【徐士鑫】Thermodynamically Consistent Modeling and Stable ALE Approximations of Reactive Semi-Permeable Interfaces

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 M$\beta$CD-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. This work is collaborated with Weidong Shi, Zhen Zhang and Quan Zhao.

徐士鑫博士现任昆山杜克大学数学助理教授。徐士鑫博士于中国海洋大学获得数学学士学位，2013年于中国科技大学获得数学博士学位。2013至2017年间分别在新加坡国立大学、美国圣母大学、美国加州大学河滨分校， 以及加拿大菲尔兹数学科学研究所做博士后研究员。徐士鑫博士的研究方向主要有机器学习和数据驱动型疾病模型、多尺度复杂流体建模、均匀化理论和数值分析。