The coalescence speed of a pendent and a sessile drop

Abstract

When two liquid drops come into contact, they coalesce rapidly, owing to the large curvature and unbalanced surface-tension forces in the neck region. We use an ultra-high-speed video camera to study the coalescence of a pendent and a sessile drop, over a range of drop sizes and liquid viscosities. For low viscosity, the outward motion of the liquid contact region is successfully described by a dynamic capillary-inertial model based on the local vertical spacing between the two drop surfaces. This model applies even when the drops are of different sizes. Increasing viscosity slows down the coalescence when the Reynolds number $\hbox{\it Re}_v \,{=}\,\rho R_{\hbox{\scriptsize\it ave}}\sigma/\mu^2\,{<}\,5000$, where $R_{\hbox{\scriptsize\it ave}}$ is the average of the tip radii of the two similar size drops, $\rho$ is the liquid density, $\sigma$ is the surface tension and $\mu$ the dynamic viscosity. At $\hbox{\it Re}_v\,{\simeq}\,50$, the growth-rate of the neck radius has reduced by a half, which for water corresponds to a drop diameter of only 2\,$\umu$m. For the largest viscosities, the neck region initially grows in size at a constant velocity. The neck curvature also becomes progressively sharper with increasing viscosity. The results are compared to previously predicted power laws, finding slight, but significant deviations from the predicted exponents. These deviations are most probably caused by the finite initial contact radius.

Hydrodynamics of Droplet Coalescence

“…The latter has recently been observed in other experiments [7,8]. We achieve in observing the linear dependence not only by increasing the viscosity considerably as, for example, very recently shown in [9,10], but also by decreasing the surface tension by 5 orders of magnitude. To this end, we use a molecular system with a variable (high) viscosity and a colloid-polymer mixture with an ultralow surface tension [11,12].…”

“…Once this problem was solved, fitting with t 0 as an adjustable parameter or choosing the frame corresponding to t 0 directly yielded similar results. It seems plausible that the observed finite initial contact radius in the experiments of Thoroddsen et al [10] is due to the shadow effect. The main difference between the values reported here and in Ref.…”

Short time dynamics of viscous drop spreading

“…1(a) is strongly reminiscent to the coalescence of two spherical drops, if we consider the substrate to act as a mirror-plane for the flow. This analogy was first employed by Biance et al 12 , who compared the spreading to the well-studied growth of the neck when two identical drops coalesce [13][14][15][16][17] . This approach has proven very successful in the low-viscosity limit.…”

A note on the critical gap of bubble coalescence during foaming process: A diffuse-interface modeling

“…Dirk et al studied droplet coalescence in a molecular system for di erent viscosities and an ultralow surface tension [21]. Thoroddsen et al used an ultra-high-speed video camera to study the coalescence for di erent drop sizes and liquid viscosities [22]. Duchemin et al studied the coalescence of two droplets where they assumed approach velocity of zero and neglected the dynamical e ects of the outer uid.…”