Jet pinch-off and drop formation in immiscible liquid±liquid systems
D. R. Webster, E. K. Longmire
Abstract The behavior of glycerin±water jets ¯owing into
immiscible ambients of Dow Corning 200 ¯uid was in-
vestigated using laser induced ¯uorescence (LIF). Undis-
torted images were obtained by matching the index of
refraction of the ¯uids. A sinusoidal perturbation was
superposed on the ¯ow to phase lock the drop formation.
The forcing frequency dramatically affected the size,
spacing, and number of drops that formed within a forcing
cycle and the angle between drops and the jet interface just
before pinch-off. Two ¯uid combinations were studied
with similar density ratios, but viscosity ratios differing by
a factor of 20. The viscosity ratio affected the jet stability as
well as pinch-off angles and drop size.
A fundamental phenomenon in ¯uid dynamics involves
changes in the topology of interfaces between nominally
immiscible ¯uids. Common examples of topological
changes are pinch-off of a continuous jet into droplets and
droplet reconnection. Because of the importance of such
¯ows, it is desirable to develop accurate models for mix-
ing, separation, and reaction rate that are applicable to a
wide variety of ¯ow geometries and parameters. Before
such models can be developed, however, it is crucial to
understand the dynamics of topological transitions.
The dynamics of topological transitions are dif®cult to
characterize for several reasons. First, a number of ¯uid
properties, such as density, viscosity, interfacial tension,
and diffusivity, may play a role in the transition process.
Second, ¯ow parameters, such as the dominant length and
velocity scales, affect the balance of inertial, buoyant,
viscous, and interfacial tension forces that determine the
timing and nature of transitions. In particular, the tran-
sitions typically result from a competition between ¯ow
instabilities due to shear or buoyancy, and stabilizing in-
¯uences due to interfacial tension and viscosity. Finally,
the transitions themselves usually occur over very short
time scales relative to local ¯ow time scales. Therefore, the
transitions are often dif®cult to observe experimentally.
The goal of this study is to investigate the fundamental
behavior of jet pinch-off and the resulting drop formation.
The ¯ow of a liquid jet into a second `immiscible'
liquid has been studied by a number of investigators due
to its occurrence in many chemical processing systems.
(For example, see Scheele and Meister 1968; Meister and
Scheele 1969a, b; Skelland and Johnson 1974; Kitamura
et al. 1982; Richards and Scheele 1985; Tadrist et al. 1991;
Richards et al. 1994.) Meister and Scheele performed
experiments on a large number of ¯uid combinations in
order to determine empirical relationships for jet length
and resulting drop size based on input parameters.
Skelland and Walker (1989) determined similar rela-
tionships that included the effects of surfactants. One
important trend shown by these experiments was the
in¯uence of Reynolds number on the `mode' of the ¯ow
downstream. In general, for low Reynolds numbers,
droplets form at and detach from the jet outlet. As Re is
increased, the injected ¯uid forms a jet that develops
axisymmetric instabilities and eventually pinches off at a
®nite length. Above a certain maximum Reynolds
number, three-dimensional instabilities occur, and the jet
length begins to decrease. The Re range corresponding to
each ¯ow mode depends signi®cantly on the other system
A number of studies have focused on the detailed be-
havior of liquid pinch-off or drop formation in air (see
recent experiments by Zhang and Basaran 1995, for ex-
ample). In theoretical work, the outer ¯uid (air) is as-
sumed to have no in¯uence on the pinch-off process.
Recent examples of this work include boundary integral
computations by Brenner et al. (1997) and Cristini et al.
(1998). Experiments by Brenner et al. (1997) showed that
the viscosity of the inner ¯uid had a strong effect on the
shape of the pinch-off region when drops formed in a
gravity-driven ¯ow with very small inertia. As inner ¯uid
viscosity was increased (above the viscosity of water), the
Experiments in Fluids 30 (2001) 47±56 Ó Springer-Verlag 2001
Received: 28 January 1999/Accepted: 20 January 2000
D. R. Webster (&)
School of Civil and Environmental Engineering,
Georgia Institute of Technology, Atlanta,
GA 30332-0355, USA
E. K. Longmire
Department of Aerospace Engineering and Mechanics,
University of Minnesota, Minneapolis,
MN 55455, USA
This work was supported by the National Science Foundation
under grant CTS-9457014 and the Engineering Research Program
of the Of®ce of Basic Energy Sciences at the Department of Energy
under grant DE-FG02-98ERI-4869. We wish to thank Derek
Gefroh and Dave Hultman for construction of the facility and
Dr. Harry Vinagre and Professor Dan Joseph for use of the
spinning drop tensiometer.