scholarly journals One-dimensional diffusion with the diffusion coefficient a linear function of concentration: reduction to an equation of the first order

1957 ◽  
Vol 15 (3) ◽  
pp. 298-303
Author(s):  
D. H. Parsons
Keyword(s):  
Diffusion Coefficient ◽  
Linear Function ◽  
One Dimensional ◽  
First Order ◽  
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.

Time of persistence of a particle in selected state during reversible first-order conversion. Application to crystal growth and dissolution

1981 ◽  
Vol 46 (5) ◽  
pp. 1217-1221 ◽  
Author(s):  
Milan Šolc ◽  
Jiří Hostomský
Keyword(s):  
Diffusion Coefficient ◽  
Crystal Growth ◽  
Rate Constants ◽  
Probability Model ◽  
Planck Equation ◽  
One Dimensional ◽  
First Order ◽  
Approximate Form ◽  
Probability Description ◽  
Dissolution Rate Constants

The distribution of the total time of persistence of a particle in a state A was derived both in an exact and an approximate form on the basis of a probability model of the conversion A ##e B. The result was applied to the probability description of a change in size of one-dimensional crystals in a double crystallizer. The time change of the distribution of the crystal sizes can be described by the Fokker-Planck equation for diffusion with a diffusion coefficient proportional to the square of the sum of values of the growth and dissolution rate constants.

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.

Zur Theorie der Gegenstromelektrolyse

1970 ◽  
Vol 25 (7) ◽  
pp. 1007-1017
Author(s):  
H. Gaus
Keyword(s):  
Aqueous Solution ◽  
Diffusion Coefficient ◽  
Dimensional Space ◽  
One Dimensional ◽  
First Order ◽  
Space Coordinate ◽  
The One ◽  
Space Dependence ◽  
Common Anion ◽  
First Order Differential Equations

In the case of stationary countercurrent electrolysis the one dimensional space dependence of the different concentrations is governed by a system of nonlinear first order differential equations. Here one takes into account the dependence of the electric field on the concentrations. One considers a mixture of completely dissociating salts with a common anion solved in an aqueous solution of the completely dissociating acid with the same anion. The equations are solved rigorously both in the homogeneous and the inhomogeneous case. One gets the concentrations and the space coordinate explicitly as a function of a parameter w, which is the electric potential divided by the diffusion coefficient. For infinitely long tubes the Kohlrausch-condition remains valid also in regions, where the profiles of the concentrations are influenced by diffusional transport. The results are applied to a process investigated by other authors

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