Mathematical modelling of mass transfer of paramagnetic ions through an inert membrane by the transient magnetic concentration gradient force

The objective of this work is to analyze the origin of the magnetic concentration gradient force. The force will be studied in a diffusion system where a paramagnetic electrolyte diffuses through a thin, inert membrane under the influence of a homogeneous magnetic field. The force will be analyzed using the theory of magnetic circuits, i.e., by the concept of minimum reluctance principles. In addition, based on some previous studies, it will be discussed whether the minimum reluctance principle can be applied to mass transfer into and out of the diffusion layer at electrode/electrolyte interfaces. The results show that the magnetic concentration gradient force arises as a consequence of the minimum reluctance principle. Applied to the diffusion system, the magnetic concentration gradient force arises in the membrane as a consequence of the concentration gradient and hence, the reluctance gradient. The force acts on the flow in such a way that the reluctance in the membrane is minimized. The force implies two interaction mechanisms: attraction of the paramagnetic electrolyte flowing into the membrane in order to decrease the reluctance, and hindrance of the paramagnetic electrolyte flowing out of the membrane in order to hinder an increase in the reluctance. Based on previous studies, it is shown that the minimum reluctance principle can be applied to mass transfer into or out of the diffusion layer at electrode/electrolyte interfaces as well.

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Confinement of paramagnetic ions under magnetic field influence: Lorentz versus concentration gradient force based explanations

Electrochemistry Communications ◽

10.1016/j.elecom.2007.07.026 ◽

2007 ◽

Vol 9 (10) ◽

pp. 2479-2483 ◽

Cited By ~ 35

Author(s):

Tom Weier ◽

Kerstin Eckert ◽

Sascha Mühlenhoff ◽

Christian Cierpka ◽

Andreas Bund ◽

...

Keyword(s):

Magnetic Field ◽

Concentration Gradient ◽

Gradient Force ◽

Paramagnetic Ions ◽

Field Influence ◽

Versus Concentration

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Diffusimetry Renounces Graham’s Law, Achieves Diffusive Convection, Concentration Gradient Induced Diffusion, Heat and Mass Transfer

Defect and Diffusion Forum ◽

10.4028/www.scientific.net/ddf.407.173 ◽

2021 ◽

Vol 407 ◽

pp. 173-184

Author(s):

Abul Khair ◽

Nilay Kumar Dey ◽

Mohammad Harun-Ur-Rashid ◽

Mohammad Abdul Alim ◽

Newas Mohammad Bahadur ◽

...

Keyword(s):

Mass Transfer ◽

Concentration Gradient ◽

Saline Water ◽

Hot Water ◽

Gradient Force ◽

Self Diffusion ◽

Diffusive Convection ◽

Low Mass ◽

Diffusion Rates ◽

Concentration Diffusion

Absolute diffusion rates of KMnO4 in vertical and flattened diffusimeters show the concentration gradient force as being stronger than the gravitational force. Hot water molecules move downward on self-diffusion against buoyancy. Diffusive convection (DC) in warm water and double-diffusive convection (DDC) in warm, saline water take place inside the diffusimeter with DDC transferring more heat than DC. In the diffusing medium the original reagents change or retain their compositions to give the diffusate molecules to diffuse. In water, the change is mostly hydration. The syngener BaCl2.2H2O separately with congeners 3CdSO4.8H2O, ZnSO4.7H2O, and ZnSO4.H2O presents two distinct pairs of overlapping concentration versus rate curves, first for having very close MWs of BaCl2 and CdSO4 and second for having ZnSO4.H2O as the common congener for both the zinc sulfates. Chlorides of Li, Na, and K diffusing at hindered rates in glucose solution show the least rate for LiCl inevitably on grounds of low mass and high Li+ hydration radius. Diffusion blocking occurs at higher glucose concentration. Diffusion of 0.6M AgNO3-0.6M NH4Cl standardizes this diffusimeter. Mass transfer of HCl, H2SO4, and H2C2O4 show oxalic acid diffusing as hydrate and 88 percentage transfer of sulfuric acid in 5 minutes. The Superdiffusive Anti Graham’s Law, Vd , is further consolidated by Ca (NO3)2-M2CO3(M = Na, K, NH4+) and Ca (NO3)2-Na2HPO4 diffusions. Odd and even diffusions are illustrated by AgNO3-NH4Cl and AgNO3-BaCl2 diffusions.

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