# Numerical Investigation of Heat Transfer and Development in Spherical Condensation Droplets

## TL;DR

This paper investigates how heat transfer and droplet growth occur during spherical condensation, offering insights to improve microprocessor cooling.

## Contribution

A novel model of droplet growth based on energy functionals and kinetic theory is proposed, explaining condensation dynamics and contact angle discrepancies.

## Key findings

- Droplet growth is divided into three stages based on critical volume thresholds of 105 nm³ and 1010 nm³.
- The model predicts droplet behavior with less than 3% error compared to experimental data.
- The model explains why observed contact angles deviate from the expected Wenzel contact angle.

## Abstract

This study establishes thermodynamic assumptions regarding the growth of condensation droplets and a mathematical formulation of droplet energy functionals. A model of the gas–liquid interface condensation rate based on kinetic theory is derived to clarify the relationship between condensation conditions and intermediate variables. The energy functional of a droplet, derived using the principle of least action, partially elucidates the inherent self-organizing growth laws of condensed droplets, enabling predictive modeling of the droplet’s growth. Considering the effects of the condensation environment and droplet heat transfer mechanisms on droplet growth dynamics, we divide the process into three distinct stages, marked by critical thresholds of 105 nm3 and 1010 nm3. Our model effectively explains why the observed contact angle fails to reach the expected Wenzel contact angle. This research presents a detailed analysis of the factors affecting surface condensation and heat transfer. The predictions of our model have an error rate of less than 3% error compared to baseline experiments. Consequently, these insights can significantly contribute to and improve the design of condensation heat transfer surfaces for the phase-change heat sinks in microprocessor chips.