Higher-order compatibility with curved-interface geometry

Establish higher-order compatibility of the corrected bulk-surface transport closure for soluble-surfactant falling films with the full curved-interface geometry by extending the asymptotic concentration-profile closure and associated surface balance.

Background

The paper constructs a corrected weighted-residual bulk-surface transport model that exactly conserves the projected surfactant inventory for smooth periodic solutions. However, the retained quadratic bulk concentration profile and leading adsorption-desorption relation do not satisfy the full finite-slope normal-flux condition. The authors therefore distinguish exact conservation within the reduced projected description from higher-order accuracy relative to the parent free-boundary problem.

Addressing the unresolved higher-order issue would require extending the asymptotic closure consistently, including revisions to the concentration profile or its closure and to the surface balance so that the geometric surface metric and normal diffusive flux are treated at the same order.