• Economic and Environmental Geology
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• v.53 no.1
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• pp.99-110
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• 2020

It is a global trend to consider contaminated low-permeability zones as one of the primary management targets for the remediation of DNAPL contaminated sites. In addition, studies on the persistence caused by back diffusion of DNAPLs from low-permeability zones have been actively conducted worldwide. On the other hand, the studies for domestic groundwater contamination with the low-permeability zones are insufficient. Therefore, this study introduces the forward and back diffusions of DNAPL through low-permeability zones and suggests the importance of them by reviewing representative previous studies, especially on back diffusion and plume persistence. We proposed six diffusion scenarios and analytical solutions based on various boundary conditions of low-permeability zones. FI (forward diffusion into infinite domain) and BI (back diffusion form infinite domain) scenarios illustrate forward and back diffusion in which the depths of a low-permeability layer are assumed to be infinite. FFN (forward diffusion into finite domain with no flux boundary) and BFN (back diffusion from finite domain with no flux boundary) scenarios describe forward and back diffusion for a finite domain of a low-permeability layer with no flux boundary at the bottom. When the bottom of a low-permeability layer is considered as flux boundary, forward and back diffusion scenarios correspond to FFF (forward diffusion into finite domain with flux boundary) and BFF (back diffusion from finite domain with flux boundary). The scenarios and analytical solutions in this study may contribute to the determination of an efficient remediation method based on site characteristics such as a thickness of low-permeability zones or duration of contamination exposure.

• Journal of computational fluids engineering
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• v.11 no.1 s.32
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• pp.8-15
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• 2006

The existing approximations of diffusion flux in unstructured cell-centered finite volume methods are examined in detail with each other and clarified to have indefinite expressions in several respects. A new numerical approximation of diffusion flux at cell face center is then proposed, which is second-order accurate even on irregular grids and may be easily implemented in CFD code using cell-centered finite volume method with unstructured grids composed of arbitrary convex polyhedral shape.

• Membrane and Water Treatment
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• v.8 no.5
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• pp.411-421
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• 2017

Forward osmosis (FO) is an emerging technology which can possibly make the desalination process more cost and energy efficient. One of the major factors impeding its growth is the lack of an appropriate draw solute. The present study deals with the identification of potential draw solutes, and rank them. The comparison was carried out among ten draw solutes on the basis of four main parameters namely; water flux, reverse salt diffusion, flux recovery and cost. Each draw solute was given three 24 hour runs; corresponding to three different concentrations; and their flux and reverse salt diffusion values were calculated. A fresh membrane was used every time except for the fourth time which was the flux recovery experiment conducted for the lowest concentration and the change of flux and reverse salt diffusion values from the initial run was noted. The organic solutes inspected were urea and tartaric acid which showed appreciable values in other parameters viz. reverse salt diffusion, flux recovery and cost although they generated a lower flux. They ranked 5th and 8th respectively. All the experimented draw solutes were ranked based on their values corresponding to each of the four main parameters chosen for comparison and Ammonium sulfate was found to be the best draw solute.

• 한국전기화학회:학술대회논문집
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• 2003.04a
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• pp.56-56
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• 2003

• Journal of Korean Ophthalmic Optics Society
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• v.13 no.3
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• pp.35-43
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• 2008

Purpose: This review article was written to investigate how the various factors, such as lacrimal thickness, CL's thickness and Dk, affects the influx of $O_2$ diffusion into the cornea. Methods: A mathematical model was proposed to analyze the oxygen diffusion reaching the cornea through the tear layers and contact lens based on Fick's law and the principle of continuity of the diffusion flux through the each layers. Results: The model predicts how the parameters such as the thickness of tear layer on the cornea, both the Dk and thickness of contact lenses etc., affect the oxygen tension at cornea and oxygen flux entering the cornea. Conclusions: It is found that either too flat or too tightly fitted contact lenses can cause the oxygen deficiency at/inside the periphery of the cornea because of the reduction of oxygen flux resulted from too thickened tear layer.

• Nuclear Engineering and Technology
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• v.45 no.6
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• pp.707-720
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• 2013

We analyze piecewise homogenization with flux-weighted cross sections and preservation of averaged currents at the boundary of the homogenized domain. Introduction of a set of flux discontinuity ratios (FDR) that preserve reference interface currents leads to preservation of averaged region reaction rates and fluxes. We consider the class of numerical discretizations with one degree of freedom per volume and per surface and prove that when the homogenization and computing meshes are equal there is a unique solution for the FDRs which exactly preserve interface currents. For diffusion submeshing we introduce a Jacobian-Free Newton-Krylov method and for all cases considered obtain an 'exact' numerical solution (eight digits for the interface currents). The homogenization is completed by extending the familiar full assembly homogenization via flux discontinuity factors to the sides of regions laying on the boundary of the piecewise homogenized domain. Finally, for the familiar nodal discretization we numerically find that the FDRs obtained with no submesh (nearly at no cost) can be effectively used for whole-core diffusion calculations with submesh. This is not the case, however, for cell-centered finite differences.

• 제어로봇시스템학회:학술대회논문집
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• 1994.10a
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• pp.747-752
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• 1994

Ussing's flux ratio theorem (1978) reflects a reciprocal relationship behavior between the unidirectional fluxes in asymmetric steady diffusion-convection in a membrane slab. This surprising result has led to many subsequent studies in a wide range of applications, in particular involving linear models of time dependent problems in biology and physiology. Ussing's theorem and its extensions are inherently linear in character. It is of considerable interest to ask to what extent these results apply, if at all, in situations involving, for example, nonlinear reaction. A physiologically interesting situation has been considered by Weisiger et at. (1989, 1991, 1992) and by McNabb et al. (1990, 1991) who studied the role of albumin in the transport of ligands across aqueous diffusion barriers in a liver membrane slab. The results are that there exist reciprocal relationships between unidirectional fluxes in the steady state, although albumin is chemically interacting in a nonlinear way of the diffusion processes. However, the results do not hold in general at early times. Since this type of study first started, it has been speculated about when and how the Ussing's flux ratio theorem fails in a general diffusion-convection-reaction system. In this paper we discuss the validity of Ussing-type theorems in time-dependent situations, and consider the limiting time behavior of a general nonlinear diffusion system with interaction.

• Korean Journal of Pharmacognosy
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• v.49 no.2
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• pp.165-171
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• 2018

Artemisiae Capillaris Herba is a dried aerial part of Asteraceae capillaris Thunb.(Compositae), which has been used in Korean traditional medicine for the treatment of various diseases. It has a variety of pharmacological activities and has been evaluated for potential as an active ingredient in cosmeceutical products. In the cosmetics industry, animal experiments is besides the major concern of ethics, there are few more disadvantages of animal experimentation like demand of skilled manpower, time consuming protocols and high cost. Therefore, various alternatives to animal experiments have been proposed. The purpose of this study was to investigate the skin permeation characteristics of chlorogenic acid and dimethyleculetin, which are constituent of Artemisiae Capillaris Herba by using Franz diffusion cell. As a result, skin permeability was characterized by flux(penetration rates) and $K_p$(permeability coefficient) value, chlorogenic acid had lower flux and $K_p$ than dimethylesculetin. According to the definitions of Marzulli, chlorogenic acid and dimethylesculetin would be classified as 'Moderate' and 'Very fast' respectively. In conclusion, skin permeation characteristics of chlorogenic acid and dimethylesculetin were confirmed through Franz diffusion cell, and suggests the direction of alternative method for skin permeation of natural compounds.

• Proceedings of the Membrane Society of Korea Conference
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• 2008.05a
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• pp.33-47
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• 2008

Non-equilibrium (irreversible) themodynamics is used to investigate colloidal back-diffusion during crossflow membrane filtration. The chemical potential is generalized as a superposition of equilibrium and irreversible contributions, originating from Brownian and shear-induced diffusion, respectively. As a result, an effective drag force is derived using the irreversible thermodynamics for a particle undergoing both Brownian and shear-induced diffusion in a sheared concentrated suspension. Using the drag force, a hydrodynamic force bias Monte Carlo method is developed for crossflow membrane filtration to determine the critical flux of hard sphere suspensions. Effects of shear rate and particle size on the critical flux are studied, and results show a good agreement with experimental observations reported in the literature.

• The Bulletin of The Korean Astronomical Society
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• v.37 no.2
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• pp.134.1-134.1
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• 2012

The radiation belt structure can be approximately reproduced by a form of diffusion equation, which takes into account the radial diffusion process as well as those in pitch angle and energy. The solution of the equation depends on several factors including initial and boundary conditions, diffusion coefficients, and plasmapause location. In this paper, we have attempted to determine a set of approximate functions for the energetic electron fluxes near the outer edge of the outer belt in terms of solar wind variable. We used the electron flux data from SST onboard the THEMIS spacecraft and determined its correlation with solar wind conditions in a systematic way. The functions were determined separately for different energy channels from ~30 keV up to 719 keV. Our determination of these functions allows us to predict the radial boundary condition for the electron flux, which can be implemented in a forecast model.