Simulations of microfluidic droplet formation using the two-phase level set method Shazia Bashir a , Julia M. Rees a,Ã , William B. Zimmerman b a School of Mathematics and Statistics, University of Sheffield, Hicks Building, Hounsfield Road, Sheffield S3 7RH, UK b Department of Chemical and Biological Engineering, University of Sheffield, Newcastle Street, Sheffield S1 3JD, UK article info Article history: Received 18 March 2011 Received in revised form 13 June 2011 Accepted 17 June 2011 Available online 25 June 2011 Keywords: Fluid mechanics Interfacial tension Simulation Wettability Multiphase flow Drop abstract Microdroplet formation is an emerging area of research due to its wide-ranging applications within microfluidic based lab-on-a-chip devices. Our goal is to understand the dynamics of droplet formation in a microfluidic T-junction in order to optimize the operation of the microfluidic device. Understanding of this process forms the basis of many potential applications: synthesis of new materials, formulation of products in pharmaceutical, cosmetics and food industries. The two-phase level set method, which is ideally suited for tracking the interfaces between two immiscible fluids, has been used to perform numerical simulations of droplet formation in a T-junction. Numerical predictions compare well with experimental observations. The influence of parameters such as flow rate ratio, capillary number, viscosity ratio and the interfacial tension between the two immiscible fluids is known to affect the physical processes of droplet generation. In this study the effects of surface wettability, which can be controlled by altering the contact angle, are investigated systematically. As competitive wetting between liquids in a two-phase flow can give rise to erratic flow patterns, it is often desirable to minimize this phenomenon as it can lead to a disruption of the regular production of uniform droplets. The numerical simulations predicted that wettability effects on droplet length are more prominent when the viscosity ratio l (the quotient of the viscosity of the dispersed phase with the viscosity of the continuous phase) is O(1), compared to the situation when l is O(0.1). The droplet size becomes independent of contact angle in the superhydrophobic regime for all capillary numbers. At a given value of interfacial tension, the droplet length is greater when l is O(1) compared to the case when l is O(0.1). The increase in droplet length with interfacial tension, s, is a function of ln s with the coefficients of the regression curves depending on the viscosity ratio. & 2011 Elsevier Ltd. All rights reserved. 1. Introduction Over the last decade droplet formation has become a very important area of research due to its wide-ranging applications in science and microprocess engineering. The ability to produce nearly monodispersed microdroplets has numerous applications within microfluidic based lab-on-a-chip devices (Yap et al., 2009). The controlled formation of aqueous phase microdroplets dis- persed in a continuous phase fluid has unique advantages as the consumption of reagents is small (Song et al., 2006; Li et al., 2008). In particular, a number of important biological molecules can be produced from microdroplet based crystallization pro- cesses utilizing small samples of solution. During these processes each microdroplet acts as an individual microreactor in which the aqueous solutions are manipulated at room temperature (Leng and Salmon, 2009). The fine controls possible over the size and shape of these microdroplets are of much importance since they influence the biological and chemical properties of microparticles (Teh et al., 2008). The major advantages of droplet based fluidic systems are the existence of a high surface-to-volume ratio, rapid mixing within the droplet or plug at low Reynolds numbers (Song et al., 2003; Tice et al., 2003) and the enclosure of a sample within a suspending liquid, eliminating several problems associated with evaporation and cross contamination between successive samples that are encountered in macroscale systems (Song et al., 2006; Leshansky and Pismen, 2009). A number of methods have been developed for droplet formation. These include droplet breakup at a symmetric T-junction (Leshansky and Pismen, 2009) or bifurca- tion junction (Jullien et al., 2009), flow focussing of a continuous stream of liquid which guides the droplets formed toward the center of the channel (Anna et al., 2003; Tan et al., 2006), perpendicular rupturing using a cross-flow microchannel (Tan et al., 2008), and the shearing of the dispersed phase stream by Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/ces Chemical Engineering Science 0009-2509/$ - see front matter & 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.ces.2011.06.034 Ã Corresponding author. E-mail addresses: app08sb@shef.ac.uk (S. Bashir), j.rees@shef.ac.uk (J.M. Rees), w.zimmerman@shef.ac.uk (W.B. Zimmerman). Chemical Engineering Science 66 (2011) 4733–4741