Axisymmetric modeling of interfacial mass transfer in two-phase flows with Marangoni effect

This study presents an axisymmetric phase field model for interfacial mass transfer in two-phase flows with solutal Marangoni effect. The governing equations are solved within the finite volume method framework, utilizing Weighted Essentially Non-Oscillatory-Z scheme for convection interpolation to ensure the accuracy and robustness. Validations demonstrate the accuracy and robustness under extreme parameter conditions. On this basis, the solutal Marangoni effects on the buoyancy-driven rising bubble are investigated at various Eo (Eötvös) conditions. For case with lower Eo, solute transfer mildly deforms the bubble and lowers its rising velocity. This retardation arises from non-uniform surface tension, where the normal surface tension forms a net force directing oppositely to the rising velocity and the tangential surface tension (i.e., the Marangoni force) provides a promoting effect. In contrast, the solute transfer only exerts slight influence on the rising velocity for the case with larger Eo. Similar mechanisms are observed in the droplet migration driven by solute concentration gradients. In this scenario, the non-uniform normal surface tension acts as the primary driving force, whereas the Marangoni force impedes droplet motion. Furthermore, the droplet migration velocity decreases when solubility in the continuous phase exceeds that in the droplet but increases when solubility inside the droplet is higher than in the surrounding fluid.