Hierarchical capillary network with graded porosity for evaporative cooling

Efficient thermal management, especially for cooling electronic components in high power context, is crucial to keep devices operating in a safe temperature range. In the two-phase cooling field, capillary flow through porous systems combined with evaporation is one of the promising solutions. As established in the literature, evaporation occurring within the porous structure reduces the thermal performance. Here, we address this issue in a fundamental way, and propose a theoretical framework to design porous networks with porosity gradients maintaining the water/vapor interface at the top surface where the liquid, pumped by capillarity, evaporates. We model evaporation at the top surface of multiscale tree-like porous networks with minimum volume, by coupling an evaporation model at pore scale and a network model relying on capillary pressure, friction, and gravity balance. The evaporation model is validated through experimental data. We present some case studies and discuss how the geometrical features of the hierarchical networks, such as pore size and number of pores, impact the heat transfer coefficient. At the scale of the porous material, we show how the permeability is related to the heat flux to maintain evaporation. This study lays the foundation for designing efficient graded porous structures for evaporative cooling.