SHAPE OF A FLUID DROP APPROACHING AN INTERFACE

The shape of a fluid drop approaching an interface does not change appreciably with time and is very close to the equilibrium dimensions, in spite of the large pressure gradient which is present in the draining film. This is because the net vertical force due to the excess pressure in the draining film above that in the drop is identical with that for an equilibrium film being zero for a plane interface and —2Rσ sin2 ϕ for a deformable interface. Employing this result in a force balance around the drop which is independent of the bulk interface shows that the area A of the draining film between a fluid drop of volume V and a deformable fluid‐liquid interface is given by (Formula Presented.) where σ is the interfacial tension and Δρ the density difference between the drop and surrounding fluid, 1/b is the curvature at the top of the drop and h is the distance between this point and the edge of the draining film which is inclined to the horizontal at an angle ϕ. When the interface is a rigid plane the overall curvature 1/R of the draining film and the volume v enclosed by it, together with the angle ϕ are all zero. The limiting cases of the expression for very small and very large drops agree with those previously established for both deformable and rigid interfaces. An approximate expression which applies when cV2/3 (where c = Δρg/σ) is between 0.6 and 13.5 and which gives A to within ± e% is (Formula Presented.) where for a rigid plane interface (Formula Presented.) and for a deformable interface (Formula Presented.) When the densities of the drop and bulk heavy fluids are equal, but their respective interfacial tensions σ12 and σ23 with the light fluids are different, the expression becomes (Formula Presented.) which estimates A/V2/3 to within about ± 25% for σ12/σ23 in the range 0.11 to 9.0 and cV2/3 (where c = Δρg/σ12) between 0.6 and 13.5. Copyright © 1969 Canadian Society for Chemical Engineering