Liquid distribution after head-on separation of two colliding immiscible liquid droplets

Equally sized droplets made of the same liquid are known to either bounce, coalesce, or separate under collision. Comparable outcomes are observed for immiscible liquids with bouncing, encapsulation instead of coalescence, and separation with two or more daughter droplets. While the transitions between these regimes have been described, the liquid distribution arising from separation remains poorly studied, especially in the case of head-on collisions, for which it cannot be predicted. This distribution can be of three types: either two encapsulated droplets form (single reflex separation), or a single encapsulated droplet plus a droplet made solely of the encapsulating liquid emerge, the latter being found either on the impact side (reflexive separation) or opposite to it (crossing separation). In this paper, a large number of experimental and simulation data covering collisions with partial and total wetting conditions and Weber and Reynolds numbers in the ranges of 2–720 and 66–1100, respectively, is analyzed. The conditions leading to the three liquid distributions are identified and described based on the decomposition of the collision in two phases: (i) radial extension of the compound droplet into a lamella and (ii) its relaxation into an elongated cylindrical droplet. In accordance with these two phases, two dimensionless parameters, $Λ = ρ i / ρ o W e i − 1 / 2$ and $N = ν o / ν i σ o / σ i o$⁠, are derived, which are built on the collision parameters and liquid properties of the encapsulated inner droplet (i) and the outer droplet (o) only. The combination of these two parameters predicts the type of liquid distribution in very good agreement with both experimental and numerical results.