MICHAEL MANGA: Recent Refereed Publications
Manga, M. and H.A. Stone (1993) Buoyancy-driven interactions between
deformable drops at low Reynolds numbers, Journal Fluid Mechanics, vol. 256,
Time-dependent interactions between two buoyancy-driven deformable
drops are studied in the low Reynolds number flow limit for sufficiently
large Bond numbers that the drops become significantly deformed.
The first part of this paper considers
the interaction and deformation of axisymmetric drop
Boundary integral calculations
are presented for Bond numbers
B= Delta rho g a^2/sigma in the
range 0.25 < B < infinity and
viscosity ratios lambda in the range 0.2 < lambda< 20.
Specifically, the case of a large drop following a smaller drop is
considered, which typically leads to the smaller drop coating the larger
drop for B >> 1.
distinct drainage modes of the thin film of fluid between the drops
characterize axisymmetric two drop interactions:
(i) rapid drainage for which the thinnest region of the film is
on the axis of symmetry, (ii) uniform drainage for which the film
has a nearly constant thickness, and (iii) dimple formation.
The initial mode of film drainage is always rapid
drainage. As the separation distance decreases, film flow
may change to uniform drainage and eventually to dimpled
Moderate Bond numbers, typically B=O(10) for
lambda=O(1), enhance dimple
formation compared to either much larger or smaller Bond
The numerical calculations also illustrate the extent to which
lubrication theory and analytical solutions in bipolar coordinates
(which assume spherical drop shapes) are applicable to deformable
The second part of this investigation considers the "stability" of axisymmetric
Laboratory experiments and two-dimensional
boundary integral simulations are used to study
the interactions between two horizontally offset drops.
For sufficiently deformable drops, alignment occurs so that the small
drop may still coat the large drop, whereas for large enough drop viscosities
or high enough interfacial tension, the small drop will be swept around
the larger drop. If the large drop is sufficiently deformable, the
small drop may then be "sucked" into the larger drop as it is being swept
around the larger drop.
In order to explain the alignment process,
the shape and translation velocities of widely separated, nearly spherical
drops are calculated
using the method of reflections and a perturbation analysis
for the deformed shapes.
The perturbation analysis demonstrates explicitly that
drops will tend to be aligned for B > O(d/a) where
d is the separation distance
between the drops.
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