Experiments in Fluids 25 (1998) 276 —279 Springer-Verlag 1998
Fluorescent solution microcapsules as ideal tracer particles in long-term tracking
of 3-D Lagrangian trajectories
T. Tajima, T. Nakamura, T. Azuma, K. Kurosawa
Fluorescent solution microcapsules (diameter
:100 m) have been invented as tracer particles suitable for
the long-term tracking of 3-D Lagrangian trajectories in the
rotating annulus ﬂuid experiments. In more than 10% of the
tracking experiments, the microcapsule was observed to follow
the ﬂow passively for more than 10 h, at their maximum 18 h.
In our preliminary experiments to study 3-D Lagrangian
motions in steady baroclinic waves produced in a differen-
tially-heated rotating ﬂuid annulus (Tajima et al. 1997), it was
required to track a tracer particle for ten hours or more to get
statistically reliable data. Though there have been already
reports of techniques that can track many 2-D trajectories for
longer than an hour (Solomon et al. 1993; 1994; Pervez and
Solomon, 1994), there are still few reports for the long-term
tracking of 3-D trajectories. The key element of the technique is
the ability of the tracer particles to be neutrally buoyant in the
ﬂuid. For this purpose we have invented ﬂuorescent solution
microcapsules, hereafter abbreviated as FSC’s. Our technique
of the long-term tracking with the use of the FSC’s and an
automated tracking method was applied to the rotating
annulus ﬂuid experiments.
The gravitational force and inertia are two main factors to
cause the tracer particle trajectories to deviate from those
for ideal passive particles. The tracer particles have been
usually made of non-liquid substances (cf. Pervez and Solomon
1994; Solomon et al. 1994). In general, the thermal expansion
T. Tajima, T. Nakamura, T. Azuma
Toyama National College of Technology
13 Hongo-machi, Toyama 939-8045, Japan
POLYMER TEC INC, 4-5-6, Higashikasai
Edogawaku, Tokyo 134-0088, Japan
Correspondence to: T. Tajima
The authors wish to thank Prof. H. L. Swinney, Prof. R. Kimura, Prof.
S. Yoden, Dr. E. R. Weeks, Dr. B. Plapp and Mr. C. Baroud for valuable
comments and encouragement.
coefﬁcients of non-liquid substances are different from that of
typical ﬂuid by a few orders. The buoyancy of the usual tracer
particles is therefore strongly dependent on the temperature
of the ﬂuid. For this reason, non-liquid substances are not
suitable for the tracer particles in the experiments with wide
thermal variations. To remedy this drawback, we invented
a new way to use liquid material as the content of the tracer
particles for the experiments where water is used as the
working ﬂuid. Fluorescent crystals (whose speciﬁc gravity is
slightly less than 1.00) are used to make the tracer particles
discriminating under ultraviolet light in the dark background.
These crystals are mixed into epoxy-type solvent (which has
speciﬁc gravity of slightly greater than 1.00 and high viscosity).
This solution is wrapped by a thin ﬁlm of melamine copolymer
to make its microcapsules whose size is typically 100 m.
While this process is carried out, the density of the ﬂuorescent
crystals and the thickness of the ﬁlm are carefully adjusted so
that the speciﬁc gravity of the microcapsules is almost around
that of the water at room temperature. The thickness of the ﬁlm
is of an order of 0.1 m.
Thermal expansion of the FSC’s is governed by the epoxy-
type solvent whose thermal expansion coefﬁcient is about four
times that of the water at room temperature. To get the same
expansion rate as the water, the FSC’s need to vary roughly
a quarter of their volume according to the temperature. This
volume is a surface layer of the FSC’s with a depth of less than
5 m. Thus some of the FSC’s can be expected to show the
neutral buoyancy under wide and quick thermal variations
because such a thin surface layer can acquire the temperature
of the water almost in an instant.
The effect of the inertia is quantiﬁed by the dimensionless
Stokes number, S:Ua2/18L, for a neutrally buoyant particle,
where a is the particle diameter, is the kinematic viscosity of
the ﬂuid, and U and L are the characteristic velocity and length
scale of the ﬂow (cf. Pervez and Solomon 1994; Solomon et al.
1994). The inertia is negligible if S1. To reduce the inertia
effect sufﬁciently, we must use the particles whose diameters
are much less than (18L/U
. In the present experiments, the
ratio of the scales L/U is greater than an order of 1 s for the
jet-streams, vortices and boundary layers. Therefore, the
diameters of the particles should be much less than 0.1 cm.
The size should be, furthermore, less than the smallest length
scale in the ﬂow, namely the thickness of the boundary layers
which is observed to be a few millimeters. The lower limit of
the size is set by the ability of the experimental apparatus to
identify the particles in the ﬂuid. It is about 10 m in our