Effective flows across diffusio-phoretic membranes

TL;DR

This paper develops a homogenized macroscopic model for flow across diffusiophoretic membranes, incorporating microscale chemical interactions to aid in designing efficient phoretic pumps.

Contribution

It introduces a homogenization-based boundary condition that captures microscale interactions in a macroscopic flow model for diffusiophoretic membranes.

Findings

Derived effective flow boundary conditions for diffusiophoretic membranes.

Demonstrated the model's application in designing minimal phoretic pumps.

Validated the model through numerical simulations.

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 homogenization-based macroscopic boundary condition which describes the effective flow across a diffusiophoretic microstructured membrane, where the interaction between the membrane walls and the solute particles is modeled 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, enabling 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 optimization procedures.