Eur. Phys. J. E (2017) 40: 31
https://doi.org/10.1140/epje/i2017-11521-9

Regular Article

Numerical simulation and scaling of droplet deformation in a hyperbolic flow

¹ Department of Physics, Shiraz University of Technology, 71555-313, Shiraz, Iran
² Department of Physics, Faculty of Sciences, Persian Gulf University, 75168, Bushehr, Iran

^* e-mail: erfan.kadivar@sutech.ac.ir

Received: 9 October 2016
Accepted: 28 February 2017
Published online: 23 March 2017

Abstract

Motivated by a recent experiment (C. Ulloa et al., Phys. Rev. E 89, 033004 (2014)), droplet deformation in a flat microfluidic channel having a cross intersection with two inlet channels and two outlet channels, i.e. hyperbolic flow, is numerically investigated. Employing the boundary element method (BEM), we numerically solve the Darcy equation in the two dimensions and investigate droplet motion and droplet deformation as the droplet enters the cross intersection. We numerically find that the maximum deformation of droplet depends on droplet size, capillary number, viscosity ratio and flow rate ratio of the two inlets. Our numerical scaling is in good agreement with the experimental scaling report.