Applicability of Goldman's constant field assumption to biological systems

MacGillivray, A. D.; Hare, Daphne

doi:10.1016/s0022-5193(69)80019-6

Cited by 70 publications

(34 citation statements)

References 11 publications

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“…These conditions were previously discussed in the case of a simple, porous membrane [13]. In addition, we pointed out [I31 that some of the earlier studies based on asymptotic [14] or numerical [lS] solutions should be, perhaps, partially revised.…”

Section: Introductionmentioning

confidence: 89%

Ionic Transport Across Porous Charged Membranes and the Goldman Constant Field Assumption

Pellicer

Mafé

Aguilella

1986

Ber Bunsenges Phys Chem

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Diffusion f Membranes 1 Nernst-Planck EquationsStarting from a simple theoretical model based on Nernst-Planck flux equations and the Donnan equilibrium relationship, the ionic transport across a porous, charged membrane is analysed and conditions are given which make exact the so-called "constant field assumption". The validity of the reported results is later verified in the case of a well-known problem: the ionic transport across a cationexchange membrane under bi-ionic conditions.

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Section: Introductionmentioning

confidence: 89%

Ionic Transport Across Porous Charged Membranes and the Goldman Constant Field Assumption

Pellicer

Mafé

Aguilella

1986

Ber Bunsenges Phys Chem

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“…MacGillivray and Hare ascertained that the electroneutrality assumption and constant field solution are in fact the limited cases of the Poisson equation. [36,37] It reduces to the electroneutrality assumption when the concentrations are high, or to the constant field condition when the concentrations are low. The modulation of the swelling degree of the hydrogels can be achieved through controlling the ionization of the fixed-charge groups (e.g., ionized HEMA carboxyl groups).…”

Section: Mathematical Model Developmentmentioning

confidence: 99%

Meshless Modeling of pH‐Sensitive Hydrogels Subjected to Coupled pH and Electric Field Stimuli: Young Modulus Effects and Case Studies

Yew

et al. 2007

Macro Chemistry & Physics

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The effect of Young's modulus on the behavior of pH‐sensitive hydrogels is studied when subjected to coupled stimuli of solution pH and externally applied electric field. The study is the first instance for coupled stimuli numerical analysis of the hydrogels, in which a multieffect‐coupling pH‐stimulus (MECpH) model is presented. The model considers ionic diffusion, electric potential, and large mechanical deformation. A correlation between diffusive hydrogen ion and charge groups fixed onto the hydrogel polymeric chains by the Langmuir absorption isotherm is incorporated into the model. To validate the model, the computed results by the meshless Hermite‐Cloud technique are compared well with experimental data available from the literature. Then several case studies are conducted for the swelling hydrogel immersed in buffered solution subject to applied electric voltage, especially for the Young modulus effects on the volume variations of the hydrogels.magnified image

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“…[3] and [4], N stands for the total number of ionic species and w is a fixed charge density in the domain. As emphasized by MacGillivray and Hare (6,7), the validity of these assumptions is limited to specific cases. In a more general model, the Poisson equation, which relates the electrical potential to the electrical charge in space, should be used (2):…”

Section: Mathematical Modelmentioning

confidence: 99%