Thermal Slip Length at a Liquid/Solid Interface: Power Law Relations From the Spatial and Frequency Attributes of the Contact Layer

Application specific integrated chips for power intensive data mining required by AI/ML now generate so much heat that data centers are having to switch from gas to liquid cooling to prevent malfunction from thermal runaway. A critical factor hindering optimization of the thermal flux crossing the liquid/solid (L/S) interface is the lack of any predictive model for the thermal slip length at non-cryogenic temperatures. This situation stands in contrast to the well known acoustic mismatch and diffuse mismatch models for predicting the Kapitza length at cryogenic temperatures. An extensive study using non-equilibrium molecular dynamics simulations of a liquid confined between a crystalline solid reveals distinct power law relations in real and reciprocal space governing the thermal slip length. These equations incorporate the influence of local temperature, in-plane translational order and vibrational frequency mismatch between the liquid contact layer and adjoining solid layer. Given that the Lennard-Jones potential used throughout this study accords with the principle of corresponding states, we expect similar relations as these to hold in many other L/S systems.