Numerical Investigation of Shape Effect on Microdroplet Evaporation on Heated Pillars

As electronic devices continue to shrink in size and increase in functionality, effective thermal management has become a critical bottleneck that hinders continued advancement. Two-phase cooling technologies are of growing interest for electronics cooling due to their high heat removal capacity and small thermal resistance (< 0.3 K-cm2/W). One typical example of a two-phase cooling method is droplet evaporation, which can provide a high heat transfer coefficient with low superheat. While droplet evaporation has been studied extensively and used in many practical cooling applications (e.g., spray cooling), the relevant work has been confined to spherical droplets with axisymmetric geometries. A rationally designed evaporation platform that yields asymmetric meniscus droplets can potentially achieve larger meniscus curvatures, which give rise to higher vapor concentration gradients along the contact line region and therefore yield higher evaporation rates. In this study, we develop a numerical model to investigate the evaporation behavior of asymmetrical microdroplets suspended on heated porous micropillar structures. The equilibrium profiles and mass transport characteristics of droplets with circular, triangular, and square contact shapes are explored using the Volume of Fluid (VOF) method. The evaporative mass transport at the liquid-vapor interface is modeled using a simplified Schrage model. The results show highly non-uniform mass transport characteristics for asymmetrical microdroplets, where a higher local evaporation rate is observed near the locations where the meniscus has high curvature. This phenomenon is attributed to a higher local vapor concentration gradient that drives faster vapor diffusion at more curved regions, similar to a lightning rod exhibiting a strong electric field along a highly curved surface. By using contact line confinement to artificially tune the droplet into a more curved geometry, we make to interesting findings: 1) For adiabatic systems, the total evaporation rate from a triangular-based droplet is enhanced by 13% compared to a spherical droplet with the same perimeter and liquid-vapor interfacial area. 2) For microdroplets on heated pillars, triangular-based droplets yield the thinnest liquid film and smallest temperature difference between saturation temperature and solid-liquid temperature, which leads to a higher heat transfer coefficient (21% percent larger than spherical droplet at a supplied heat flux of 500 W/cm2). 3) When the supplied heat increase to a higher value (e.g., 1000 W/cm2), the interfacial temperature became a dominant role in the heat transfer and the shape effect became less important. These three findings can guide the design and optimization of geometric features to improve evaporation in high performance electronics cooling systems.