Session G30: Drops: Coalescence I

Jump-to-Contact between Viscous Drops under van der Waals Attraction

The coalescence of viscous drops is significantly affected by any drop deformation prior to contact. For slowly moving drops in close proximity, van der Waals attraction between the drops overcomes surface tension and initiates a dynamic 'jump-to-contact' process where the van der Waals attraction deforms the drops' surfaces so that they make contact. This process sets the initial surface profile for the subsequent coalescence of the drops.

This talk will discuss the jump-to-contact process across an inviscid gap, showing that as contact is approached the dynamics are self-similar with both the radial and gap scales varying as t'^1/3. for time until contact t'. The leading order balance is between van der Waals attraction and viscous forces. Although surface tension is subdominant, it selects the observed t'^1/3 behaviour from a continuous range of possible time-exponents. Interestingly, the self-similar profiles are non-universal and retain some memory of the initial conditions. The self-similar surface profiles will inform suitable initial conditions for subsequent drop coalescence.   

Coalescence of viscoelastic sessile drops

Coalescence and breakup are classic problems in fluid physics that often involve self-similarity and singularity formation. Although the coalescence of sessile drops is inherently three dimensional, it has only been studied so far in two dimensions. Here, we experimentally and theoretically study the dynamic evolution of the three-dimensional shape of the interface during the coalescence of sessile drops. First, we will briefly summarize our findings regarding the three-dimensional self-similarity of the coalescence of Newtonian drops (joint work with A. A. Pahlavan and N. Xue). Then, we will explore some of the influences of elasticity on the dynamics. For polymeric drops, we show that the dynamics of the width of the bridge that grows outward on the substrate differs from the Newtonian case. We further study the three-dimensional evolution of the interface and investigate how elasticity modifies the coalescence behavior.   

Role of interfacial viscosity on droplet coalescence

In this work, we perform boundary-integral simulations to explore the role of surface viscosity on the early stages of coalescence of two equal-sized droplets in an axisymmetric extensional flow under the Stokes flow limit. We model the surface rheology of the droplet using the Boussinesq–Scriven constitutive relationship for a Newtonian interface. Previous studies have shown that colliding droplets at low capillary numbers (i.e., low impact velocities) remain almost spherical up to the point of film rupture, while droplets at large values of capillary number form dimples during the early stages of coalescence that significantly slows down the drainage time. We present how the interfacial viscosity affects the dimple formation during a head-on collision and the scaling of the film drainage time with capillary number values in the range 10^-4 - 10^-2. We observe that the surface viscosity significantly arrests the thinning of the film between the coalescing droplets compared to a clean interface. We find that the film drainage time at a given capillary number increases upon increasing the Boussinesq parameter for total surface viscosity and is independent of the ratio of surface dilational viscosity to the surface shear viscosity. We also explore the coupled influence of surface viscosity and Marangoni stresses on droplet coalescence. We incorporate the effect of surfactant transport by solving the time-dependent convection-diffusion equation and consider a nonlinear equation of state (Langmuir adsorption isotherm) to correlate the interfacial tension with the changes in surfactant concentration. 

    

Molecular simulation study of the initial stages of droplet coalescence

Coalescence plays a crucial role in nature and industry. In prior continuum analyses, a microscopic bridge joining two drops is assumed to have already formed at the start of coalescence. At these early times, the bridge curvature is exceedingly large, yielding a diverging Laplace pressure at the point of contact between the drops. This singularity generates a flow that leads to drop merging. Continuum analyses identify two regimes for the temporal growth of the bridge. Coalescence, however, is initiated at length and time scales at which the discrete nature of matter is of importance and a continuum description provides no information about the actual formation of the bridge. To provide molecular-level insights, we study the initial stages of coalescence using a hybrid Monte Carlo-Molecular Dynamics (MC-MD) simulation method. We reduce the required computational effort by only simulating those parts of the drops directly facing each other. Particle reservoirs, along with grand canonical MC steps (GCMC), are used to maintain the bulk densities of the drops at specified values. These GCMC steps also enable the drops to be both thermally and chemically equilibrated prior to coalescence eliminating any potential evaporative phenomena that may confound the analysis.