Two-perspective ﬂuorescence analysis of droplets creeping
down a tilted plate
Received: 31 October 2012 / Revised: 19 November 2013 / Accepted: 23 November 2013 / Published online: 6 December 2013
Ó Springer-Verlag Berlin Heidelberg 2013
Abstract Many experimental techniques have been
developed and applied to investigate hydrodynamics of
liquid ﬁlms and single droplets on solid substrates. A
simple but reliable measurement technique has been
recently proposed to quantify thickness and apparent con-
tact angles of droplets and rivulets (Hagemeier et al. Exp
Fluids 52(2):361–374, 2012). However, this technique
leads to ambiguities for any contact angle exceeding 90°.
An improved version has thus been derived to solve the
most important issues associated with the original method.
For this purpose, top and sideways two-perspective images
are acquired simultaneously, both relying on ﬂuorescence.
Analyzing the data obtained from both views, a correlation
between ﬂuorescence intensity and droplet shape can be
derived. Furthermore, advancing and receding contact
angles can be determined in this manner. A new and par-
ticularly important feature of the improved technique is the
estimation of the contact line velocity at various locations,
all around the moving droplet. The in-plane velocity
components show a clear dependency on the Bond number
and on the position around the droplet circumference.
Many publications are available concerning experimental
investigations of droplets moving on solid substrates. The
motion can be induced by different driving forces, for
instance: gravity for droplets on inclined surfaces, shear
forces for droplets exposed to a gas ﬂow (Ding and Spelt
2008) or Marangoni effects induced by temperature or
concentration gradients. In this paper, we describe an
experimental method suitable for the investigation of
droplets moving down inclined plates of different materi-
als. Earlier publications considered similar problems of
sliding droplets on inclined plates, delivering both quali-
tative (droplet shape) and quantitative (contact angles)
information, e.g., Podgorski et al. (2001), ElSherbini and
Jacobi (2004) or Le Grand et al. (2005). The receding side
of droplets and rivulets has attracted much interest as well.
In particular, Snoeijer et al. (2005) and Peters et al. (2009)
studied the formation of corner tips at the droplet rear.
They applied imaging techniques in order to capture the
contact line geometry and analyzed the limit curvature at
the droplet rear. Snoeijer et al. (2005) evaluated the three-
dimensional droplet shape of sliding droplets from top and
side views. Additionally, they added tracer particles to the
ﬂuid and used particle image velocimetry (PIV) to quantify
the velocity ﬁelds within the droplets. Daerr et al. (2003)
provided a detailed ﬂow map of droplet shapes for droplets
sliding down an inclined plate.
Often, these experimental investigations have been
accompanied by theoretical descriptions in terms of wetting
models, like in S
ikalo et al. (2005), Snoeijer et al. (2007),
(2011) and recently by Annapragada et al. (2012a, b).
However, there is still a lack of reliable experimental
data concerning the measurement of contact line velocity
together with contact angle and droplet thickness. Such
simultaneous measurements would be very important to
support or improve current model developments. The focus
of the present investigation is the estimation of contact line
velocity of single droplets creeping down an inclined plate.
This article is part of the Topical Collection on Application of Laser
Techniques to Fluid Mechanics 2012.
T. Hagemeier (&) Á R. Borda
s Á K. Za
hringer Á D. The
Institute of Fluid Dynamics and Thermodynamics, University of
Magdeburg ‘‘Otto von Guericke’’, Universitaetsplatz 2, 39106
Exp Fluids (2014) 55:1639