Water-in-oil emulsion drop-wall impact: Effect of viscosity and water particles on slip length over an oleophilic surface

The study is focused on the numerical simulation of the boundary slip of a water-in-oil (W/O) emulsion along an oleophilic surface in a 2D axisymmetric formulation of the Navier–Stokes equations for an incompressible laminar flow. Drops of emulsions with a volume fraction of the dispersed phase of 0.04–0.34 collide with a smooth glass wall at initial velocities of 1.2–3.6 m/s; the motion of the interface between the liquid and gas phases is resolved by the level set method. The influence of the wall wettability by oily liquids is demonstrated by varying the static contact angle up to 0.5° and by considering the dynamic one as a function of the empirically measured contact line velocity of the liquid drop according to Tanner's law. Numerical simulation of emulsion drop spreading dynamics reveals that the boundary slip of a heterogeneous liquid along a smooth oleophilic wall is different from that of a homogeneous. The temporal changes in the average viscous stress allowed the illustration of the interrelated effects of emulsion viscosity and the presence of disperse phase particles on the boundary slip of a heterogeneous liquid and its motion in the viscous boundary layer. The analytical expression evaluating the slip length for an arbitrary W/O emulsion was derived using the effective properties of the liquid. In testing the expression, the values of the maximum spreading factor of drops of an arbitrary W/O emulsion predicted by numerical simulation correspond to those determined from experiments at a moderate error of 7.4%.