Chemical Engineering Science 63 (2008) 1842 – 1849 www.elsevier.com/locate/ces Breakup of shear-thinning liquid jets with surfactants Zhengjun Xue a , Carlos M. Corvalan a , ∗ , Vineet Dravid b , Paul E. Sojka b a Department of Food Science, 745 Agricultural Mall Drive, Purdue University, West Lafayette, IN 47907, USA b Maurice J. Zucrow Laboratories, School of Mechanical Engineering, 500 Allison Rd., Purdue University, West Lafayette, IN 47907, USA Received 21 August 2006; received in revised form 15 November 2007; accepted 8 December 2007 Available online 15 December 2007 Abstract In this work we consider the nonlinear dynamics of a Carreau liquid jet whose interface is covered with an insoluble surfactant. We solved the fully coupled system of governing equations that includes the two-dimensional (three-dimensional axisymmetric) continuity and momentum equations and the one-dimensional (two-dimensional axisymmetric) surfactant convection–diffusion equation using a finite element method with an adaptive mesh that conforms to the moving interface. After favorably comparing our predictions against limiting theoretical solutions, the role of the interactions between non-Newtonian and surfactant factors was investigated. The results indicate a strong synergistic interaction that plays a key role in the formation of satellite drops. Findings reported here could help reduce inefficiency and environmental pollution in various technological processes based on jet breakup such as spray drying, crop spraying and ink jet printing by controlling the formation of undesired satellite drops.  2008 Elsevier Ltd. All rights reserved. Keywords: Fluid mechanics; Nonlinear dynamics; Non-Newtonian fluids; Interface; Stability; Surfactant; Spray drift 1. Introduction Breakup of liquid jets into drops is of primary importance in applications such as spray drying, crop spraying (Wirth et al., 1991), microarraying (Okamoto et al., 2000) and ink jet print- ing (Le, 1998) among many others (Basaran, 2002). While the desired drop sizes differ widely among these applications, the underlying goal is to produce a narrow distribution of sizes centered about the targeted value. However, wide drop size dis- tributions frequently appear, typically caused by the formation of smaller satellite drops among the main drops. The forma- tion of these undersized satellite drops is a common cause of waste and inefficiency in processes based on jet breakup and, through spray drift, it is an important source of environmental pollution (USEPA, 1999). Because of its important practical implications, the ability to predict jet breakup from theory and modeling has being actively pursued as reviewed by Yarin (1993), Eggers (1997) and Basaran (2002). The majority of these studies are concerned with the dynamics of Newtonian liquid jets in the absence of ∗ Corresponding author. Tel.: +1 765 4948262. E-mail address: corvalac@purdue.edu (C.M. Corvalan). 0009-2509/$ - see front matter  2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.ces.2007.12.011 surfactants. In contrast, for reasons related to theoretical and ex- perimental difficulties, the dynamics of jets with surfactants and the dynamics of non-Newtonian liquid jets have received com- paratively much less attention, despite the fact that applications frequently involve the use of such complex fluids (Pangalos et al., 1985; Fernandez et al., 1998; Mun et al., 1999; McKinley and Sridhar, 2002; Bergeron, 2003; Liu, 2004; Steckel and Brandes, 2004). Recent theoretical and computational works on the effect of surfactants on Newtonian liquid jets include linear sta- bility models (Hansen et al., 1999; Timmermans and Lister, 2002), and nonlinear models based on one-dimensional ap- proximations to the exact two-dimensional (three-dimensional axisymmetric) governing equations (Kwak and Pozrikidis, 2001; Timmermans and Lister, 2002; Craster et al., 2002; see also Ambravaneswaran and Basaran (1999) for related work on the deformation of stretching liquid bridges). From these works, Marangoni stresses—tangential interfacial stresses that arise owing to interfacial gradients in surfactant concentration (Scriven and Sternling, 1960)—emerged as a critical issue in the field of jet dynamics. However, linear stability models, being limited to the onset of the jet instability, fail to pro- vide insight into the subsequent mechanisms leading to drop