scholarly journals Transport of Microplastic Particles in Saturated Porous Media

Water ◽  
2019 ◽  
Vol 11 (12) ◽  
pp. 2474 ◽  
Author(s):  
Xianxian Chu ◽  
Tiantian Li ◽  
Zhen Li ◽  
An Yan ◽  
Chongyang Shen
Keyword(s):  
Porous Media ◽  
Glass Bead ◽  
Fate And Transport ◽  
Breakthrough Curves ◽  
Polystyrene Latex ◽  
Order Kinetic ◽  
Saturated Porous Media ◽  
Convection Diffusion ◽  
Convection Diffusion Equation ◽  
First Order

This study used polystyrene latex colloids as model microplastic particles (MPs) and systematically investigated their retention and transport in glass bead-packed columns. Different pore volumes (PVs) of MP influent suspension were first injected into the columns at different ionic strengths (ISs). The breakthrough curves (BTCs) were obtained by measuring the MP concentrations of the effluents. Column dissection was then implemented to obtain retention profiles (RPs) of the MPs by measuring the concentration of attached MPs at different column depths. The results showed that the variation in the concentrations of retained MPs with depth changed from monotonic to non-monotonic with the increase in the PV of the injected influent suspension and solution IS. The non-monotonic retention was attributed to blocking of MPs and transfer of these colloids among collectors in the down-gradient direction. The BTCs were well simulated by the convection-diffusion equation including two types of first-order kinetic deposition (i.e., reversible and irreversible attachment). However, this model could not well simulate the non-monotonic retention profiles due to the fact that the transfer of colloids among collectors was not considered. The results in this study are critical to developing models to simulate the fate and transport of MPs in porous media such as soil.

Stability estimate for an inverse problem of the convection-diffusion equation

2020 ◽  
Vol 28 (1) ◽  
pp. 71-92
Author(s):  
Mourad Bellassoued ◽  
Imen Rassas
Keyword(s):  
Inverse Problem ◽  
Diffusion Equation ◽  
Scalar Potential ◽  
Stability Estimate ◽  
Inverse Boundary ◽  
Convection Diffusion ◽  
Convection Diffusion Equation ◽  
First Order ◽  
Order Coefficient ◽  
Dirichlet To Neumann Map

AbstractWe consider the inverse boundary value problem for the dynamical steady-state convection-diffusion equation. We prove that the first-order coefficient and the scalar potential are uniquely determined by the Dirichlet-to-Neumann map. More precisely, we show in dimension {n\geq 3} a log-type stability estimate for the inverse problem under consideration. The method is based on reducing our problem to an auxiliary inverse problem and the construction of complex geometrical optics solutions of this problem.

Approximation of 3D convection diffusion equation using DQM based on modified cubic trigonometric B-splines

2020 ◽  
pp. 1-10
Author(s):  
Mohammad Tamsir ◽  
Neeraj Dhiman ◽  
F.S. Gill ◽  
Robin
Keyword(s):  
Diffusion Equation ◽  
Numerical Solutions ◽  
Basis Functions ◽  
B Spline ◽  
Convection Diffusion ◽  
B Splines ◽  
Convection Diffusion Equation ◽  
First Order ◽  
The Stability ◽  
Derivatives Of

This paper presents an approximate solution of 3D convection diffusion equation (CDE) using DQM based on modified cubic trigonometric B-spline (CTB) basis functions. The DQM based on CTB basis functions are used to integrate the derivatives of space variables which transformed the CDE into the system of first order ODEs. The resultant system of ODEs is solved using SSPRK (5,4) method. The solutions are approximated numerically and also presented graphically. The accuracy and efficiency of the method is validated by comparing the solutions with existing numerical solutions. The stability analysis of the method is also carried out.

Temperature and Chemistry Effects in Porous-Media Electrokinetics

1996 ◽  
Vol 463 ◽  
Author(s):  
David B. Pengra ◽  
Po-Zen Wong
Keyword(s):  
Porous Media ◽  
Fluid Flow ◽  
Electric Fields ◽  
Glass Bead ◽  
Pore Surface ◽  
Saturated Porous Media ◽  
Electrokinetic Phenomena ◽  
Sample Group ◽  
Natural Rock ◽  
Brine Chemistry

ABSTRACTElectrokinetic phenomena in brine-saturated porous media, such as electroosmosis (fluid-flow induced by applied electric fields) and streaming current (the complementary process) depend on the density of ions adsorbed on the pore surface and the characteristic thickness of the diffuse space-charge layer λ. These, in turn, depend on brine chemistry, ambient temperature and possibly other parameters. We report on a series of measurements of natural rock and synthetic glass-bead samples: for one sample group, we varied the temperature over 0–50 ° C; for another, we changed the brine cation species. We find that the electrokinetic coefficients depend only weakly on temperature; this is shown to follow from the expected trends in λ, η, and σ. The chemistry dependence follows qualitatively but not quantitatively the predictions of the Debye-Hiickel approximation.

Difference Schemes on Uniform Grids for an Initial-Boundary Value Problem for a Singularly Perturbed Parabolic Convection-Diffusion Equation

2020 ◽  
Vol 20 (4) ◽  
pp. 709-715 ◽  
Author(s):  
Grigorii I. Shishkin ◽  
Lidia P. Shishkina
Keyword(s):  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Maximum Norm ◽  
Order Accuracy ◽  
Convection Diffusion ◽  
Convection Diffusion Equation ◽  
First Order ◽  
Grid Approximation ◽  
Uniform Grids ◽  
Initial Boundary Value

AbstractThe convergence of difference schemes on uniform grids for an initial-boundary value problem for a singularly perturbed parabolic convection-diffusion equation is studied; the highest x-derivative in the equation is multiplied by a perturbation parameter ε taking arbitrary values in the interval {(0,1]}. For small ε, the problem involves a boundary layer of width {\mathcal{O}(\varepsilon)}, where the solution changes by a finite value, while its derivative grows unboundedly as ε tends to zero. We construct a standard difference scheme on uniform meshes based on the classical monotone grid approximation (upwind approximation of the first-order derivatives). Using a priori estimates, we show that such a scheme converges as {\{\varepsilon N\},N_{0}\to\infty} in the maximum norm with first-order accuracy in {\{\varepsilon N\}} and {N_{0}}; as {N,N_{0}\to\infty}, the convergence is conditional with respect toN, where {N+1} and {N_{0}+1} are the numbers of mesh points in x and t, respectively. We develop an improved difference scheme on uniform meshes using the grid approximation of the first x-derivative in the convective term by the central difference operator under the condition{h\leq m\varepsilon}, which ensures the monotonicity of the scheme; here m is some rather small positive constant. It is proved that this scheme converges in the maximum norm at a rate of {\mathcal{O}(\varepsilon^{-2}N^{-2}+N^{-1}_{0})}. We compare the convergence rate of the developed scheme with the known Samarskii scheme for a regular problem. It is found that the improved scheme (for {\varepsilon=1}), as well as the Samarskii scheme, converges in the maximum norm with second-order accuracy inx and first-order accuracy int.

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