We develop a thermodynamically consistent phase-field framework, permeating CHNS (pCHNS), for solvent transport across semi-permeable interfaces driven by osmotic and hydrostatic pressure differences. The model establishes a bidirectional coupling: the fluid advects solute, while solute gradients regulate cross-interface solvent flux via osmotic pressure. An energy-variational derivation yields a closed energy-dissipation law, which we leverage to construct fully discrete, energy-stable, high-order algorithms: LDG spatial discretization, a decoupled first-order scheme with unconditional energy stability, and a semi-implicit spectral deferred correction (SDC) upgrade for high-order temporal accuracy while preserving dissipation. Asharp-interface asymptotic analysis shows that, under natural scalings, the diffuse model converges to a sharp-interface problem with the expected kinematic law, normal-stress jump, and solute impermeability conditions, thereby establishing diffuse-to-sharp consistency. Numerically, a space-time convergence study confirms design orders and energy decay; a 1D no-flow calibration demonstrates quantitative convergence to the sharp-interface prediction as the interface thickness vanishes; and 2D simulations examine how permeability, solute load, and shear shape droplet evolution and equilibrium morphology. The contributions are methodological and analytical, providing a robust computational framework for coupled fluid-interface-transport problems.

Publication:

JOURNAL OF COMPUTATIONAL PHYSICS

http://dx.doi.org/10.1016/j.jcp.2026.115036

Author:

Guo, Ruihan

Zhengzhou Univ, Sch Math & Stat, Zhengzhou 450001, Peoples R China

Shen, Jie

Eastern Inst Technol, Sch Math Sci, Ningbo 315200, Peoples R China

Xu, Shixin (corresponding author)

Duke Kunshan Univ, Zu Chongzhi Ctr, 8 Duke Ave, Kunshan 215316, Jiangsu, Peoples R China

Email address: shixin.xu@dukekunshan.edu.cn

Xu, Xianmin

Chinese Acad Sci, Acad Math & Syst Sci, State Key Lab Math Sci, Beijing 100190, Peoples R China