Scalings in Coalescence of Liquid Droplets

TL;DR

This paper develops a scaling theory for the coalescence of viscous liquid droplets, analytically solving the evolution of the neck radius and capturing the viscous-inertial crossover observed experimentally.

Contribution

It introduces a new analytical solution to the coalescence problem that unifies viscous and inertial regimes and explains experimental crossover behavior.

Findings

Analytical solutions reproduce known viscous and inertial scaling laws.

The theory captures the viscous-inertial crossover observed experimentally.

Fitting relations approximate the general solution, collapsing data across viscosities.

Abstract

This letter presents a scaling theory of the coalescence of two viscous spherical droplets. An initial value problem was formulated and analytically solved for the evolution of the radius of a liquid neck formed upon droplet coalescence. Two asymptotic solutions of the initial value problem reproduce the well-known scaling relations in the viscous and inertial regimes. The viscous-to-inertial crossover experimentally observed by Paulsen et al. [Phys. Rev. Lett. 106, 114501 (2011)] manifests in the theory, and their fitting relation, which shows collapse of data of different viscosities onto a single curve, is an approximation to the general solution of the initial value problem.