One-dimensional diffusion with the diffusion coefficient a linear function of concentration

1952 ◽  
Vol 48 ◽  
pp. 887 ◽  
Author(s):  
R. H. Stokes
Keyword(s):  
Diffusion Coefficient ◽  
Linear Function ◽  
One Dimensional ◽  
Dimensional Diffusion

scholarly journals Role of Time Relaxation in a One-Dimensional Diffusion-Advection Model of Water and Salt Transport

2015 ◽  
Vol 2015 ◽  
pp. 1-6 ◽  
Author(s):  
Igor Medved’ ◽  
Robert Černý
Keyword(s):  
Diffusion Coefficient ◽  
Structural Damage ◽  
Building Materials ◽  
Chloride Transport ◽  
Salt Transport ◽  
One Dimensional ◽  
Advection Diffusion ◽  
Dimensional Diffusion ◽  
Lime Plaster

The transport of salt, necessarily coupled with the transport of water, through porous building materials may heavily limit their durability due to possible deterioration and structural damage. Usually, the binding of salt to the pore walls is assumed to occur instantly, as soon as the salt is transported by water to a given position. We consider the advection-diffusion model of the transport and generalize it to include possible delays in the binding. Applying the Boltzmann-Matano method, we calculate the diffusion coefficient of the salt in dependence on the salt concentration and show that it increases with the rate of binding. We apply our results to an example of the chloride transport in a lime plaster.

Certain Problems with the Application of Stochastic Diffusion Processes for the Description of Chemical Engineering Phenomena. Numerical Simulation of One-Dimensional Diffusion Process

1996 ◽  
Vol 61 (4) ◽  
pp. 512-535 ◽  
Author(s):  
Pavel Hasal ◽  
Vladimír Kudrna
Keyword(s):  
Numerical Simulation ◽  
Diffusion Coefficient ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Chemical Engineering ◽  
Diffusion Processes ◽  
Stochastic Integral ◽  
Random Motion ◽  
One Dimensional ◽  
Dimensional Diffusion

Some problems are analyzed arising when a numerical simulation of a random motion of a large ensemble of diffusing particles is used to approximate the solution of a one-dimensional diffusion equation. The particle motion is described by means of a stochastic differential equation. The problems emerging especially when the diffusion coefficient is a function of spatial coordinate are discussed. The possibility of simulation of various kinds of stochastic integral is demonstrated. It is shown that the application of standard numerical procedures commonly adopted for ordinary differential equations may lead to erroneous results when used for solution of stochastic differential equations. General conclusions are verified by numerical solution of three stochastic differential equations with different forms of the diffusion coefficient.

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