Journal of Fluid Mechanics


The coalescence speed of a pendent and a sessile drop

a1 Mechanical Engineering, National University of Singapore, 9 Engineering Drive 1, Singapore 117576
a2 Civil and Environmental Engineering, Kinki University, Higashi-Osaka 577-8502, Japan

Article author query
thoroddsen st   [Google Scholar] 
takehara k   [Google Scholar] 
etoh tg   [Google Scholar] 


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.

(Published Online March 9 2005)
(Received February 11 2004)
(Revised September 27 2004)