A model of electrodiffusion and osmotic water flow and its energetic structure

Abstract. We derive a model of the coupled mechanical and electrochemical effects of polyelectrolyte gels. We assume that the gel, which is immersed in a fluid domain, is an immiscible and incompressible mixture of a solid polymeric component and the fluid. As the gel swells and de-swells, the gel-fluid interface can move. Our model consists of a system of partial differential equations for mass and linear momentum balance of the polymer and fluid components of the gel, the NavierStokes equations in the surrounding fluid domain, and the Poisson-Nernst-Planck equations for the ionic concentrations on the whole domain. These are supplemented by a novel and general class of boundary conditions expressing mass and linear momentum balance across the moving gel-fluid interface. Our boundary conditions include the permeability boundary conditions proposed in earlier studies. A salient feature of our model is that it satisfies a free energy dissipation identity, in accordance with the second law of thermodynamics. We also show, using boundary layer analysis, that the well-established Donnan condition for equilibrium arises naturally as a consequence of taking the electroneutral limit in our model.

show abstract

“…We point out that a related energy identity for a different system was proved recently in [36]. 11).…”

Section: Electrodiffusion Of Ionsmentioning

confidence: 64%

A Dynamic Model of Polyelectrolyte Gels

Mori¹,

Chen

Micek³

et al. 2013

SIAM J. Appl. Math.

Self Cite

View full text Add to dashboard Cite

show abstract

“…This predicts a logarithmic dependency of the flow rate with the ratio C To go further in the quantitative analysis requires entering into more details in the description of both the theoretical modeling of (diffusio-)osmotic effects [7,8,20] and the experimental configuration. Indeed, for electrolytes as solutes, it was predicted that the diffusio-osmotic response D DO can be split into two contributions [7],…”

mentioning

confidence: 99%

Osmotic Flow through Fully Permeable Nanochannels

et al. 2014

View full text Add to dashboard Cite

“…The new observation here is that, by appropriately defining a free energy function (that is to say, the left hand side of (2.13)), this thermodynamic property can be turned into a mathematical statement about system (2.11). We also point out that a similar identity valid for a system of partial differential equations describing electrodiffusion and osmosis was proved in Mori et al (2011). In subsequent sections we will use this as a tool to study stability of states.…”

Section: Model Formulation and The Free Energy Identitymentioning

confidence: 78%

“…Free energy dissipation identities similar to (2.13) are present in many models of soft-condensed matter physics (Doi and Edwards 1988;Doi 2009), and can be used as a guiding principle in formulating models in dissipative systems (Eisenberg et al 2010;Mori et al 2011). The present work owes much of its inspiration to this body of work.…”

Section: Discussionmentioning

confidence: 99%

Erratum to: Mathematical properties of pump-leak models of cell volume control and electrolyte balance

Mori

2012

J. Math. Biol.

Self Cite

View full text Add to dashboard Cite

Homeostatic control of cell volume and intracellular electrolyte content is a fundamental problem in physiology and is central to the functioning of epithelial systems. These physiological processes are modeled using pump-leak models, a system of differential algebraic equations that describes the balance of ions and water flowing across the cell membrane. Despite their widespread use, very little is known about their mathematical properties. Here, we establish analytical results on the existence and stability of steady states for a general class of pump-leak models. We treat two cases. When the ion channel currents have a linear current-voltage relationship, we show that there is at most one steady state, and that the steady state is globally asymptotically stable. If there are no steady states, the cell volume tends to infinity with time. When minimal assumptions are placed on the properties of ion channel currents, we show that there is an asymptotically stable steady state so long as the pump current is not too large. The key analytical tool is a free energy relation satisfied by a general class of pump-leak models, which can be used as a Lyapunov function to study stability.Keywords Cell volume control · Electrolyte balance · Free energy · Lyapunov function · Differential algebraic systemDue to typographical errors inadvertently introduced into the orignal manuscript during the publisher's production process, the original publication is incorrect. The complete and correct version is given here.The online version of the original article can be found under

show abstract

A model of electrodiffusion and osmotic water flow and its energetic structure

Cited by 50 publications

References 66 publications

A Dynamic Model of Polyelectrolyte Gels

A Dynamic Model of Polyelectrolyte Gels

Osmotic Flow through Fully Permeable Nanochannels

Erratum to: Mathematical properties of pump-leak models of cell volume control and electrolyte balance

Contact Info

Product

Resources

About