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.

The effects of electrolyte concentration, ion species and pH on the zeta potential and electrokinetic charge density of montmorillonite

Clay Minerals ◽  
2006 ◽  
Vol 41 (4) ◽  
pp. 853-861 ◽  
Author(s):  
E. E. Saka ◽  
C. Güler
Keyword(s):  
Zeta Potential ◽  
Charge Density ◽  
Negative Charge ◽  
Electrolyte Concentration ◽  
Great Influence ◽  
Electrolyte Solutions ◽  
Ionic Species ◽  
Positive Sign ◽  
Ion Species ◽  
Influence Of Ph

AbstractIn this study, the influence of pH, electrolyte concentration and type of ionic species (such as LiCl, NaCl, KCl, RbCl, CsCl, CaCl2, AlCl3) on the electrokinetic properties (zeta potential and electrokinetic charge density) of montmorillonite has been quantified. The zeta potential of montmorillonite particles did not change significantly with change in pH. The valencies of the ions have proven to have a great influence on the electrokinetic behaviour of the suspension. There is a gradual decrease in the zeta potential (from —24 mV to —12 mV) with increase in monovalent electrolyte concentration (from 10-4 M to 10-1 M). At any monovalent electrolyte concentration, the magnitude of the zeta potential increased with the electrolytes in the order Li+ > Na+ > K+ > Rb+ > Cs+. The zeta potential of the montmorillonite minerals in CaCl2 solutions illustrated the same behaviour as the monovalent cations. Less negative values were obtained for the CaCl2 electrolyte (∼–10 mV) due to the greater valence of the ions. A sign reversal was observed at an AlCl3 concentration of 5 x 10-4 M, and, at greater concentrations, zeta potential values had a positive sign (∼20 mV).The electrokinetic charge density of montmorillonite showed similar trends of variation in mono and divalent electrolyte solutions. Up to concentrations of ∼10-3 M, it remained practically constant at ∼0.5 x 10-3Cm-2, while for greater electrolyte concentrations the negative charge produced more negative values (–16 x 10-3Cm-2). The electrokinetic charge density of montmorillonite particles was constant at low AlCl3 concentrations, but at certain concentrations it increased rapidly and changed sign to positive.

scholarly journals Electroosmotic Flow Hysteresis for Fluids with Dissimilar pH and Ionic Species

Micromachines ◽  
2021 ◽  
Vol 12 (9) ◽  
pp. 1031
Author(s):  
An Eng Lim ◽  
Yee Cheong Lam
Keyword(s):  
Zeta Potential ◽  
Electroosmotic Flow ◽  
Flow Direction ◽  
Velocity Model ◽  
Ionic Species ◽  
Dependent Behavior ◽  
Nacl Concentration ◽  
Solution Pair ◽  
Current Monitoring ◽  
Ion Species

Electroosmotic flow (EOF) involving displacement of multiple fluids is employed in micro-/nanofluidic applications. There are existing investigations on EOF hysteresis, i.e., flow direction-dependent behavior. However, none so far have studied the solution pair system of dissimilar ionic species with substantial pH difference. They exhibit complicated hysteretic phenomena. In this study, we investigate the EOF of sodium bicarbonate (NaHCO3, alkaline) and sodium chloride (NaCl, slightly acidic) solution pair via current monitoring technique. A developed slip velocity model with a modified wall condition is implemented with finite element simulations. Quantitative agreements between experimental and simulation results are obtained. Concentration evolutions of NaHCO3–NaCl follow the dissimilar anion species system. When NaCl displaces NaHCO3, EOF reduces due to the displacement of NaHCO3 with high pH (high absolute zeta potential). Consequently, NaCl is not fully displaced into the microchannel. When NaHCO3 displaces NaCl, NaHCO3 cannot displace into the microchannel as NaCl with low pH (low absolute zeta potential) produces slow EOF. These behaviors are independent of the applied electric field. However, complete displacement tends to be achieved by lowering the NaCl concentration, i.e., increasing its zeta potential. In contrast, the NaHCO3 concentration has little impact on the displacement process. These findings enhance the understanding of EOF involving solutions with dissimilar pH and ion species.

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.

scholarly journals Anomalous Anisotropic Diffusion of Electron Swarms in AC Electric Fields

1995 ◽  
Vol 48 (6) ◽  
pp. 925 ◽  
Author(s):  
RD White ◽  
RE Robson ◽  
KF Ness
Keyword(s):  
Electric Fields ◽  
Diffusion Coefficients ◽  
Anisotropic Diffusion ◽  
Time Varying ◽  
Longitudinal Diffusion ◽  
Temporal Behaviour ◽  
Ac Electric Fields ◽  
Wide Range ◽  
First Time ◽  
And Diffusion

A time-dependent multi-term solution of the Boltzmann equation is used to calculate the drift and diffusion coefficients of electron swarms in gases under the influence of a time varying electric field. Two model gases are considered and for a.c. electric fields results are presented for a wide range of applied frequencies. Of particular interest is the anomalous temporal behaviour of the longitudinal diffusion coefficient, which is discussed here for the first time.

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