Exp Fluids (2017) 58:13
Surfactant-laden drop jellyﬁsh-breakup mode induced
by the Marangoni eﬀect
· Wen-Bin Zhang
· Jian-Liang Xu
· Wei-Feng Li
· Hai-Feng Liu
Received: 25 October 2016 / Revised: 26 December 2016 / Accepted: 27 December 2016 / Published online: 6 February 2017
© Springer-Verlag Berlin Heidelberg 2017
aerodynamic forces to restorative surface tension forces
and is the most important parameter when describing liquid
breakup and atomization. It is deﬁned as
We = 𝜌
are the density and velocity of gas, respec-
is the diameter of the initial spherical drop, and
is the surface tension.
For increasing values of We, the modes of liquid drop
breakup are described in terms of morphology as no
breakup, bag breakup, multimode breakup, sheet-thinning
breakup, and catastrophic breakup (Guildenbecher et al.
2009; Jain et al. 2015; Sichani and Emami 2015), or in
terms of mechanism as Rayleigh–Taylor piercing breakup
and shear-induced entrainment breakup (Theofanous 2011).
The bag-breakup mode is especially important, because it
is the criterion for the onset of drop breakup (Wang et al.
2014; Kulkarni and Sojka 2014), where the critical Weber
number (the beginning of bag breakup) is close to 12.
Viscosity hinders drop deformation and dissipates
energy supplied by aerodynamic forces. Thus, the critical
Weber number increases with viscosity. To account for this,
many studies use the Ohnesorge number,
are the density and viscosity of the liquid,
respectively. This represents the ratio of a drop’s viscous
forces to its surface tension forces. Therefore, the critical
Weber number increases with the Ohnesorge number (Guil-
denbecher et al. 2009).
In the bag-breakup mode, the spherical drop will deform
to a disk-like shape and then the thin ﬁlm is deﬂected by
aerodynamic force. The morphology of the bag-breakup
mode is composed of a thin membrane-like bag attached to
a thicker rim; the bag disintegrates ﬁrst, followed by the rim
(ring). Rayleigh–Taylor instability can be regarded as the
cause of bag breakup (Theofanous et al. 2004; Theofanous
2011; Guildenbecher et al. 2009; Zhao et al. 2010, 2011;
Abstract Drop breakup is a familiar event in both nature
and technology. In this study, we ﬁnd that the bag breakup
mode can be replaced by a new breakup mode: jellyﬁsh
breakup, when the surfactant concentration of a surfactant-
laden drop is high. This new breakup mode has a morphol-
ogy resembling a jellyﬁsh with many long tentacles. This is
due to the inhomogeneous distribution of surfactant in the
process of drop deformation and breakup. The thin ﬁlm of
liquid can remain stable as a result of the Marangoni eﬀect.
Finally, we propose that the dimensionless surfactant con-
centration can serve as a criterion for breakup mechanisms.
Drop deformation and breakup is a common phenomenon
in nature and in scientiﬁc and engineering applications
(Krzeczkowski 1980; Pilch and Erdman 1987; Wierzba
1990; De Bruijn 1993; Liu and Reitz 1997; Chou and Faeth
1998; Villermaux and Bossa 2009; Betz et al. 2010; Liu
et al. 2012; Moita and Moreira 2012; Sahu et al. 2013;
Opfer et al. 2014; Davanlou et al. 2015; Jiang and Agrawal
2015; Pawar et al. 2015; Kékesi et al. 2016). A falling drop
encounters an ambient ﬂow ﬁeld, and then, aerodynamic
forces cause the drop to deform and break apart into frag-
ments. The Weber number (We) is the ratio of disruptive
* Hai-Feng Liu
Key Laboratory of Coal Gasiﬁcation and Energy Chemical
Engineering of Ministry of Education, East China University
of Science and Technology, No.130 Meilong Road, P.O.
Box 272, Shanghai 200237, People’s Republic of China
Shanghai Engineering Research Center of Coal Gasiﬁcation,
Shanghai, People’s Republic of China