Universality in the viscous-to-inertial coalescence of liquid droplets

Abstract

We present a theory on the coalescence of 2 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 2 asymptotic approximations reproducing the well-known scaling relations in the inertially limited viscous and inertial regimes. The viscous-to-inertial crossover observed in previous research is also recovered by the theory, rendering the collapse of data of different viscosities onto a single curve.

Universality in coalescence of polymeric fluids

“…We have also confirmed that 42 R c = OhD o and t c = ZOhD o /s taking DI water as a Newtonian fluid. We have extended the importance of Oh as an important non-dimensional number for polymeric fluids through the inclusion of l in the characteristic scales to hallmark the distinction of a polymeric fluid.…”

“…For a Newtonian fluid, the nondimensional neck radius R 1 * = R/OhD o and nondimensional time t 1 * = ts/ZOhD o results in the scaling of R 1 * p t 1 * 0.5 in the inertial regime. 42 Such scaling for DI water is shown in Fig. S1 in ESI, † for the inertial regime.…”

“…In the literature, regime-wise universality in droplet coalescence has been demonstrated, both experimentally and analytically [24][25][26][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42] for Newtonian fluids. For such drops, it has been established that the kinematics of the phenomenon is governed by the growth of the liquid bridge that can be typically characterized by the temporal change of the neck radius.…”

Self-Similar Liquid Lens Coalescence

“…Subsequently, we develop a fully quantitative slender description for each of these regimes based on the self-similar nature of coalescence. In the spirit of recent work on spherical drops [10,30], we identify the master curve for all data, including the crossover between the two regimes. Unlike for any other coalescence problem, however, the master curve here is obtained without any adjustable parameter.…”

Surface bubble coalescence

“…If , further neck growth is inertial: (Paulsen et al. 2012), and a unified theory for this transition was identified by Xia, He & Zhang (2019).…”