Diffusion with general boundary conditions in electrochemical systems

Criado, C.; Galán‐Montenegro, P.; Velásquez, Pablo; Ramos-Barrado, J.R.

doi:10.1016/s0022-0728(00)00188-1

Cited by 41 publications

(28 citation statements)

References 9 publications

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“…One can argue that for sufficiently small τ 0 , this inequality may be satisfied, and the wave equation of diffusion seems to be affirmed in some experiments [30,31].…”

Section: Entropy Growthmentioning

confidence: 91%

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Random Walk, Diffusion and Wave Equation

Wojnar¹

2013

Acta Phys. Pol. B

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One-dimensional random walk is analyzed. First, it is shown that the classical interpretation of random walk reaching Lord Rayleigh's analysis should be completed. Further, an attention is called to the fact that the parabolic diffusion is not an unique interpretation, but also the wave (or hyperbolic) equation can be deduced. It depends on the accepted scale of the length of step h and duration of the step τ in the walk, whether Fick-Smoluchowski's diffusion or a wave process is obtained. Only additional arguments, such as positivity of distribution function or positivity of the entropy growth, can help to choose the proper physical model. Also, the infinite diffusion velocity paradox in connection with Einstein's formula is explained.

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“…One can argue that for sufficiently small τ 0 , this inequality may be satisfied, and the wave equation of diffusion seems to be affirmed in some experiments [30,31].…”

Section: Entropy Growthmentioning

confidence: 91%

“…To avoid such contradiction, called a paradox, they use a hyperbolic diffusion equation (15), instead of the parabolic (9). For example, they use the hyperbolic diffusion equation to study the transport process of electrolytes in media such as gels and porous media [30,31].…”

Section: Fick's Diffusionmentioning

confidence: 99%

Random Walk, Diffusion and Wave Equation

Wojnar¹

2013

Acta Phys. Pol. B

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“…Modeling Fick's laws of diffusion with electrical R-C transmission lines have been proposed [67] and the relationships between diffusion, Warburg-like impedances, and transmission lines have been presented [68]. In this work, an R-C transmission line circuit model in one-dimension is developed to model the in vivo biofuel cell diffusion dynamics.…”

Section: B Dynamic Modelmentioning

confidence: 99%

Electrical Circuit Model and Dynamic Analysis of Implantable Enzymatic Biofuel Cells Operating In Vivo

et al. 2014

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This paper provides an overview of enzymatic biofuel cell theory and a summary of experimental results up to date, while discussing key electronic interfacing issues that must be considered in practical in vivo application of biofuel cells as power sources.ABSTRACT | This paper presents an electric circuit model and a dynamic analysis of enzymatic biofuel cells. The model is consistent with classical double-layer capacitance electrode behavior, fuel cell polarization models, and fuel diffusion limits, and may be extracted from commonly used electrochemical measurements. It is shown to accurately predict the observed experimental behavior of implantable enzymatic biofuel cells operating in vivo. The model is analyzed under various power loading conditions to consider runtime and fuel replenishment implications. A case study for powering a pacemaker is considered; and the results and SPICE simulations are shown to be in excellent agreement with experimental observations. The model can be used to identify areas for future biofuel cell improvement and to provide insight into critical electrical interface and system-level issues that must be addressed to advance the adoption of in vivo application of biofuel cells.

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“…ሺxሻ for xϵ ∂Ω ଵ c ୧ ሺxሻ = c ୧ ୖ ሺxሻ for xϵ ∂Ω ଶ , i = Na ା , K ା , Cl ି [10] We assume that no charge can leave the channel through ∂Ω ଷ and this fragment is described by zero-flux boundary condition: ሺJ ሚ ୧ • nሻሺxሻ = 0 for x ∈ ∂Ω ଷ [11] where n is a vector normal to the wall at x. The above condition is equivalent to:…”

Section: Modelmentioning

confidence: 99%

“…Although modeling of ionic transport throughout the channels presents a difficult task, it covers extensively developed research activity (7,(9)(10)(11). It is also believed that learning of selectivity of ionic channels will give also rise to design and fabricate artificial architectures that are designed by "learning from nature" and mimic the functions of biological ion channels (12,13).…”

Section: Introductionmentioning

confidence: 99%

Electrochemistry of Symmetrical Ion Channel: A Three-Dimensional Nernst-Planck- Poisson Model

et al. 2014

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The paper provides a physical description of ionic transport through the rigid symmetrical channel. A three-dimensional mathematical model, in which the ionic transport is treated as the electrodiffusion of ions, is presented. It allows simulating the transport characteristics at the steady-state and time evolution of the system. The numerical solutions of the coupled differential diffusion equation system are obtained by finite element method. Examples are presented in which the flow characteristics at the stationary state and during time evolution are compared. It is shown that the stationary state is achieved after about 10 -7 s since the process beginning. The model can be applied to simulate transport in polymer membranes and nanopores which might be useful in designing biosensors and nanodevices.

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Diffusion with general boundary conditions in electrochemical systems

Cited by 41 publications

References 9 publications

Random Walk, Diffusion and Wave Equation

Random Walk, Diffusion and Wave Equation

Electrical Circuit Model and Dynamic Analysis of Implantable Enzymatic Biofuel Cells Operating In Vivo

Electrochemistry of Symmetrical Ion Channel: A Three-Dimensional Nernst-Planck- Poisson Model

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