Numerical investigation of ultra-rapid cooling characteristics of droplets on a cryogenic substrate

Abstract

Solid surface cryopreservation method has emerged as a pivotal technology for long-term storage of biomaterials, effectively addressing challenges such as the Leidenfrost phenomenon. However, the intricate thermodynamic and non-isothermal crystallization mechanisms of ultra-rapid cooling droplets remain inadequately addressed, as well as the combined influence of the droplet geometry and cryogenic substrate conditions. This study aims to reveal the characteristics of droplets undergoing ultra-rapid cooling on cryogenic surfaces and particularly emphasize the influence of droplet shape on substrates. A thermodynamic model coupled with non-isothermal crystallization kinetics was developed with temperature-dependent physical properties and actual measured droplet geometries. For cryopreservation agents comprising 2.5 mol/L ethylene glycol and 2.5 mol/L propylene glycol, an experimental system was established to obtain the ultra-rapid cooling rate of the droplet, validating the accuracy of simulations. It was found that smaller static contact angles and droplet volumes contributed to enhancing the cooling rates and reducing the maximum crystallinity. And their relationships were described by mathematical equations. Additionally, ultra-rapid cooling resulted in nonlinear crystallization patterns along the vertical direction of the droplets. Furthermore, predictive equations were proposed to estimate the average cooling rates and crystallinity as functions of static contact angles and droplet volumes, eliminating the necessity of individually modeling and calculating each condition. The present functions can serve as tools for evaluating and screening hydrophilic solid substrates and cryopreservation agents for the solid surface cryopreservation method.