External Stefan and Internal Marangoni Thermo-Fluid Dynamics for Evaporating Capillary Bridges

We probe the evaporation mechanisms of wettability-moderated, confined capillary bridges and bulges. For the first time, we explore the internal Marangoni hydrodynamics and external Stefan advection dynamics in the surrounding gaseous domain due to evaporative effects. A transient simulation approach based on the level set (LS) method and the Arbitrary Lagrangian-Eulerian (ALE) framework was adopted to computationally model the capillary bridge profiles and evaporation phenomenon with generic contact line dynamics (both CCR and CCA modes). The governing equations corresponding to the transport processes in both the liquid and gaseous domains are simulated in a fully coupled manner with appropriate boundary conditions to precisely trace the liquid-vapor interface and the three-phase contact point during evaporation. The effect of the bridge confinement phenomenon, i.e., the extent of confined ambient surrounding the liquid-vapor interface between the solid surfaces, is explored. Also, the role of wetting state and contact line dynamics during CCR and CCA modes of evaporation were probed, and good agreement with experimental observations was noted. Results show that the evaporation rate is primarily dictated by the confinement phenomenon, and wettability effects play a marginal role. A higher confinement curtails the evaporation rate due to an increased local vapor concentration around the liquid bridges. However, the wetting state substantially affects the internal Marangoni effect dynamics and the Stefan advection dynamics due to its explicit influence on the nonuniform evaporative flux along the liquid-vapor interface. Between superhydrophobic confinements, the contact lines are confined in the wedge-shaped region, thereby locally augmenting the vapor concentration. As a result, the large evaporative flux near the bulge region develops a higher temperature gradient, thereby inducing upscaled thermal Marangoni flow compared to hydrophilic confinements. These findings may have significant implications for the efficient designing and development of thermofluidic systems involving thermal transport, mixing, and deposition of dissolved particles in liquid bridges.