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Recent investigations into coalescence dynamics of complex fluid droplets revealed the existence of sub-Newtonian behaviour for polymeric fluids (elastic and shear thinning). We hypothesize that such delayed coalescence or sub-Newtonian coalescence dynamics may be extended to the general class of shear thickening fluids. To investigate this droplets of aqueous corn-starch suspensions were chosen and its coalescence in sessile pendant configuration was probed by high-speed real time imaging. Temporal evolution of the neck (growth) during coalescence was quantified as a function of suspended particle weight fraction \phi_w. The necking behaviour was found to evolve as the power-law relation $R=at^b$ where R is neck radius with exponent $\b\le0.5$ implying it is a subset of the generic sub-Newtonian coalescence. Second significant delay in the coalescence dynamics is observed for particle fractions beyond the jamming fraction {\ \phi}_w>\ \phi_J\geq0.35}. Our proposed theoretical model captures this delay implicitly through altered suspension viscosity stemming from increased particle content.

Coalescence event in pendant and sessile drop is distinguished by the formation and evolution of the liquid bridge created upon singular contact. The bridge radius, $R$, is known to evolve as $R\sim t^b$, with power-law exponent, $b$, signifying the dominant governing forces. In this work, we experimentally explore the phenomenon in sub-classes of complex fluids namely, colloidal and non-colloidal suspensions that have particle hydrodynamic interactions as origin of viscoelasticity. Our observations suggest that such fluids have flow dependent thinning response with finite elasticity in shear flows but negligible in extensional flows. Based on these, the study extends the Newtonian universality of $b=0.5$ to these thinning fluids. Further we fortify these observations through a theoretical model developed by employing Ostwald-de Waele constitutive law. Finally, we utilize this theoretical model to inspect the existence of arrested coalescence in generalized Newtonian fluids.

We present a theoretical framework for capturing the coalescence of a pendant drop with a sessile drop in polymeric fluids. The framework is based on the unification of various constitutive laws under high Weissenberg creeping flow limit. Our results suggests that the phenomenon comes under a new regime namely, the sub-Newtonian regime followed by the limiting case of arrested coalescence with the arrest angle $\theta_{arrest}\propto Ec^{-1/2}$, where $Ec$ is the Elasto-capillary number. Further, we propose a new time scale $T^*$ integrating the continuum variable $Ec$ and the macromolecular parameter $N_e$, the entanglement density to describe the liquid neck evolution. Finally, we validate the framework with high speed imaging experiments performed across different molecular weights of Poly(ethylene oxide) (PEO).

Recent investigations on the coalescence of polymeric droplets on a solid substrate have reported strong disagreements; the heart of the issue is whether coalescence of polymeric drops is similar to that of Newtonian fluid and is independent of molecular relaxation, or whether the role of entanglement of polymeric chains leads to a transition kinetics different from that of Newtonian fluid. Via this report, we resolve the disagreements through a discussion on the effects of merging method on the dominant forces governing the coalescence process, i.e., inertia, dissipation, and relaxation. Our study unveils that the coalescence dynamics of polymeric drops is not universal and in fact, it is contingent of the method by which the coalescence is triggered. Additionally, we demonstrate the spatial features of the bridge at different time instants by a similarity analysis. We also theoretically obtain a universal bridge profile by employing the similarity parameter in a modified thin film lubrication equation for polymeric fluids.

Dynamics of the pendant drop coalescing with a sessile drop to form a single daughter droplet is known to form a bridge. The bridge evolution begins with a point contact between the two drops leading to a liquid neck of size comparable to the diameter of the drops. To probe this phenomenon in polymeric fluids, we quantify the neck radius growth during coalescence using high speed imaging. In the current study, we unveil the existence of three regimes on basis of concentration ratio $c/c^*$ namely, inertio-elastic $c/c^*20$. Our results suggest that the neck radius growth with time (t) obeys a power-law behaviour $t^b$, such that the coefficient $b$ has a steady value in inertio-elastic and viscoelastic regimes, with a monotonic decrease in elasticity dominated regime. Based on this dependence of $b$ on concentration ratios, we propose a new measurement technique Rheocoalescence to obtain the relaxation time of the these fluids. We also show a deviation from universality proposed in literature for the elasticity dominated regime.

Coalescence of sessile polymeric fluid drops on a partially wettable substrate exhibits a transition from inertial to viscoelastic regime at concentration ratio $c/c^* \sim 1$. Our findings unveil that the temporal evolution of the growing bridge height follows a power-law behaviour $t^b$, such that the coefficient $b$ continuously decreases from 2/3 in the inertial regime ($c/c^*<1$) to an asymptotic value of 1/2 in the visco-elastic regime ($c/c^*>1$). To account for fluid elasticity and characteristic time-scale in the viscoelastic regime, a modified thin film equation under lubrication approximation has been proposed using the linear Phan-Thien- Tanner constitutive equation. The temporal evolution of the droplet has been evaluated by solving the modified one-dimensional thin-film equation using a marching explicit scheme. The initial droplet shapes are obtained by re-sorting to energy minimization. A good agreement between numerical and experimental results is obtained.

Coalescence of liquid droplets involves an interplay between capillary forces, viscous forces and inertial forces. Here, we unveil a universal temporal evolution of the neck radius during the coalescence of two polymeric drops. Through high speed imaging we demonstrate that drops of polyacrylamide (PAM), poly-vinyl alcohol (PVA), polyethylene oxide (PEO), polyethylene glycol (PEG) and xanthan gum (XG) depict a universal behavior $R/\sqrt(\nu_0\lambda) \sim (t/\lambda)^{0.36}(C/C^{*})^{-0.83}$ over a dilute, semi-dilute and non-dilute range of concentrations. A linear Phan-Thein-Tanner viscoelastic model captures the temporal aspect of universality., Comment: 3 Figures. Soft Matter, 2020