Work

Effective flows across diffusio-phoretic membranes

Year: 2025

Type: article

Abstract: Flows enabled by phoretic mechanisms are of significant interest in several biological and biomedical processes, such as bacterial motion and targeted drug delivery. Here, we develop a homogenisation-based macroscopic boundary condition that describes the effective flow across a diffusio-phoretic microstructured membrane, where the interaction between the membrane walls and the solute particles is modelled via a potential approach. We consider two cases where potential variations occur (i) at the pore scale and (ii) only in the close vicinity of the boundary, allowing for a simplified version of the macroscopic flow description, in the latter case. Chemical interactions at the microscale are rigorously upscaled to macroscopic phoretic solvent velocity and solute flux contributions, and added to the classical permeability and diffusivity properties of the membrane. These properties stem from the solution of Stokes advection–diffusion problems at the microscale, some of them forced by an interaction potential term. Eventually, we show an application of the macroscopic model to develop minimal phoretic pumps, showcasing its suitability for efficient design and optimisation procedures.

Source: Journal of Fluid Mechanics

DOI: 10.1017/jfm.2025.10686

Authors: Kevin Wittkowski, Pier Giuseppe Ledda, Edoardo Carlo Giordano, François Gallaire, Giuseppe Antonio Zampogna

Institutions: École Polytechnique Fédérale de Lausanne, University of Cagliari, University of Genoa

Language: English

Topic: Advanced Mathematical Modeling in Engineering

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,550

Funders: National Science Foundation, Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung