Abstract
<p>The aim of this paper is to present some numerical simulations for different values of parameters and to compare their influence for a reaction-diffusion model which describes chemotaxis phenomena in a bioremediation process of a polluted environment (soil or water). We set a model of Keller-Segel type, and we consider for this model a small influence of the degradation rate of pollutant () and its diffusion coefficient (). For the numerical simulations, we used the package COMSOL Multiphysics v3.5a, working with the finite element method. </p>
Highlights
Chemotaxis is a biological phenomenon describing the change of motion when a population of individuals reacts in response to an external stimulus spread in the environment by another population or substance
In the case of soil bioremediation it must be satisfied some conditions: the bacteria must exist in this environment and the soil must have suitable nutrients and a convenient temperature to sustain the growth of bacteria and its activity
A mathematical reaction-diffusion model of chemotaxis is expressed by a system of partial differential equations for the movement of bacteria whose density is denoted by b in response to chemical gradients emitted by the pollutant c [10]
Summary
Chemotaxis is a biological phenomenon describing the change of motion when a population of individuals (in particular, bacteria that have a density denoted by b ) reacts in response to an external stimulus spread in the environment by another population or substance (chemoattractant c ). In which besides the pollutant, flow other fluids influencing pollutant and bacteria concentrations and the porosity of soil can be found in [6,7,8]. In order to make the model be as real, we will consider that the kinetic term and the diffusion coefficient of the pollutant c have a weak influence on the flow. This means that the rate of degradation of the chemoattractant is slow and it diffuses very little (as in the case of oil) [9]. The main aim of this work is to make some numerical simulations for this model of reaction-diffusion with chemotaxis and to compare the influence of different parameter values on the systems
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