Generalized Nernst–Planck and Stefan–Maxwell equations for membrane transport

Mehta, Gitanjali; Morse, Theodore F.; Mason, Edward A.; Daneshpajooh, M.H.

doi:10.1063/1.432021

Cited by 44 publications

(16 citation statements)

References 17 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Instead, in the present work we combine a two-dimensional (2D) model for the spacer channels with a detailed description of transport of ions and water through the membranes [24,25], thus providing a full description of transport phenomena in the channels and in the membranes. In the 2D model, one coordinate axis runs through the cell (from entrance to exit), and one coordinate is directed towards and through the membranes, see Fig.…”

Section: General Aspects Of Ion Transport In Liquid-filled Membrane Pmentioning

confidence: 99%

Nernst-Planck transport theory for (reverse) electrodialysis: II. Effect of water transport through ion-exchange membranes

Tedesco¹,

Hamelers²,

Biesheuvel³

2017

Journal of Membrane Science

140

121

View full text Add to dashboard Cite

Transport of water through ion-exchange membranes is of importance both for electrodialysis (ED) and reverse electrodialysis (RED). In this work, we extend our previous theory [J. Membrane Sci., 510, (2016) 370-381] and include water transport in a two-dimensional model for (R)ED. Following a Maxwell-Stefan (MS) approach, ions in the membrane have friction with the water, pore walls, and one another. We show that when ion-ion friction is neglected, the MS-approach is equivalent to the hydrodynamic theory of hindered transport, for instance applied to nanofiltration. After validation against experimental data from literature for ED and RED, the model is used to analyze single-pass seawater ED, and RED with highly concentrated solutions. In the model, fluxes and velocities of water and ions in the membranes are self-consistently calculated as function of the driving forces. We investigate the influence of water and coion leakage under different operational conditions.

show abstract

Section: General Aspects Of Ion Transport In Liquid-filled Membrane Pmentioning

confidence: 99%

Nernst-Planck transport theory for (reverse) electrodialysis: II. Effect of water transport through ion-exchange membranes

Tedesco¹,

Hamelers²,

Biesheuvel³

2017

Journal of Membrane Science

140

121

View full text Add to dashboard Cite

show abstract

“…The operating conditions, such as pressure and temperature, can also alter the flow scheme. A universal theory developed by Mason and his associates [48][49][50][51] simultaneously incorporates all of these mechanisms but is less used by the membrane community due to its complexity. This is called the "dusty-gas model."…”

Section: -5 Dual-mode Sorption Modelmentioning

confidence: 99%

Fundamentals of membrane transport

Hwang

2010

Korean J. Chem. Eng.

View full text Add to dashboard Cite

A review is presented to give a generalized membrane transport theory based on the principles of nonequilibrium thermodynamics. This theory is then used to develop specific flux equations for gas separation, pervaporation, osmosis, reverse osmosis, nanofiltration, ultrafiltration, microfiltration, dialysis, and electrodialysis. All membrane processes suffer from boundary layer mass transfer resistances caused by concentration polarization. The convective motions parallel and perpendicular to the membrane surface are distinguishable, and the former becomes more relevant than the latter in the boundary layer mass transfer. The modified Péclet number is introduced and its importance is discussed in characterizing the boundary layer mass transfers of various membrane processes. Many different transport mechanisms through membrane itself are reviewed including the solution-diffusion model, pore model, permeation through composite membranes, and transport through inorganic membranes. Finally, the differences between membrane mass transfer and other mass transfer are delineated, including a discussion of negative mass transfer coefficient.

show abstract

“…In the simplest case of ion diffusion between two media when diffusion coefficients do not vary across the interface separating the media, the potential difference existing in the system at the stationary state can be inferred as follows. Although more detailed methods do exist for the physical treatment of ionic diffusion in solution (6,7,8), we resorted to the Smoluchowski treatment of mass transport taking place by virtue of concentration gradient and external force which exerts upon the diffusible particles. That is, one can write the following equations for the flux of cations and anions which diffuse freely across an interface:…”

Section: Resultsmentioning

confidence: 99%

Characterization of electrical charge separation at the interface of two aqueous solutions in the presence of concentration gradients and cation/anion mobility ratio asymmetry

Cernescu

Luchian

2005

Open Physics

View full text Add to dashboard Cite

Physical consequences of ionic diffusion processes play a major role on the outcome of electrophysiology experiments due to both their contribution to the ionic transmembrane transport and phenomena taking place at the measuring instruments interface. As most of the time heterogenities in biological media with respect to ionic diffusion constants are disregarded, we intended to look upon the general case of ionic diffusion at the interface of two liquids on which gradients of these diffusion constants no longer can be neglected. We developed a theoretical model for the diffusion potential which emerges at an aqueous interface under gradients of concentration and diffusion constants. The experimental validation of our model was achieved through potential difference measurements of the diffusion potential between two solutions containing sodium chloride (NaCl) and glycerine solutions of various concentrations. Within the studied domain of the electrical charge mobility ratio, we noticed that experimental results are in agreement with the theoretically inferred diffusion potential values. This demonstrates that the resulting relationship for the diffusion potential inferred from our model could be applied for other cases, as well. When the ionic solutions contains an indefinite quantity of glycerine or an unknown substance able to modify diffusion constants of sodium and chloride, it was shown that through measurements of the diffusion potential one can infer the unknown concentration of glycerine and the modified ionic mobility ratio. This, in turn, builds up the foundation for a novel yet simple and efficient analitycal sensing device for quantitative determination in the field.

show abstract

Generalized Nernst–Planck and Stefan–Maxwell equations for membrane transport

Cited by 44 publications

References 17 publications

Nernst-Planck transport theory for (reverse) electrodialysis: II. Effect of water transport through ion-exchange membranes

Nernst-Planck transport theory for (reverse) electrodialysis: II. Effect of water transport through ion-exchange membranes

Fundamentals of membrane transport

Characterization of electrical charge separation at the interface of two aqueous solutions in the presence of concentration gradients and cation/anion mobility ratio asymmetry

Contact Info

Product

Resources

About