Uphill transport in competitive drift-diffusion models with volume exclusion

TL;DR

This paper investigates uphill particle transport phenomena in drift-diffusion models with volume exclusion, connecting microscopic exclusion processes to continuum models and exploring conditions for uphill flow in nanoscale and membrane systems.

Contribution

It characterizes uphill transport regimes in exclusion processes and links these to continuum models like Poisson-Nernst-Planck, advancing understanding of transport phenomena across scales.

Findings

Uphill transport persists across microscopic and continuum models.

Conditions for uphill flow are precisely characterized.

Implications for nanoscale electrolytes and membrane technologies.

Abstract

This paper addresses uphill transport (defined as a regime in which particle flow is opposite to the prescriptions of Fick's diffusion) in drift-diffusion particle transport constrained by volume exclusion. Firstly, we show that the stationary hydrodynamic limit of a multispecies, weakly asymmetric exclusion process (SHDL) naturally predicts precisely characterized uphill regimes in the space of external drivings. Then, with specific reference to systems of oppositely charged particles, we identify well-defined model hypotheses and extensions whereby the SHDL converges to the modified Poisson-Nernst-Planck model, thus bridging the gap between exclusion-based particle models and continuum descriptions commonly used in engineering. The merits and limitations of the models in describing the particle fluxes and predicting uphill transport conditions are investigated in detail with respect to the adopted approximations and simplifications. The results demonstrate the persistence of uphill transport phenomena across modeling scales, clarify the conditions under which they occur, and suggest that uphill transport may play a significant role in nanoscale electrolytes, confined ionic and iontronic devices, and membrane-based technologies.