Description of segregation in a horizontal drum mixer by use of the diffusion equation

An attempt has been made to describe the axial segregation of solid particles of two dimensions in a horizontal drum mixer. For this purpose the Kolmogorov's forward diffusion equation with variable diffusion coefficient and zero drift velocity was used. For the case of "pure" segregation this approach has given good results.

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Analysis of the long-time asymptotic behaviour of the solution of a two-dimensional reaction-diffusion equation

International Journal of Applied Mathematical Research ◽

10.14419/ijamr.v4i2.4426 ◽

2015 ◽

Vol 4 (2) ◽

pp. 332

Author(s):

Joel Ndam

Keyword(s):

Diffusion Coefficient ◽

Diffusion Equation ◽

Asymptotic Behaviour ◽

Reaction Diffusion ◽

Two Dimensions ◽

Reaction Diffusion Equation ◽

Two Dimensional ◽

Variable Diffusion Coefficient ◽

Long Time ◽

Variable Diffusion

<p>A reaction-diffusion equation in two dimensions is considered. The long-time asymptotic behaviour of the solution of this equation is examined in terms of uniform diffusion as well as density-dependent diffusion. The results show that in both cases, the solution attains a steady state, but does so more slowly with the variable diffusion coefficient when its magnitude d<1.</p>

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Stochastic Modelling of Particle Segregation in a Horizontal Drum Mixer

Collection of Czechoslovak Chemical Communications ◽

10.1135/cccc19922100 ◽

1992 ◽

Vol 57 (10) ◽

pp. 2100-2112 ◽

Cited By ~ 4

Author(s):

Vladimír Kudrna ◽

Pavel Hasal ◽

Andrzej Rochowiecki

Keyword(s):

Differential Equation ◽

Diffusion Coefficient ◽

Stochastic Model ◽

Diffusion Process ◽

Stochastic Modelling ◽

Solid Particles ◽

Kolmogorov Equation ◽

Particle Segregation ◽

Drum Mixer ◽

Horizontal Drum

A process of segregation of two distinct fractions of solid particles in a rotating horizontal drum mixer was described by stochastic model assuming the segregation to be a diffusion process with varying diffusion coefficient. The model is based on description of motion of particles inside the mixer by means of a stochastic differential equation. Results of stochastic modelling were compared to the solution of the corresponding Kolmogorov equation and to results of earlier carried out experiments.

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Chebyshev collocation method for the variable-order fractional diffusion equation with a variable diffusion coefficient

10.22541/au.161148571.13930687/v1 ◽

2021 ◽

Author(s):

Rupali GUPTA ◽

Sushil Kumar

Keyword(s):

Diffusion Coefficient ◽

Diffusion Equation ◽

Fractional Power ◽

Pseudospectral Method ◽

Fractional Diffusion ◽

Fractional Diffusion Equation ◽

Variable Order ◽

Maximum Absolute Error ◽

Variable Diffusion Coefficient ◽

Variable Diffusion

In this paper, we study the space-time variable-order fractional diffusion equation with a variable diffusion coefficient. The fractional derivatives of variable-orders are considered in the Caputo sense. We propose a numerically efficient pseudospectral method with Chebyshev polynomial as an orthogonal basis function. Also, we examine the error analysis of the given numerical approach. A variation on the maximum absolute error with the different variable orders in space and time are studied. Some illustrative examples are presented with different boundary conditions, e.g., Dirichlet, mixed, and non-local. The applicability of the method is also tested with the problem that has fractional power in solution. The results obtained from the proposed method prove the efficacy and reliability of the method.

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