Thermodynamically consistent modeling and stable ALE approximations of reactive semi-permeable interfaces

Reactive, semi-permeable interfaces play important roles in key biological processes such as targeted drug delivery, lipid metabolism, and signal transduction. These systems involve coupled surface reactions, transmembrane transport, and interfacial deformation, often triggered by local biochemical signals. The strong mechanochemical couplings complicate the modeling of such interfacial dynamics. We propose a thermodynamically consistent continuum framework that integrates bulk fluid motion, interfacial dynamics, surface chemistry, and selective solute exchange, derived via an energy variation approach to ensure mass conservation and energy dissipation. To efficiently solve the resulting coupled system, we develop a finite element scheme within an arbitrary Lagrangian-Eulerian (ALE) framework, which can preserve conservation laws for the discrete numerical solutions. Numerical experiments verify the convergence and conservation properties of the scheme and demonstrate its ability in capturing complex interfacial dynamics. Two biologically inspired examples showcase the model's versatility: cholesterol depletion via the MeβCD-Chol complex, involving multistage interfacial reactions and HDL uptake; and a self-propelled droplet system with reaction-activated permeability, mimicking drug release in pathological environments. This work provides a unified computational platform for studying strongly coupled biochemical and mechanical interactions at interfaces, offering new insights into reactive transport processes in both biological and industrial contexts.

Duke Scholars

Author Shixin Xu DKU Faculty