SIAM Journal on Applied Mathematics, Volume 81, Issue 3, Page 965-981, January 2021.
Diffusive transport of small ionic species through mucus layers is a ubiquitous phenomenon in physiology. However, some debate remains regarding how the various characteristics of mucus (charge of the polymers themselves, binding affinity of ions with mucus) impact the rate at which small ions may diffuse through a hydrated mucus gel. Indeed, it is not even clear if small ionic species diffuse through mucus gel at an appreciably different rate than they do in aqueous solution. Here, we present a mathematical description of the transport of two ionic species (hydrogen and chloride) through a mucus layer based on the Nernst--Planck equations of electrodiffusion. The model explicitly accounts for the binding affinity of hydrogen to the mucus material as well as the Donnan potential that occurs at the interface between regions with and without mucus. Steady-state fluxes of ionic species are quantified, as are their dependencies on the chemical properties of the mucus gel and the composition of the bath solution. We outline a mechanism for generating enhanced diffusive flux of hydrogen across the gel region and hypothesize how this mechanism may be relevant to the apparently contradictory experimental data in the literature.

中文翻译：

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增强跨粘液层的电扩散传输

SIAM Journal on Applied Mathematics，第 81 卷，第 3 期，第 965-981 页，2021 年 1 月。
小离子物质通过粘液层的扩散运输是生理学中普遍存在的现象。然而，关于粘液的各种特性（聚合物本身的电荷、离子与粘液的结合亲和力）如何影响小离子通过水合粘液凝胶扩散的速率，仍有一些争论。事实上，甚至不清楚小离子物质是否以与在水溶液中明显不同的速度通过粘液凝胶扩散。在这里，我们基于电扩散的能斯特-普朗克方程提出了两种离子物质（氢和氯）通过粘液层的传输的数学描述。该模型明确说明了氢对粘液材料的结合亲和力，以及出现在有和没有粘液的区域之间的界面处的唐南电位。离子物质的稳态通量被量化，因为它们依赖于粘液凝胶的化学性质和浴液的组成。我们概述了一种在凝胶区域产生增强的氢扩散通量的机制，并假设这种机制可能与文献中明显矛盾的实验数据有关。