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Significance 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.

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