A numerical study of droplet deformation and droplet breakup in a non-orthogonal cross-section
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ORIGINAL CONTRIBUTION
A numerical study of droplet deformation and droplet breakup in a non-orthogonal cross-section Erfan Kadivar1 · Behnaz Shamsizadeh1 Received: 5 March 2020 / Revised: 13 August 2020 / Accepted: 19 August 2020 / Published online: 21 September 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract In this work, we numerically investigate the deformation and breakup of a droplet flowing along the centerline of a microfluidic non-orthogonal intersection junction. The relevant boundary data of the velocity field is numerically computed by solving the depth-averaged Brinkman equation via a self-consistent integral equation using the boundary element method. The effect of the capillary number, droplet size, intersection angle, and ratio of outlet channel width to inlet channel width on maximum droplet deformation are studied. We study droplet deformation for the capillary numbers in the range of 0.080.3 and find that the maximum droplet deformation scales with the capillary number with power law with an exponent 1.10. We also investigate the effect of droplet size and intersection angle on the maximum droplet deformation and observe that the droplet deformation is proportional to droplet volume and square root of intersection angle, respectively. In continue, we study the droplet breakup phenomenon in an orthogonal intersection junction. By increasing the capillary number, the deformation of a droplet traveling in the cross-junction region becomes larger, until the droplet shape is no longer observed and droplet breakup takes place at a critical value of capillary number. We present a phase diagram for droplet breakup as a function of undeformed droplet radius. Keywords Non-orthogonal cross-section · Droplet deformation · Droplet breakup · Brinkman equation · Boundary element method
Introduction Dispersed droplets are an important subject in the rheological science. The droplet deformation (Delaby et al. 1995; Malkin et al. 2004), droplet breakup (Marshall and Walker 2019; Niedzwiedz et al. 2010), and droplet coalescence (Grizzuti and Bifulco 1997; Verdier and Brizard 2002) are interesting subject of rheological studies, due to practical application as well as due to rheological effects. Dispersed droplet generation and its manipulation are two important processes in the droplet dynamics in the microfluidic systems. The channel geometry has good ability to produce and control the external and internal forces that create, flow, breakup, and coalesce droplets (Bremond et al. 2008a; Baret et al. 2009; Baret 2012; Salkin et al. 2013). In recent years, numerous studies have been carried out on the dynamics Erfan Kadivar
[email protected] 1
Department of Physics, Shiraz University of Technology, Shiraz, 71555-313, Iran
of droplet motion in microchannels such as droplet deformation (Chang et al. 2019; Tr´egou¨et et al. 2018), droplet sorting (Kadivar et al. 2013; Kadivar 2016), droplet breakup (Link et al. 2004; Salkin et al. 2013), and droplet coalescence (Bremond et al. 2
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