scholarly journals Anomalous Solute Transport in a Cylindrical Two-Zone Medium with Fractal Structure

2020 ◽  
Vol 10 (15) ◽  
pp. 5349
Author(s):  
Bakhtiyor Khuzhayorov ◽  
Azizbek Usmonov ◽  
N.M.A. Nik Long ◽  
Bekzodjon Fayziev
Keyword(s):  
Porous Medium ◽  
Solute Transport ◽  
Fractional Derivatives ◽  
Fractal Structure ◽  
Solute Concentration ◽  
Fast Diffusion ◽  
High Permeability ◽  
Diffusion Term ◽  
Permeability Characteristics ◽  
Pressure Fields

In this paper, a problem of anomalous solute transport in a coaxial cylindrical two-zone porous medium with fractal structure is posed and numerically solved. The porous medium is studied in the form of cylinder with two parts: macropore—with high permeability characteristics in the central part and micropore—with low permeability around it. Anomalous solute transport is modeled by differential equations with a fractional derivative. The solute concentration and pressure fields are determined. Based on numerical results, the influence of the fractional derivatives order on the solute transport process is analysed. It was shown that with a decrease in the order of the derivatives in the diffusion term of the transport equation in the macropore leads to a “fast diffusion” in both zones. Characteristics of the solute transport in both zones mainly depend on the concentration distribution and other hydrodynamic parameters in the macropore.

Effect of adsorption, radioactive decay and fractal structure of matrix on solute transport in fracture

2020 ◽  
Vol 378 (2172) ◽  
pp. 20190283 ◽  
Author(s):  
Vladimir Chugunov ◽  
Sergei Fomin
Keyword(s):  
Porous Medium ◽  
Mass Transport ◽  
Fractional Derivatives ◽  
Fractal Structure ◽  
Radioactive Decay ◽  
Developed Countries ◽  
Porous Matrix ◽  
Solute Concentration ◽  
Radioactive Contaminant ◽  
Fractional Differential

Reservoir contamination by various contaminants including radioactive elements is an actual environmental problem for all developed countries. Analysis of mass transport in a complex environment shows that the conventional diffusion equation based on Fick's Law fails to model the anomalous character of the diffusive mass transport observed in the field and laboratory experiments. These complex processes can be modelled by non-local advection–diffusion equations with temporal and spatial fractional derivatives. In the present paper, fractional differential equations are used for modelling the transport of radioactive materials in a fracture surrounded by the porous matrix of fractal structure. A new form of fractional differential equation for modelling migration of the radioactive contaminant in the fracture is derived and justified. Solutions of particular boundary value problems for this equation were found by application of the Laplace transform. Through the use of fractional derivatives, the model accounts for contaminant exchange between fracture and surrounding porous matrix of fractal geometry. For the case of an arbitrary time-dependent source of radioactive contamination located at the inlet of the fracture, the exact solutions for solute concentration in the fracture and surrounding porous medium are obtained. Using the concept of a short memory, an approximate solution of the problem of radioactive contaminant transport along the fracture surrounded by the fractal type porous medium is also obtained and compared with the exact solution. This article is part of the theme issue ‘Advanced materials modelling via fractional calculus: challenges and perspectives’.

scholarly journals Solute Transport in the Element of Fractured Porous Medium with an Inhomogeneous Porous Block

Symmetry ◽  
2020 ◽  
Vol 12 (6) ◽  
pp. 1028
Author(s):  
Bakhtiyor Khuzhayorov ◽  
Jabbor Mustofoqulov ◽  
Gafurjan Ibragimov ◽  
Fadzilah Md Ali ◽  
Bekzodjon Fayziev
Keyword(s):  
Porous Medium ◽  
Solute Transport ◽  
Solute Concentration ◽  
Graphical Form ◽  
Asymmetric Distribution ◽  
Nonlinear Kinetics ◽  
Kinetics Of Adsorption ◽  
Fractured Porous Medium ◽  
Slowing Down ◽  
Porous Block

In this paper, the problem of solute transport in a fractured-porous medium taking into account the non-equilibrium adsorption kinetic is studied. The solute transport in fractured-porous medium consisting of two fractures and a porous block between them located in a symmetric form is considered. The problem is then solved numerically by using the finite difference method. Based on the numerical results, the solute concentration and adsorption fields in the fractures and porous blocks are shown in graphical form. The effect of adsorption on the solute transport in a fractured-porous medium is then analyzed. In the case of different parameters in two zones, asymmetric distribution of the solute concentration and adsorption is obtained. The nonlinear kinetics of adsorption leads to an increase in the adsorption effects, conversely slowing down the rate of the distribution of concentration of the solute in the fluid.

Analysis of two-dimensional solute transport through heterogeneous porous medium

2018 ◽  
Vol 2 (3) ◽  
Author(s):  
Atul Kumar ◽  
◽  
Lav Kush Kumar ◽  
Shireen Shireen ◽  
◽  
...  
Keyword(s):  
Porous Medium ◽  
Solute Transport ◽  
Two Dimensional ◽  
Heterogeneous Porous Medium

Effect of water content on solute transport in a porous medium containing reactive micro-aggregates

1998 ◽  
Vol 33 (1-2) ◽  
pp. 211-230 ◽  
Author(s):  
Claudia Fesch ◽  
Peter Lehmann ◽  
Stefan B. Haderlein ◽  
Christoph Hinz ◽  
René P. Schwarzenbach ◽  
...  
Keyword(s):  
Porous Medium ◽  
Solute Transport ◽  
Water Content ◽  
Effect Of Water

Novel Fluorescent Visualization Method to Characterize Transport Properties in Micro/Nano Heat Pipe Wick Structures

2009 ◽  
Author(s):  
Pramod Chamarthy ◽  
H. Peter J. de Bock ◽  
Boris Russ ◽  
Shakti Chauhan ◽  
Brian Rush ◽  
...  
Keyword(s):  
Heat Pipe ◽  
High Performance ◽  
Gravitational Force ◽  
Driving Forces ◽  
Electronics Cooling ◽  
Heat Pipes ◽  
High Permeability ◽  
Permeability Characteristics ◽  
Wick Structure ◽  
Initial Results

Heat pipes have been gaining a lot of popularity in electronics cooling applications due to their ease of operation, reliability, and high effective thermal conductivity. An important component of a heat pipe is the wick structure, which transports the condensate from condenser to evaporator. The design of wick structures is complicated by competing requirements to create high capillary driving forces and maintain high permeability. While generating large pore sizes will help achieve high permeability, it will significantly reduce the wick’s capillary performance. This study presents a novel experimental method to simultaneously measure capillary and permeability characteristics of the wick structures using fluorescent visualization. This technique will be used to study the effects of pore size and gravitational force on the flow-related properties of the wick structures. Initial results are presented on wick samples visually characterized from zero to nine g acceleration on a centrifuge. These results will provide a tool to understand the physics involved in transport through porous structures and help in the design of high performance heat pipes.

On the continuity of solutions of the equations of a porous medium and the fast diffusion with weighted and singular lower-order terms

2021 ◽  
Vol 18 (1) ◽  
pp. 104-139
Author(s):  
Yevhen Zozulia
Keyword(s):  
Porous Medium ◽  
Parabolic Equation ◽  
Harnack Inequality ◽  
Lower Order ◽  
Riesz Potential ◽  
Fast Diffusion ◽  
Right Hand ◽  
Continuity Of Solutions ◽  
The Right ◽  
Lower Order Terms

For the parabolic equation $$ \ v\left(x \right)u_{t} -{div({\omega(x)u^{m-1}}} \nabla u) = f(x,t)\: ,\; u\geq{0}\:,\; m\neq{1} $$ we prove the continuity and the Harnack inequality for generalized k solutions, by using the weighted Riesz potential on the right-hand side of the equation.

scholarly journals Flattening of Diluted Species Profile via Passive Geometry in a Microfluidic Device

Micromachines ◽  
2019 ◽  
Vol 10 (12) ◽  
pp. 839
Author(s):  
Michael Miles ◽  
Biddut Bhattacharjee ◽  
Nakul Sridhar ◽  
Apresio Kefin Fajrial ◽  
Kerri Ball ◽  
...  
Keyword(s):  
Solute Transport ◽  
Concentration Profile ◽  
Microfluidic Channel ◽  
Region Of Interest ◽  
Solute Concentration ◽  
Cross Sectional ◽  
Driven Systems ◽  
Solute Profile ◽  
Dynamics Simulations ◽  
Pressure Driven

In recent years, microfluidic devices have become an important tool for use in lab-on-a-chip processes, including drug screening and delivery, bio-chemical reactions, sample preparation and analysis, chemotaxis, and separations. In many such processes, a flat cross-sectional concentration profile with uniform flow velocity across the channel is desired to achieve controlled and precise solute transport. This is often accommodated by the use of electroosmotic flow, however, it is not an ideal for many applications, particularly biomicrofluidics. Meanwhile, pressure-driven systems generally exhibit a parabolic cross-sectional concentration profile through a channel. We draw inspiration from finite element fluid dynamics simulations to design and fabricate a practical solution to achieving a flat solute concentration profile in a two-dimensional (2D) microfluidic channel. The channel possesses geometric features to passively flatten the solute profile before entering the defined region of interest in the microfluidic channel. An obviously flat solute profile across the channel is demonstrated in both simulation and experiment. This technology readily lends itself to many microfluidic applications which require controlled solute transport in pressure driven systems.

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