Coalescence of sessile drops

TL;DR

This paper investigates the rapid coalescence and relaxation dynamics of water drops on a solid surface, revealing an exceptionally large relaxation time influenced by phase change kinetics, supported by experimental and theoretical analysis.

Contribution

It introduces a model explaining the large relaxation time involving phase change kinetics near the contact line, supported by experimental data.

Findings

Relaxation time is proportional to final drop radius R*

Relaxation time is about 10^7 times larger than capillary relaxation time

Model predicts exponential relaxation consistent with experiments

Abstract

We present an experimental and theoretical description of the kinetics of coalescence of two water drops on a plane solid surface. The case of partial wetting is considered. The drops are in an atmosphere of nitrogen saturated with water where they grow by condensation and eventually touch each other and coalesce. A new convex composite drop is rapidly formed that then exponentially and slowly relaxes to an equilibrium hemispherical cap. The characteristic relaxation time is proportional to the drop radius R * at final equilibrium. This relaxation time appears to be nearly 10 7 times larger than the bulk capillary relaxation time t b = R * $\eta$/$\sigma$, where $\sigma$ is the gas--liquid surface tension and $\eta$ is the liquid shear viscosity. In order to explain this extremely large relaxation time, we consider a model that involves an Arrhenius kinetic factor resulting from a liquid--vapour phase change in the vicinity of the contact line. The model results in a large relaxation time of order t b exp(L/RT) where L is the molar latent heat of vaporization, R is the gas constant and T is the temperature. We model the late time relaxation for a near spherical cap and find an exponential relaxation whose typical time scale agrees reasonably well with the experiment. 1. Introduction Fusion or coalescence between drops is a key process in a wide range of phenomena: phase transition in fluids and liquid mixtures or polymers, stability of foams and emulsions, and sintering in metallurgy (Eggers 1998), which is why the problem of coalescence has already received considerable attention. Most of the studies of this process so far have been devoted to the coalescence of two spherical drops floating in a medium. The kinetics of the process before and after the drops have touched each other is governed by the hydrodynamics inside and outside the drops and by the van der Waals forces when the drops are within mesoscopic distance from each other (Yiantsios \& Davis 1991). The composite drop that results from the coalescence of two drops relaxes to a spherical shape within a time which is dominated by the relaxation of the flow inside and outside (Nikolayev, Beysens \& Guenoun 1996; Nikolayev \& Beysens 1997). There are no studies, to our knowledge, of the coalescence of two sessile drops after they touch each other. In this paper, we report a preliminary study of the dynamics and morphology of this process, in the case of hemispherical water droplets which grow slowly on a plane surface at the expense of the surrounding atmosphere, forming what is called 'dew' or 'breath figures' (Beysens et al. 1991; Beysens 1995). The drops eventually touch each other and coalesce to form an elongated composite