# Coalescence of Leidenfrost drops: Numerical simulations using the dynamic van der Waals theory

## TL;DR

This study uses numerical simulations based on the dynamic van der Waals theory to investigate how Leidenfrost drops repel each other and resist coalescence due to vapour build-up, revealing size-dependent effects.

## Contribution

It introduces a detailed numerical model for Leidenfrost drop interactions, highlighting the role of vapour pressure in short-range repulsion and coalescence prevention.

## Key findings

- Strong short-range repulsion due to vapour build-up
- Repulsion scales with vapour pressure similar to single drop models
- Existence of a threshold size for overcoming repulsion

## Abstract

The Leidenfrost effect describes liquid drops under gravity levitating on a vapour cushion, which is sourced at the liquid-vapour interface from evaporation caused by the hot substrate below. It has been experimentally observed that when two or more Leidenfrost drops approach one another, there is a short-range repulsion that can prevent coalescence. In the present work, we investigate the coalescence process of initially momentum-less Leidenfrost drops. This is carried out by numerically simulating two-dimensional systems of liquid and vapour using the recently developed dynamic van der Waals theory, in which the two-phase hydrodynamics is coupled with liquid-vapour transition. It is confirmed that Leidenfrost drops experience a remarkably strong short-range repulsion, due to a build-up of vapour in the common space under both drops. This resistive force scales in a similar manner to the pressure-sourced force from the vapour layer under a single drop, in concurrence with intuition, with good agreement seen in the simulation results. A threshold drop size therefore exists in order for an applied horizontal acceleration to overcome the repulsion, while only very small drops are predicted to experience significant viscous effects.