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

Abstract

Head-on collisions of two immiscible liquid droplets lead to a collision complex, which may either remain stable in the form of a single compound drop, or fragment into two main daughter droplets. This paper investigates the liquid distribution developing in the two daughter droplets and which can be of three types. Either two encapsulated droplets (single reflex separation) form, or a single encapsulated drop plus a droplet made solely of the encapsulating liquid, which can be found either on the impact side (reflexive separation) or opposite to it (crossing separation). A large number of experimental and simulation data covering collisions with partial and total wetting conditions and with Weber and Reynolds numbers in the ranges of 2 - 720 and 66 - 1100, respectively, is analyzed. The conditions leading to the three mentioned 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, $\Lambda = {\rho_i/\rho_o} {{We_i}^{-1/2}}$ and $N = {\nu_o/\nu_i}~{\sigma_{o}/\sigma_{io}}$, are derived, which are built on the collision parameters and liquid properties of the encapsulated inner droplet (i) and the outer droplet (o) only. In agreement with the proposed interpretation, the combination of these two parameters predicts the type of liquid distribution. The predictions are found to be in very good agreement with both experimental and numerical results.