scholarly journals Effects of Diffusion Coefficients and Permanent Charge on Reversal Potentials in Ionic Channels

Entropy ◽  
2020 ◽  
Vol 22 (3) ◽  
pp. 325 ◽  
Author(s):  
Hamid Mofidi ◽  
Bob Eisenberg ◽  
Weishi Liu
Keyword(s):  
Diffusion Coefficients ◽  
Electrical Potential ◽  
Ionic Channels ◽  
Current Case ◽  
Singular Perturbation Analysis ◽  
Zero Current ◽  
Ion Species ◽  
Electrochemical Potentials ◽  
Reversal Potentials ◽  
Positively Charged

In this work, the dependence of reversal potentials and zero-current fluxes on diffusion coefficients are examined for ionic flows through membrane channels. The study is conducted for the setup of a simple structure defined by the profile of permanent charges with two mobile ion species, one positively charged (cation) and one negatively charged (anion). Numerical observations are obtained from analytical results established using geometric singular perturbation analysis of classical Poisson–Nernst–Planck models. For 1:1 ionic mixtures with arbitrary diffusion constants, Mofidi and Liu (arXiv:1909.01192) conducted a rigorous mathematical analysis and derived an equation for reversal potentials. We summarize and extend these results with numerical observations for biological relevant situations. The numerical investigations on profiles of the electrochemical potentials, ion concentrations, and electrical potential across ion channels are also presented for the zero-current case. Moreover, the dependence of current and fluxes on voltages and permanent charges is investigated. In the opinion of the authors, many results in the paper are not intuitive, and it is difficult, if not impossible, to reveal all cases without investigations of this type.

scholarly journals A Flux Ratio and a Universal Property of Permanent Charges Effects on Fluxes

2018 ◽  
Vol 6 (1) ◽  
pp. 28-40 ◽  
Author(s):  
Weishi Liu
Keyword(s):  
Boundary Conditions ◽  
Flux Ratio ◽  
Universal Property ◽  
Charge Effects ◽  
Channel Geometry ◽  
Flow Through ◽  
Charged Ions ◽  
Ion Species ◽  
Positively Charged ◽  
Anion Species

AbstractIn this work, we consider ionic flow through ion channels for an ionic mixture of a cation species (positively charged ions) and an anion species (negatively charged ions), and examine effects of a positive permanent charge on fluxes of the cation species and the anion species. For an ion species, and for any given boundary conditions and channel geometry,we introduce a ratio _(Q) = J(Q)/J(0) between the flux J(Q) of the ion species associated with a permanent charge Q and the flux J(0) associated with zero permanent charge. The flux ratio _(Q) is a suitable quantity for measuring an effect of the permanent charge Q: if _(Q) > 1, then the flux is enhanced by Q; if _ < 1, then the flux is reduced by Q. Based on analysis of Poisson-Nernst-Planck models for ionic flows, a universal property of permanent charge effects is obtained: for a positive permanent charge Q, if _1(Q) is the flux ratio for the cation species and _2(Q) is the flux ratio for the anion species, then _1(Q) < _2(Q), independent of boundary conditions and channel geometry. The statement is sharp in the sense that, at least for a given small positive Q, depending on boundary conditions and channel geometry, each of the followings indeed occurs: (i) _1(Q) < 1 < _2(Q); (ii) 1 < _1(Q) < _2(Q); (iii) _1(Q) < _2(Q) < 1. Analogous statements hold true for negative permanent charges with the inequalities reversed. It is also shown that the quantity _(Q) = |J(Q) − J(0)| may not be suitable for comparing the effects of permanent charges on cation flux and on anion flux. More precisely, for some positive permanent charge Q, if _1(Q) is associated with the cation species and _2(Q) is associated with the anion species, then, depending on boundary conditions and channel geometry, each of the followings is possible: (a) _1(Q) > _2(Q); (b) _1(Q) < _2(Q).

Coupled multi-ion electrodiffusion analysis for clay soils

2004 ◽  
Vol 41 (2) ◽  
pp. 287-298 ◽  
Author(s):  
Christian Jungnickel ◽  
David Smith ◽  
Stephen Fityus
Keyword(s):  
Diffusion Coefficients ◽  
Reactive Transport ◽  
Clayey Soil ◽  
Transport Model ◽  
Ion Pairing ◽  
Diffusion Cell ◽  
Coupled Transport ◽  
Exchange Reactions ◽  
Clay Liners ◽  
Ion Species

For a well-engineered compacted clay landfill liner, diffusive transport through the liner is the main mass transport mechanism from the landfill. Therefore, accurate estimates of diffusion coefficients for clay liners are essential for the engineering design of liner systems. A long-standing problem has been the effect of ion pairing on the estimation of diffusion coefficients for multicomponent ionic solutions migrating through clay liners. This paper considers the solution of a fully coupled set of transport equations describing the simultaneous diffusion of several ion species through a clayey soil. The analysis takes into account the diffusion coefficient for each ion species, ion pairing (as required by electroneutrality of the solution), and time-dependent first-order ion and (or) ligand exchange reactions with the clay particles. The behaviour of a double-reservoir diffusion cell, often employed for the estimation of diffusion coefficients in the laboratory, is analyzed using the coupled transport model. A detailed theoretical analysis is made of sodium fluoride transport through saturated kaolinitic clay.Key words: multi-ion diffusion, finite element analysis, reactive transport, kaolinite, double-reservoir diffusion cell.

Some Methodological Modifications of Determination of Diffusion Coefficients in Compacted Bentonite

2006 ◽  
Vol 932 ◽  
Author(s):  
Dušan Vopálka ◽  
Helena Filipská ◽  
Antonín Vokál
Keyword(s):  
Diffusion Coefficients ◽  
Effective Porosity ◽  
Diffusion Method ◽  
Dry Density ◽  
Diffusion Cell ◽  
Compacted Bentonite ◽  
Method Of Evaluation ◽  
Exclusion Effect ◽  
Positively Charged

ABSTRACTThe results of 3H, 36Cl and 137Cs diffusion experiments through compacted bentonite using a new design of diffusion cell and a new methodology of diffusion coefficients evaluation are presented. The diffusion cell was made from the stainless steel and enables to connect it directly to the input and/or output reservoirs without any tubing. The evaluation of diffusion coefficients utilizes a compartmental model developed in the environment of the GoldSim transport code. It enables to determine diffusion coefficients for various types of boundary conditions, including also input and output filters. The influence of the diffusion through filters on the determined values of both effective (De) and apparent (Da) diffusion coefficients was numerically demonstrated for the through diffusion method. This effect is most important for Da, the value of which would be underestimated using standard ways of evaluation for neutral and positively charged species, mainly in the case of high effective porosity.The comparison of standard and the newly developed method of evaluation of diffusion coefficients showed a significant influence of diffusion in filters for HTO. Contrary to the standard method of evaluation, the evaluation taking into account filters showed here no difference between total and effective porosity. The effect of filter resistance was negligible for Cl-, especially at high dry density of compacted bentonite, due to the anion exclusion effect. The numerical model developed enabled to determine Da values of Cs+ from the concentration change in the inlet reservoir.

Analysis of the Dynamic Permeation Experiment with Implication to Cartilaginous Tissue Engineering

2004 ◽  
Vol 126 (4) ◽  
pp. 485-491 ◽  
Author(s):  
W. Y. Gu ◽  
D. N. Sun ◽  
W. M. Lai ◽  
V. C. Mow
Keyword(s):  
Tissue Engineering ◽  
Constitutive Model ◽  
Electrolyte Solution ◽  
Diffusion Coefficients ◽  
Electrical Potential ◽  
Fluid Pressure ◽  
Spatial Distributions ◽  
Cartilaginous Tissue ◽  
Fixed Charge Density ◽  
Ion Concentrations

In the present study, a 1-D dynamic permeation of a monovalent electrolyte solution through a negatively charged-hydrated cartilaginous tissue is analyzed using the mechano-electrochemical theory developed by Lai et al. (1991) as the constitutive model for the tissue. The spatial distributions of stress, strain, fluid pressure, ion concentrations, electrical potential, ion and fluid fluxes within and across the tissue have been calculated. The dependencies of these mechanical, electrical and physicochemical responses on the tissue fixed charge density, with specified modulus, permeability, diffusion coefficients, and frequency and magnitude of pressure differential are determined. The results demonstrate that these mechanical, electrical and physicochemical fields within the tissue are intrinsically and nonlinearly coupled, and they all vary with time and depth within the tissue.

scholarly journals Study on Diffusion Coefficient of Fluorophores in 3D Hydrogel with Cationic Charge using Microchip

2019 ◽  
Author(s):  
Juyoung Jin ◽  
Jaesool Shim ◽  
Jinseok Kim
Keyword(s):  
Diffusion Coefficients ◽  
Rhodamine 6G ◽  
Measurement Techniques ◽  
Time Measurement ◽  
Diffusivity Measurement ◽  
Long Time ◽  
Fluorescence Images ◽  
Short Time ◽  
Positively Charged ◽  
Convective Movement

The diffusion coefficients of ions are measured in a microchip filled with a cationic charged 3D hydrogel in order to study the effect of cationic charged 3D hydrogel on the diffusivity of ions. In this study, poly-diallyl-dimethyl-ammoniumchloride (poly-DADMAC) is used to produce a 3D hydrogel. Four different fluorophores are used in the 3D hydrogel rhodamine 6G, rhodamine-BSA, fluorescein isothio-cyanate (FITC) and FITC-BSA. The rhodamine 6G and rhodamine-BSA are positively charged (cations), while fluorescein isothio-cyanate (FITC) and FITC-BSA are negatively charged (anions). Two widely used techniques which are short time diffusivity measurement technique and long time diffusivity measurement techniques are used to measure the diffusion coefficients. For the short time measurement, Fluorescence recovery after photo-bleaching (FRAP) is used by a 3D confocal microscope. For the long time measurement, fluorescence images are taken for 11 days to observe a pure diffusivity without any convective movement. As a result, the diffusivity of the cations was found to be lower than that of the anions in the cationic charged hydrogel.

Sounder Accelerated Particles at Mars: Observations, Mechanisms, and Applications

2020 ◽  
Author(s):  
Andrii Voshchepynets ◽  
Stas Barabash ◽  
Mats Holmstrom ◽  
Rudy Frahm ◽  
Andrew Kopf
Keyword(s):  
Magnetic Field ◽  
Strong Magnetic Field ◽  
Plasma Frequency ◽  
Ion Beams ◽  
Spacecraft Charging ◽  
Accelerated Electrons ◽  
Charged Ions ◽  
Ion Species ◽  
Positively Charged ◽  
Accelerated Particles

&lt;p&gt;We report the first observations of sounder accelerated particles (SAP) in the ionosphere of a planet which does not possess a strong magnetic field (Mars). These observations were conducted onboard the Mars Express spacecraft by the ion and electron sensors of the Analyzer of Space Plasmas and Energetic Atoms (ASPERA-3) experiment and the powerful topside sounder: Mars Advanced Radar for Subsurface and Ionosphere Sounding (MARSIS). Accelerated ions (O2+ , O+, and lighter ions) are observed in an energy range up to 800 eV when MARSIS transmits at a frequency close to the plasma frequency. Individual observations consist of almost monoenergetic ion beams either aligned with the MARSIS antenna or lying in the perpendicular plane. The observed ion beams are often accompanied by a decrease in the electron flux. Accelerated electrons are observed at energies up to 400 eV when MARSIS transmits at a frequency between the local plasma frequency and its harmonics (up to four times the plasma frequency). The majority of the sounder accelerated electrons are recorded close to the regions of intense crustal magnetic fields. The voltage applied to the MARSIS antenna causes spacecraft charging to 100&amp;#8217;s of volts by electrons from the ambient plasma. Positively charged ions are accelerated when the spacecraft discharges. Accelerated photoelectrons are released by the highly charged spacecraft and after one gyration in the strong magnetic field, return to the spacecraft which has already discharged. The acceleration effect influences which ions can be observed by increasing the energy of the thermal ion species making it possible to detect them whereas they would be indistinguishable under normal circumstances. We present the relevant data and discuss how these effects can be used for diagnostic of the local plasma.&lt;/p&gt;

Calcium movement in nerve fibres

1979 ◽  
Vol 12 (3) ◽  
pp. 371-460 ◽  
Author(s):  
J. Requena ◽  
L. J. Mullins
Keyword(s):  
Divalent Cations ◽  
Electrical Potential ◽  
Extracellular Fluid ◽  
Giant Axon ◽  
Cell Interior ◽  
Nerve Fibres ◽  
Internal Concentration ◽  
The Media ◽  
Na Ions ◽  
Positively Charged

Given the existence of a difference in electrical potential between the interior of a nerve cell and the media surrounding it, where the cytoplasm is some 70 mV negative (Hodgkin, 1958), it must be expected that any positively charged ion to which the cell membrane is permeable is more concentrated in the cell interior. For monovalent cations such as Na and divalent cations such as Ca and Mg this is not the case in the majority of the cells such as the squid giant axon. In other words, nerve cells maintain a lower intracellular concentration of these ions, as compared with their concentration in the extracellular fluid. For Mg, Ca and Na ions, this lower internal concentration must, in the steady state, be effected by some membrane based mechanism which consumes energy.

The Equilibrium Stability of a System of Disk Dynamos

1960 ◽  
Vol 56 (2) ◽  
pp. 154-173 ◽  
Author(s):  
Norman R. Lebovitz
Keyword(s):  
Equilibrium State ◽  
Viscous Damping ◽  
Equilibrium Stability ◽  
Stability Criteria ◽  
Equilibrium Solutions ◽  
Current Case ◽  
Zero Current ◽  
Single Disk ◽  
The Stability ◽  
Disk Dynamo

ABSTRACTThe stability of the equilibrium solutions of the equations describing the behaviour of a system of coupled disk dynamos is investigated. In the absence of viscous damping, it is found that systems consisting of more than two dynamos are unstable. That a single disk dynamo is stable is known. The stability of the undamped two-dynamo system has not been ascertained. When viscous damping is present, there are two equilibrium solutions, one in which all the currents are zero, and one in which they are finite. In the zero-current case, a stability criterion is found. Stability criteria are also found in the finite-current case. Further, the existence of the finite-current equilibrium state excludes the stability of the zero-current equilibrium state.

scholarly journals Relative dielectric constants and selectivity ratios in open ionic channels

2017 ◽  
Vol 5 (1) ◽  
pp. 125-137 ◽  
Author(s):  
Bob Eisenberg ◽  
Weishi Liu
Keyword(s):  
Ion Channels ◽  
Mathematical Analysis ◽  
Applied Mathematics ◽  
Ionic Channels ◽  
Dielectric Constants ◽  
Singularly Perturbed ◽  
Singularly Perturbed Problems ◽  
Dielectric Coefficient ◽  
Ion Species ◽  
Crucial Parameter

Abstract We investigate the effects of the relative dielectric coefficient on ionic flows in open ion channels, using mathematical analysis of reasonably general Poisson-Nernst-Planck type models that can include the finite sizes of ions. The value of the relative dielectric coefficient is of course a crucial parameter for ionic behavior in general. Using the powerful theory of singularly perturbed problems in applied mathematics, we show that some properties of open channels are quite insensitive to variation in the relative dielectric coefficient, thereby explaining such effects seen unexpectedly in simulations. The ratio between the total number of one ion species and that of another ion species, and the ratio between the flux of one ion species and that of another ion species do not depend significantly on the relative dielectric coefficient.

Mathematical analysis of reactive ion transport in dynamic equilibrium: The case of two ionic species

1992 ◽  
Vol 70 (6) ◽  
pp. 1604-1611 ◽  
Author(s):  
Koichi Iinuma ◽  
Masahiro Takebe
Keyword(s):  
Exact Solution ◽  
Mathematical Analysis ◽  
Diffusion Coefficients ◽  
Drift Tube ◽  
Dynamic Equilibrium ◽  
Ionic Species ◽  
Approach To Equilibrium ◽  
Longitudinal Diffusion ◽  
Approximate Formulation ◽  
Ion Species

An exact solution for the transport of two reacting ion species in a drift tube is developed. The calculation of the temporal variation of ion fluxes is simplified using an approximate formulation in terms of the reaction frequencies, drift velocities, and longitudinal diffusion coefficients. The exact and approximate formulations are compared for the case of (N2+, N4+)/N2 with a view to establishing the approach to equilibrium.

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