A Computational Investigation of the “Equivalent Substrates” in the Evaporation of Sessile Droplets

This paper investigates the coupled relationship between solid-phase temperature fields and droplet evaporation, focusing on the effects of substrate thermal conduction properties on droplet evaporation behavior. A mathematical model is developed to analyze the impacts of substrate thermal conductivity, thickness, and lower-surface temperature on evaporation rate, surface temperature, and evaporation flux. A dimensionless relative evaporation rate (HCs) is introduced to characterize the influence of substrate thermal conduction. Results show that increasing substrate thermal conductivity enhances droplet surface temperature and evaporation flux, thereby monotonically increasing evaporation rate until it approaches the rate of the evaporative cooling model. Conversely, increasing substrate thickness lengthens the heat transfer path, reducing heat conducted to the solid–liquid interface and decreasing evaporation rate. Changes in substrate lower-surface temperature significantly affect evaporation rate, but HCs remains nearly unaffected. The concept of equivalent substrates is proposed and verified through dimensionless analysis and simulations. It is found that different combinations of substrate thickness and thermal conductivity exhibit consistent effects on droplet evaporation, with minimal relative errors in evaporation rate and total heat transfer at the solid–liquid interface. This confirms the existence of the equivalent substrate phenomenon. Additionally, the effects of droplet properties, such as contact angle and evaporative cooling coefficient (Ec), on the equivalent substrate phenomenon are explored, revealing negligible impacts. These findings provide theoretical guidance for optimizing droplet evaporation processes in practical applications, such as micro/nanoscale thermal management systems.