# Experimental–theoretical analysis of cooling and freezing of a droplet in contact with a cold substrate: influence of substrate wettability

## TL;DR

This paper studies how droplets cool and freeze on cold surfaces, using experiments and models to show how surface properties affect the process.

## Contribution

The study introduces a new mixed lumped-differential model for heat transfer during droplet freezing, validated with experimental data.

## Key findings

- The mixed model accurately predicts droplet surface temperatures during supercooling.
- Hydrophilic and hydrophobic substrates significantly influence freezing dynamics.
- Classical lumped system analysis fails to capture the observed freezing behavior.

## Abstract

The physics and modelling of cooling and freezing of droplets in contact with a colder substrate are of interest in various engineering applications. This work provides experimental results of this process employing infrared thermography for temperature measurements at the droplet’s surface. Also, a high-speed camera is employed to observe the recalescence period and measure the freezing front movement and the droplet shape change. Three substrates are prepared with distinct wettability ranges, i.e. one hydrophilic and two hydrophobic surfaces. From the experimental observation of a solidification front parallel to the substrate plane, a mixed lumped-differential model of the heat transfer process based on the Coupled Integral Equations Approach is proposed, reformulating the two-dimensional partial differential formulation in cylindrical coordinates into a one-dimensional transient energy equation for the droplet external surface temperature. Direct comparisons of the experimental and theoretical results for the supercooling period show excellent agreement for the droplet surface temperatures at different heights and for different values of the substrate–droplet contact angle. It is also shown that the classical partial lumped system analysis does not provide adequate predictions in the present problem. Finally, the dynamics of the recalescence and freezing stages are experimentally evaluated and physically interpreted.

This article is part of the theme issue ‘Heat and mass transfer in frost and ice’.