(627e) A Novel Hydrodynamic Film Drainage between an Emulsion Drop and a Surface to Predict Key Surface Wetting Rates

Emulsions represent a family of complex fluids consisting of a liquid drop phase existing in metastable equilibrium inside a second, immiscible suspending phase. Despite their universal occurrence across several industries, the formulation of emulsions still occurs through trial-and-error, or via semi-empirical approaches, as fundamental relationships between their composition, processing, structure, and function/properties remain unknown. Over longer timescales, a settling emulsion drop will eventually phase separate and wet the substrate surface (figure 1(a)). A well-designed emulsion should therefore remain uniformly dispersed and not coarsen and phase separate over its target shelf-life. Detailed asymptotic analysis^[1] by Yiantsios and Davis have attempted to understand the deformation of such a viscous drop, under creeping flow conditions with asymptotically low Bond numbers and neglecting Gibbs-Marangoni effects. They reveal that the lubrication film retains the spherical film up to a point, after which the film may transition to a dimpled shape. The drainage timescale t in the spherical field relates to the film height h logarithmically (t∝ln h), and as h∼t^-1/2 when the film starts to dimple strongly. But it is evident by performing a simple scaling analysis (table 1) that there must exist a transition regime B prior to the film flattening out, where the drop continues to retain its spherical shape, yet the drainage timescale relies on the interfacial tension γ, a deformation parameter. Likewise, before the film experiences strong dimpling, another “weakly dimpled” regime D must also exist. The incorporation of these two regimes, in addition to the previously detected ones, forms a complete picture of emulsion drainage.

In this work, a novel hydrodynamic scaling theory is derived to quantitatively describe the descent dynamics of an emulsion drop settling towards a rigid substrate surface, under low Reynolds and Bond number conditions. We postulate the existence of five key drainage regimes (figure 1(b)) that the drop encounters, prior to wetting the surface. Glycerol–silicone oil emulsion systems approaching differently treated mica surfaces (pristine, native SU8 coated, plasma treated SU8) were studied in our experiments. Film drainage dynamics of the glycerol drop are imaged using Reflection Interference Contrast Microscopy (RICM), under two different wavelengths (λ_Blue=485 nm, λ_Green=549 nm). Post-processing of the captured image frames was performed using ImageJ and MATLAB, and dual wavelength theory, with an enhanced back-ray tracing improvement algorithm (accounting for angular averaging), is employed to reconstruct spatiotemporal height profiles and obtain the minimum heights. Fitted dimensionless equations corresponding to each regime, within a 95% confidence interval, are obtained and all associated pre-factors are evaluated out. There are five regimes that a settling drop of an undeformed drop radius R_d encounters, prior to wetting a rigid surface. Regime A corresponds to an initially spherical drop settling in the far-field; regime B is encountered when the drop continues to remain spherical, but the film pressure P_f steadily approaches the Laplace pressure γ/R_d. When the film pressure begins to scale as the Laplace pressure i.e., P_f∼γ/R_d, the drop flattens out, entering the flat film regime C. In the flat film configuration, the pressure is higher at the centre of the film and decreases to the ambient pressure at the edge. This results in the film slightly deforming into a weakly dimpled configuration, i.e., regime D. Eventually, the thin film experiences even stronger dimpling and enters the final regime E. Two of these regimes (B and D) are novel; and existence of the weak dimpling regime D also serves to formally distinguish between the flat film regime C and the strong dimpling regime E, which have been traditionally mistaken to be one, as an identical scaling of h_min∼t^-1/2 arises in both. Finally, a composite wetting equation is obtained to describe the drainage time required, for these systems. With the exception of when the drop lies in the extreme far field (h_min∼e^-t), minimum film heights for each regimes scale as inverse negative fractional powers of the drainage time (h_min∼t^-1, h_min∼t^-1/2, h_min∼t^-2/3 and h_min∼t^-1/2). Although this theory does not incorporate non-hydrodynamic interactions and considers rather small drops (R_d∼O (few hundred μms)) undergoing purely axisymmetric drainage, the match with experiments is found to be excellent. The scaling theory will be followed by detailed hydrodynamic theory based on the boundary integral method. Direct application of such a composite wetting theory is to apriori predict the shelf-lives of several commercially/industrially relevant emulsions, thereby shifting the design procedure towards more quantitative, reproducible pathways.

Reference:

[1] G. Yiantsios and R.H. Davis, J. Fluid Mech. 217, 547–573 (1990).