The Choice of Reference Frame in the Treatment of Membrane Transport by Nonequilibrium Thermodynamics

Mikulecky, Donald C.; Caplan, S. Roy

doi:10.1021/j100882a006

Cited by 42 publications

(27 citation statements)

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“…Therefore, the presence of the membrane could then be incorporated into the phenomenological coefficients that finally must be evaluated'by using a microscopic theory or laboratory measurements [10,18]. In this way, the system of equations (16)(17)(18) derived in the previous section, will be particularized for several membrane transport cases. We shall not try to solve this set of equations for any general situation, instead we show that several well-known results are in fact contained in them, and that other new results can also be derived.…”

Section: Results For Membrane Transportmentioning

confidence: 99%

“…Comparison between equations (14) and (15) leads to the following time evolutions equations for the non-conserved variables (16) dt…”

Section: Extended Thermodynamic Descriptionmentioning

confidence: 99%

“…However, this term has been obtained before by using different points of view. For instance, using LIT Lorimer [15], Mikulecky and Caplan [16] have shown the proper generalization of the thermodynamic forces when a viscous contribution is present. Under steady states, in the entropy production they introduce a term proportional to grad ñ given by…”

Section: Substituting This Equation Into (25) We Getmentioning

confidence: 99%

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Extended Thermodynamics and Membrane Transport

Castillo¹,

Rodríguez²

1989

Journal of Non-Equilibrium Thermodynamics

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We use Extended Irreversible Thermodynamics (EIT) to describe transport phenomena in membranes. The basic assumptions of EIT are summarized and the membrane is regarded as a passive phase where diffusive and viscous flow of a binary solution may occur. It is shown that in contrast to Linear Irreversible Thermodynamics (LIT), EIT is adequate to describe noninstantaneous transport processes across membranes. This is illustrated by showing that EIT predicts that the concentration profile inside the membrane obeys the telegraph equation instead of the usual diffusion equation. As a result we find that for dynamic osmosis the initial pressure gradient should grow as t 3 instead of the linear dependence implied by LIT. This and other differences between LIT and EIT are pointed out and the sense in which the latter may be considered as a generalization of the former is also discussed. IntroductionThe most widely used theoretical tools in the study of the rich variety of transport phenomena through membranes have been linear irreversible thermodynamics [1], Navier-Stokes hydrodynamics (NSH) [2], and nonequilibrium statistical mechanics [3]. In fact, in spite of the undeniable success of LIT and NSH to deal with many irreversible processes in open, semipermeable or leaky membranes, they are limited to the description of linear processes due to the fact that both formalisms are constructed upon the local equilibrium assumption. But there are transport phenomena in membranes, such as flow through very narrow interstices, that do not fit into the scheme of LIT [2] and for which the local equilibrium assumption is no longer valid.One theory aiming at overcaming the limitations of LIT and NSH is extended irreversible thermodynamics. The basic idea of this approach is to modify the local equilibrium assumption by including the fluxes of the system as independent variables [4]. This theory has been successfully applied to many systems such as diffusion in a binary mixture [5], viscoelastic fluids [6], polar and electrical solids [7], systems with internal degrees of freedom [8], etc. The basic purpose of this work is to exhibit how BIT may fte used to describe transport across a membrane. We show that this theory is specially appropriate to describe phenomena associated with a transient response of the membrane. We exhibit how the structure of the theory incorporates in a unified and systematic way several features of transport through membranes that have been proposed in the literature using a variety of different approaches. In particular, it will be shown that the results of LIT can be derived from EIT and other new results will be discussed.

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Section: Results For Membrane Transportmentioning

confidence: 99%

“…Comparison between equations (14) and (15) leads to the following time evolutions equations for the non-conserved variables (16) dt…”

Section: Extended Thermodynamic Descriptionmentioning

confidence: 99%

Section: Substituting This Equation Into (25) We Getmentioning

confidence: 99%

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Extended Thermodynamics and Membrane Transport

Castillo¹,

Rodríguez²

1989

Journal of Non-Equilibrium Thermodynamics

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“…Alternative theories were suggested by Kobatake and Fujita (9) and Meares and Page (11). The former belongs to the class of macroscopic theory involving a twovariable model while the latter theories are concerned with the microscopic details (20) of the phenomenon involving a singlevariable model.…”

Section: Theoreticalmentioning

confidence: 99%

Bistability and Electrokinetic Oscillations

Rastogi

Mishra

Pandey

et al. 1999

Journal of Colloid and Interface Science

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“…This has facilitated the theoretical analysis of the system and permitted a quantitative comparison between theory and experiment. It has been found that an approach along the lines laid down by Kobatake and Fujita (1964) and by Mikulecky and Caplan (1966) successfully describes the stationary-state properties of the oscillator. These give rise to the so-called "flip-flop" phenomena.…”

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The Teorell membrane oscillator as a mechano-electric transducer

Meares

Page

1973

J. Membrain Biol.

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Summary. The results of a recent quantitative analysis of the Teorell membraneoscillator are utilized to explore its role as an excitability analogue. Special attention is paid to its role as a mechano-electric transducer. A membrane of exceptionally welldefined pore structure has been used in this study. The analogue properties arise from nonlinear coupling between water and salt fluxes. When the membrane is simultaneously subjected to controlled gradients of hydrostatic pressure, electrical potential and concentration, bi-stable stationary states can be produced. These arise from the opposing effects of pressure and electro-osmosis on the volume flow. Transitions between these states show hysteresis. The factors governing such transitions are analogous to certain types of stimuli encountered in the natural excitation process. The membrane system also shows oscillatory behavior when the hydrostatic pressure gradient is allowed to vary under constant current conditions. This property is related to the bi-stable stationary state phenomena and is compared to the regenerative behavior found in biologically excitable tissues. Particular emphasis is placed upon analogies between the membrane oscillator and certain natural tissues. The importance of the nonlinear nature of the forceflux coupling in the analogue is stressed, and its possible relevance to biological excitability indicated. Some consideration is also given to the role of electro-osmotic flux coupling in biological tissues.The Teorell membrane oscillator consists of a broad-pored membrane of low effective internal electric charge separating concentrated and dilute solutions of the same electrolyte. The passage of an appropriate electric current through the membrane gives rise to an electro-osmotic flux directed from the dilute to the concentrated solution. This is opposed by a hydrodynamic flow induced by pressure applied across the membrane.This membrane system may exist in either one of two stable states depending on the magnitudes of the membrane potential and the applied pressure differential. The occurrence of transitions between these states for a given inelastic membrane and pair of solutions is a function only of potential, pressure and temperature. Thus, pressure impulses can be turned 15 J. Membrane Biol. 11

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The Choice of Reference Frame in the Treatment of Membrane Transport by Nonequilibrium Thermodynamics

Cited by 42 publications

References 0 publications

Extended Thermodynamics and Membrane Transport

Extended Thermodynamics and Membrane Transport

Bistability and Electrokinetic Oscillations

The Teorell membrane oscillator as a mechano-electric transducer

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