The interaction of falling water drops: coalescence

Abstract

Experimental studies have been conducted of the interaction of falling water drops of radii R and r (R > r), density $\rho $ and surface tension $\sigma $ colliding in air with a relative velocity U and a perpendicular distance X between the centre of one drop and the undeflected trajectory of the other. R and r were varied from 150 to 750 $\mu m$, R/r from 1.0 to 2.5, U from 0.3 to 3.0 m s$^{-1}$ and X from 0 (head-on collisions) to the maximum value for contact, R+r. Four types of interaction were observed: (1) bouncing; (2) permanent coalescence; (3) coalescence followed by separation; (4) coalescence followed by separation and the formation of satellite drops. The principal effort was devoted to a study of the critical conditions under which drops will separate after coalescence. It was found that there was a critical value of X, denoted by $X_{\text{c}}$, below which the coalesced drops remained united and above which there was sufficient angular momentum for the drops to separate after coalescence. For a wide range of values of r, R and U the coalescence efficiency $\epsilon =X_{\text{c}}/R+r)^{2}$ was found to lie between 0.1 and 0.4 for drops of identical size and about 0.2 and 0.6 for drops with R/r = 2.0. A theoretical analysis based on energy concepts predicted that the coalescence efficiency is given by the equation $\epsilon =2.40\left(\frac{\sigma}{U^{2}r\rho}\right)f(R/r)$, where $f(R/f)$ is a function which varies from 1.3 for R/r = 1 and 3.8 for R/r = 3. The predictions of this equation were in excellent agreement with the experimental results over the entire range of conditions studied. Investigations are also described of the critical conditions for the bouncing of colliding drops, the influence of electric charges upon the interactions and the elongation and splitting of a rotating drop.