Spreading of water-in-oil emulsion drop on oleophilic surface

This study deals with three-dimensional numerical simulation of the drop spreading of water-in-oil (W/O) emulsions with different concentrations of dispersed phase on a solid oleophilic wall. The apparent viscosity values measured by rotational and drop impact viscometry (DIV) are used to describe high-shear rate rheological behavior; the Hershel-Bulkley emulsions are modeled for shear-thinning behavior. The vortex flow from dispersed phase microdroplets in the spreading drop volume and in the boundary layer is modeled using the standard k-ϵ and Langtry-Menter k-ω shear stress transport models, respectively. Due to the proper packing of the dispersed phase, the influence of vortex flow on the maximum spreading is strongest at a mean emulsion concentration of 30 wt. %, as well as at higher drop impact velocities U₀. As U₀ rises, a fourfold increase in the vorticity magnitude is found in the vicinity of the boundary layer. The study employs a DIV-based approach to estimate the viscosity at shear rates relevant to drop impact that are not accessible with conventional rheological methods, thereby confirming the complexity of emulsion rheology at high shear rates. In interconnected numerical simulation of complex rheology and vortex flow of the dispersed phase of emulsions with respect to maximum spreading, the validity of the empirical expression for predicting the maximum spreading factor of emulsion drops β_max = 0.82(We/Oh)^0.15 [Semyonova et al., “Dynamic and kinematic characteristics of unsteady motion of a water-in-oil emulsion droplet in collision with a solid heated wall under conditions of convective heat transfer,” Int. Commun. Heat Mass Transfer 137, 106277 (2022)] is substantiated. The results are critical in developing the emulsions in terms of high-shear rate rheology and optimizing ink spray, inkjet, and drop-on-demand processes.