmann equation.

Main Results:

  • The ratio of consecutive terms in the series approximates the mean persistence ratio.
  • An improved diffusion coefficient formula was developed.
  • The improved formula shows excellent agreement with DSMC simulations across various mass ratios.

Conclusions:

  • The mean-square free path and mean persistence ratio are sufficient to determine diffusion coefficients.
  • The new diffusion formula offers improved accuracy, outperforming Sonine approximations for light intruder molecules.