Exp Fluids (2015) 56:163
Cross‑sectional imaging of refractive‑index‑matched
· Hervé Capart
Received: 6 April 2015 / Revised: 20 June 2015 / Accepted: 10 July 2015 / Published online: 1 August 2015
© Springer-Verlag Berlin Heidelberg 2015
Flows that mobilize solid grains immersed in liquids inter-
vene in many contexts, including chemical processes,
dredging operations and geomorphologic phenomena like
bed-load transport, sediment sheet-ﬂow and debris surges.
Although much can be learned by studying these ﬂows in
conditions approximating their complex context of appli-
cation, it has also proved useful to investigate simpler ide-
alizations (Bagnold 1956). Most typically, idealized experi-
ments have dealt with identical spheres immersed in a
Newtonian liquid, ﬂowing in simple geometries like upright
columns (Haam et al. 2000), straight channels (Aussillous
et al. 2013), or annular shear cells (Houssais et al. 2015).
Even in such simpliﬁed conditions, however, measurements
of ﬂow behavior involve considerable challenges.
Because probes excessively perturb the ﬂows, the pre-
ferred approach is to acquire non-intrusive measurements.
These are, however, made difﬁcult by the heterogeneity of
the medium. Unless the grains and liquid are both transpar-
ent with matched refractive indexes, in particular, occlu-
sion and refraction prevent optical access to the ﬂow inte-
rior (Cui and Adrian 1997). Various approaches have been
adopted to address this difﬁculty. First, many experiment-
ers have worked with opaque grains immersed in water or
other transparent liquids, and simply focused on observing
the ﬂow behavior near transparent boundaries, leaving the
internal ﬂow unobserved (e.g., Sumer et al. 1996; Capart
et al. 2002; Spinewine et al. 2003, 2011; Armanini et al.
2005; Capart and Fraccarollo 2011; Spinewine and Capart
2013). A second approach has been to work with narrow
channels in which a single granular layer is held between
parallel channel walls (Böhm et al. 2006; Frey 2014). This
makes the whole system observable, but reduces the three-
dimensional ﬂow to a two-dimensional analog.
Abstract In channelized liquid-granular ﬂows, the liquid
velocity, granular velocity and solid fraction all vary over
transverse cross sections. A major experimental challenge
is then to acquire internal measurements of these three
ﬁelds. One useful ﬁrst step, achievable using various mate-
rials, is to make the medium transparent by matching the
refractive indexes of the liquid and granular phases. Tak-
ing full advantage of this optical access, however, requires
the development of new imaging methods. In this paper, we
propose a new approach applicable to steady uniform ﬂows
and spherical immersed grains. The approach combines
laser scans in the transverse and longitudinal directions.
Using the transverse scans, liquid and granular motions in
the laser plane can be captured by particle-tracking veloci-
metry. The longitudinal scans, on the other hand, allow
granular positions and velocities to be deduced from indi-
vidual grain crossing events. These occur when ﬂowing
grains move across the laser plane and when the laser plane
sweeps across stationary grains. The approach therefore
applies to ﬂows over erodible beds featuring both moving
and stationary grains. Using suitable algorithms, we show
how to process these scans to map granular velocity, liq-
uid velocity and granular concentration over the entire ﬂow
cross section, at resolutions ﬁner than the grain diameter by
a factor of 10.
* Hervé Capart
Department of Civil Engineering and Hydrotech Research
Institute, National Taiwan University, Taipei, Taiwan