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.

Fast Inverse-Analysis Calculation of Diffusion Coefficient for Salt Transport in Porous Building Materials

2015 ◽  
Vol 1126 ◽  
pp. 117-122 ◽  
Author(s):  
Igor Medveď ◽  
Zbyšek Pavlík ◽  
Milena Pavlíková ◽  
Robert Černý
Keyword(s):  
Diffusion Coefficient ◽  
Inverse Analysis ◽  
Analytical Approach ◽  
Building Materials ◽  
Salt Transport ◽  
Porous Building Materials ◽  
Advection Diffusion ◽  
Analysis Calculation ◽  
Salt Diffusion

An analytical approach to the determination of a varying salt diffusion coefficient is discussed. It is argued that the approach is fast and reliable and can be very convenient in various civil engineering applications dealing with the transport of salts in porous building materials. The advection-diffusion model of Bear and Bachmat is used to describe the salt transport, and the Bolztmann-Matano inverse analysis is applied to calculate the salt diffusion coefficient. Possible extensions to other models of transport are pointed out. The results are applied to a sandstone from the Msene quarry, Czech Republic.

scholarly journals Mechanics of peristaltic locomotion and role of anchoring

2011 ◽  
Vol 9 (67) ◽  
pp. 222-233 ◽  
Author(s):  
Yoshimi Tanaka ◽  
Kentaro Ito ◽  
Toshiyuki Nakagaki ◽  
Ryo Kobayashi
Keyword(s):  
Source Term ◽  
Biological Action ◽  
The Body ◽  
Directional Migration ◽  
Flexible Bodies ◽  
One Dimensional ◽  
Dimensional Diffusion ◽  
Time Space ◽  
Locomotion Speed

Limbless crawling is a fundamental form of biological locomotion adopted by a wide variety of species, including the amoeba, earthworm and snake. An interesting question from a biomechanics perspective is how limbless crawlers control their flexible bodies in order to realize directional migration. In this paper, we discuss the simple but instructive problem of peristalsis-like locomotion driven by elongation–contraction waves that propagate along the body axis, a process frequently observed in slender species such as the earthworm. We show that the basic equation describing this type of locomotion is a linear, one-dimensional diffusion equation with a time–space-dependent diffusion coefficient and a source term, both of which express the biological action that drives the locomotion. A perturbation analysis of the equation reveals that adequate control of friction with the substrate on which locomotion occurs is indispensable in order to translate the internal motion (propagation of the elongation–contraction wave) into directional migration. Both the locomotion speed and its direction (relative to the wave propagation) can be changed by the control of friction. The biological relevance of this mechanism is discussed.

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.

COMMENSURABILITY EFFECTS ON DIFFUSION PROCESS IN STEPPED STRUCTURES

2011 ◽  
Vol 25 (21) ◽  
pp. 1749-1760 ◽  
Author(s):  
Y. LACHTIOUI ◽  
M. MAZROUI ◽  
Y. BOUGHALEB
Keyword(s):  
Diffusion Coefficient ◽  
Diffusion Process ◽  
Ground State ◽  
Nearest Neighbor ◽  
Diffusion Rate ◽  
Dimensional System ◽  
One Dimensional ◽  
Substrate Potential ◽  
Numerical Studies

This study deals with the investigation of diffusion process of one-dimensional system with steps for adsorbates interacting via the nearest-neighbor harmonic forces. The results are obtained from numerical studies, utilizing the method of stochastic Langevin dynamics. To study commensurability effects and the role of steps in the behavior of the diffusing particles, we have computed the diffusion coefficient for large concentrations and several interaction strengths. Our numerical results show that the diffusive behavior is reduced for commensurate structure case when the ground state has only one particle per one period of the substrate potential and enhanced for incommensurate density. Furthermore, the dynamic is qualitatively similar to that obtained in the case of no steps but with a clear reduction of the diffusion rate. Implications of these findings are discussed.

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