PT - JOURNAL ARTICLE
AU - Xia, Xi
AU - He, Chengming
AU - Zhang, Peng
TI - Universality in the viscous-to-inertial coalescence of liquid droplets
AID - 10.1073/pnas.1910711116
DP - 2019 Nov 19
TA - Proceedings of the National Academy of Sciences
PG - 23467--23472
VI - 116
IP - 47
4099 - http://www.pnas.org/content/116/47/23467.short
4100 - http://www.pnas.org/content/116/47/23467.full
SO - Proc Natl Acad Sci USA2019 Nov 19; 116
AB - Most existing literature considers the viscous and inertial regimes of droplet coalescence separately. A recent experiment indicated a universality in the neck-evolution process for coalesced droplets of various viscosities. This work presents a theory that resolves the unified neck evolution in the viscous-to-inertial combined coalescence process. The 2 asymptotic approximations of the theory recover the well-known scaling relations in the inertially limited viscous and the inertial regimes, respectively, with the scaling coefficients predicted explicitly by the solution. Our approach also sets an example of how viscous-to-inertial transition might be dealt with analytically in other similar problems.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.