# Unified Viscous-to-inertial Scaling in Liquid Droplet Coalescence

## TL;DR

This paper develops a unified theory for liquid droplet coalescence that accurately describes the transition from viscous to inertial regimes, matching experimental data without free parameters.

## Contribution

It introduces an exact, parameter-free solution for the neck radius evolution during droplet coalescence, unifying viscous and inertial scaling laws.

## Key findings

- Exact solution reproduces known scaling laws
- Unified description captures viscous-inertial crossover
- Data collapse onto a single curve across viscosities

## Abstract

This letter presents a theory on the coalescence of two spherical liquid droplets that are initially stationary. The evolution of the radius of a liquid neck formed upon coalescence was formulated as an initial value problem and then solved to yield an exact solution without free parameters, with its two asymptotic approximations reproducing the well-known scaling relations in the viscous and inertial regimes. The viscous-to-inertial crossover observed by Paulsen et al. [Phys. Rev. Lett. 106, 114501 (2011)] is also recovered by the theory, rendering the collapse of data of different viscosities onto a single curve.