On solute dispersion in an oscillatory magneto-hydrodynamics porous medium flow under the effect of heterogeneous and bulk chemical reaction

Abstract

It is well known to all of us that there is a shortage of pure drinking water across the globe. Different types of pollutants (metallic and non-metallic) mix with the water and they cause several diseases like cholera, typhoid, various kinds of skin diseases and even, it is found that these kinds of particles may cause skin cancer. In the current study, an analytical solution of a two-dimensional convection-diffusion equation is obtained using Mei's multi-scale homogenization technique to investigate the influences of homogeneous and heterogeneous reactions on dispersion phenomena of the solute in an oscillatory magneto-hydrodynamics porous medium flow. In the appearance of the applied transverse magnetic field and oscillatory pressure gradient, a mathematical model of magneto-hydrodynamics dispersion between two parallel plates is presented. The analytical expressions of Taylor dispersivity, longitudinal mean \& real concentration distributions, transverse concentration distribution and transverse uniformity rate of the concentration are obtained. Also, the effect of various flow parameters such as P\'eclet number, Hartmann number, Schmidt number, Darcy number, oscillatory Reynolds number, porous parameter, dispersion time, downstream and upstream locations, chemical heterogeneous boundary reaction and bulk reaction are discussed. How the transport phenomena of the solute display different natures with the various ranges of Darcy and Hartmann numbers with the aid of homogeneous and heterogeneous boundary reactions are highlighted. To show the effect of the absorption parameters on the transport coefficient, the third-order approximation of concentration is performed.

Multi-scale analysis of concentration distribution in unsteady Couette–Poiseuille flows through a porous channel

“…studying solute dispersion under the effect of heterogeneous and chemical bulk reaction (e.g. see Poddar et al [40]), surface reaction such as adsorption and desorption (e.g. see Jiang et al [45]).…”

“…With false(x′,y′false) Cartesian coordinate system, the velocity is denoted by boldV′=false(u′,v′false). The flow inside the porous channel is governed by the Brinkman–Navier–Stokes equation supported by the conservation of mass (incompressible fluid) given respectively by [39,40,49,50] right left right left right left right left right left right left3pt0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0emtrueρ(normal∂V'normal∂t+V'.normal∇V')=−∇p+μnormaleffnormal∇2boldV'−μKboldV',∇.boldV'=0,due to the incompressibility of the fluid. Here, ρ is the density, μ is the dynamic viscosity, μeff is the effective viscosity of the fluid inside the porous medium and K is the permeability of the porous medium which characterizes the ability of fluid flowing inside the pores.…”

“…With (x , y ) Cartesian coordinate system, the velocity is denoted by V = (u , v ). The flow inside the porous channel is governed by the Brinkman-Navier-Stokes equation supported by the conservation of mass (incompressible fluid) given respectively by [39,40,49,50]…”

“…Numerous fields of research and engineering, such as metallurgy, earth science and nuclear engineering, are involved in the study of the flow of an electrically conducting fluid through a porous media in the presence of a magnetic field [25,39]. Very recently, Poddar et al [40] studied a more complex model of solute transport process in a MHD porous medium with the aid of oscillatory pressure gradient under the influence of heterogeneous and bulk chemical reactions. It is noted by them that the dispersion coefficient due to purely time-dependent flow increases with the permeability of the medium.…”

“…Solute transport in liquid-filled porous medium flows offers some insights to understand the scientific and technological significance due its potential applications in engineering and biological situations, such as the movement of minerals (such as fertilizers) in soils, the transport of contaminants in soils, the movement of nutrients in bones, the intrusion of salt in fresh water in soils near ocean coasts, secondary recovery methods in oil reservoirs (where the injected fluid dissolves the reservoir's soil), the use of tracers in petroleum engineering, solute transport in the CNS, blood transport in impeded blood vessels and many more (see the studies by Goldsztein [34]; Bear [41]; Wu et al [28]; Dentz et al [42]; Sharp et al [37]; Jiang & Chen [43]; Roy et al [38]; Yang et al [44]; Poddar et al [40]; Jiang et al [45]). Because of the relevance of wetland flows with the porous media flows, it has also received attention in the field of wastewater treatment, ecological restoration, flood management, biodiversity protection and ecological remodelling [26][27][28][29].…”