Theoretical description of molecular permeation via surface diffusion through graphene nanopores

2021 ◽  
Author(s):  
Chengzhen Sun ◽  
Kailin Luo ◽  
Runfeng Zhou ◽  
Bofeng Bai
Keyword(s):  
Theoretical Model ◽  
Diffusion Equation ◽  
Surface Diffusion ◽  
Theoretical Description ◽  
Two Dimensional ◽  
Fick’S Law ◽  
Fick's Law

We establish a theoretical model to describe the surface molecular permeation through two-dimensional graphene nanopores based on the surface diffusion equation and Fick’s law. The model is established by considering...

scholarly journals Comparisons of Two Types of Particle Tracking Models Including the Effects of Vertical Velocity Shear

Water ◽  
2020 ◽  
Vol 12 (12) ◽  
pp. 3535
Author(s):  
Inhwan Park ◽  
Jaehyun Shin ◽  
Hoje Seong ◽  
Dong Sop Rhee
Keyword(s):  
Particle Tracking ◽  
Analytic Solution ◽  
Initial Period ◽  
Computation Method ◽  
Two Dimensional ◽  
Fick’S Law ◽  
Dispersion Process ◽  
Fick's Law ◽  
Shear Dispersion ◽  
Tracking Model

In this study, two types of particle tracking models were presented to investigate the applicability in the two-dimensional solute mixing simulations. The conventional particle tracking model, denoted as PTM, was developed based on Fick’s law, which adopted the dispersion coefficient to calculate the random displacements. The other model is the particle dispersion model (PDM), which computes the shear dispersion process by dividing into two computation procedures as the shear translation and the vertical mixing. The PTM and the PDM included the effects of vertical profiles of velocity in the computation of dispersion coefficients and the shear translation step, respectively. The main difference between the two models is whether the shear dispersion process is reproduced using Fick’s law or the direct computation method. These differences were clearly revealed by comparing with the analytic solution of the advection-dispersion equation. The concentration curve resulting from the PTM shows the Gaussian curves, which were well-fitted with the analytic solution in both initial and Taylor periods. Meanwhile, the PDM presented skewed curves in the initial period and gradually turned to the symmetric shape in the Taylor period. The inherent differences of the two particle tracking models were scrutinized against the two-dimensional tracer test results, which show the non-Fickian mixing properties. The comparisons of concentration–time curves reveal that the PDM reproduced a more accurate shape of the curves than the results by the PTM by demonstrating skewed concentration curves.

The nonexistence of the linear diffusion equation beyond Fick's law

Physica ◽  
1974 ◽  
Vol 75 (1) ◽  
pp. 1-36 ◽  
Author(s):  
I.M. De Schepper ◽  
H. Van Beyeren ◽  
M.H. Ernst
Keyword(s):  
Diffusion Equation ◽  
Fick’S Law ◽  
Linear Diffusion ◽  
Fick's Law

scholarly journals Numerical Analysis WSGD Scheme for One- and Two-Dimensional Distributed Order Fractional Reaction–Diffusion Equation with Collocation Method via Fractional B-Spline

2021 ◽  
Vol 7 (2) ◽  
Author(s):  
Mohammad Ramezani
Keyword(s):  
Diffusion Equation ◽  
Collocation Method ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equation ◽  
Two Dimensional ◽  
Algebraic Equations ◽  
B Spline ◽  
Computational Work ◽  
Distributed Order ◽  
Fractional Reaction

AbstractThe main propose of this paper is presenting an efficient numerical scheme to solve WSGD scheme for one- and two-dimensional distributed order fractional reaction–diffusion equation. The proposed method is based on fractional B-spline basics in collocation method which involve Caputo-type fractional derivatives for $$0 < \alpha < 1$$ 0 < α < 1 . The most significant privilege of proposed method is efficient and quite accurate and it requires relatively less computational work. The solution of consideration problem is transmute to the solution of the linear system of algebraic equations which can be solved by a suitable numerical method. The finally, several numerical WSGD Scheme for one- and two-dimensional distributed order fractional reaction–diffusion equation.

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