Particle tracking for polydisperse sedimenting droplets in phase
Received: 22 June 2011 / Revised: 9 November 2011 / Accepted: 24 November 2011 / Published online: 20 December 2011
Ó The Author(s) 2011. This article is published with open access at Springerlink.com
Abstract When a binary ﬂuid demixes under a slow
temperature ramp, nucleation, coarsening and sedimenta-
tion of droplets lead to an oscillatory evolution of the
phase-separating system. The advection of the sedimenting
droplets is found to be chaotic. The ﬂow is driven by
density differences between two phases. Here, we show
how image processing can be combined with particle
tracking to resolve droplet size and velocity simulta-
neously. Droplets are used as tracer particles, and the
sedimentation velocity is determined. Taking these effects
into account, droplets with radii in the range of 4-40 lm
are detected and tracked. Based on these data, we resolve
the oscillations in the droplet size distribution that are
coupled to the convective ﬂow.
The characterization of particle distributions in ﬂuids is
important to control and optimize processes in food,
pharmaceutical, oil and chemical industry (Heffels et al.
(1998)). To determine the particle mass ﬂux, particle sizes
and velocities have to be measured simultaneously, which
was achieved by Petrak (2002).
Here, we present a particle tracking algorithm, which
uses droplets as marker particles to measure the ﬂow ﬁeld.
They are created naturally in the phase separation process
of demixing binary systems. Droplet positions and radii are
detected simultaneously. The radius can therefore be used
as a criterion to identify droplets in subsequent images.
Assuming Stokes law, the sedimentation velocity can be
calculated from the droplet radius. The droplet velocity is
decomposed into sedimentation velocity and advection by
the ﬂow. By subtracting the sedimentation velocity from
the droplet velocity, the advection of all droplets can be
used to measure the ﬂow ﬁeld. With the advective ﬂow
ﬁeld and the sedimentation velocity of each droplet, its
position in the next frame can be predicted and compared
to the image.
Previous studies have extensively used particle tracking
velocimetry as a measurement technique to investigate
turbulent ﬂows carrying small particles (Maas et al. 1993;
Malik et al. 1993; Ouellette et al. 2006; Kreizer et al.
2010). To that end, monodisperse tracer particles are added
to the ﬂuid whose position is detected by image processing
of high-speed camera data. While this procedure is followed
successfully for monodisperse particles in single-phase
ﬂows, it is not easily applicable for measuring ﬂow patterns
in demixing binary systems, which have been studied by
Vollmer et al. (1997, 2002) and Emmanuel and Berkowitz
(2006). Tracer particles cannot be added as they would act
as nucleation centers and therefore affect the droplet num-
ber density. Furthermore, colloidal particles aggregate on
the interfaces and change the growth and coalescence rate,
as Thijssen and Clegg (2010) have shown. For a review of
the stabilizing effect of colloidal particles in emulsions, see
Binks (2002) and Aveyard et al. (2003).
There also is a broad range of acoustic/electroacoustic
and optical techniques for the measurement of droplet size
distributions, an overview given by Maass et al. (2009).
Several laser-based techniques measure chord lengths that
have to be transferred into droplet size distributions
T. Lapp (&) Á M. Rohloff Á J. Vollmer Á B. Hof
Max-Planck-Institute for Dynamics and Self-Organization,
37073 Goettingen, Germany
T. Lapp Á M. Rohloff Á J. Vollmer
Faculty for Physics, University of Goettingen,
37077 Goettingen, Germany
Exp Fluids (2012) 52:1187–1200