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Analytical Solution of Nonlinear Diffusion Equation Describing Interdiffusion of Gases

100%
Janavičius A., Jurgaitis D.
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EN
The diffusion is the result of Brownian movement and occurs with a finite velocity. We consider the nonlinear diffusion equation, with diffusion coefficient directly proportional to the impurities concentration. In this case of diffusion from the constant source, the maximum displacements of diffusing particles are proportional to the square root of diffusion time. This result coincides with Brownian movement theory. The obtained analytically solutions were successfully applied for describing the diffusion and superdiffusion experiments' in solids. After theoretical consideration of application of this equation for diffusion in gases, we are investigating here the binary nonlinear diffusion in gases. We obtained the nonlinear interdiffusion equation, for the spherical symmetric case, and presented the approximate analytical solutions.
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The Nonlinear Diffusion Equation Describing Spread of Impurities of High Density

81%
Janavičius A., Lūža G., Jurgaitis D.
Acta Physica Polonica A
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2004
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vol. 105
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issue 5
475-483
EN
The nonlinear diffusion equation is derived by taking into account the local variations in the solvent density, within a mechanism of diffusion driven by random particle collisions. Analytical solutions for the case of spherical-symmetric nonlinear diffusion equation for spread of impurities in gas and solids are obtained and discussed. In this case, the solutions of the nonlinear diffusion equation are similar to solutions of Bernoulli equation. We note that the obtained solutions can be used to describe the shapes of impurity gas of high concentration or smoke clouds.
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