The relaxation and breakup of Newtonian droplets is considered using the advected field approach. This method allows one to follow the deformation of interfaces using an order parameter field [Biben, Europhys. Lett. 63, 623 (2003)] based on a Ginzburg-Landau equation. Using this method, it is possible to follow the breakup of droplets and stability curves can be obtained in both two- and three-dimensional shear and elongational flows. Finally, relaxation of a droplet is considered, following the application of an elongational flow. The results are compared with previous experimental data [Ha and Leal, Phys. Fluids 13, 1568 (2001)], and are found to be in satisfactory agreement. The method is general enough to be applied to other non-Newtonian fluids, such as Oldroyd-B fluids or viscoplastic materials.
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