Deformation and breakup of a Newtonian droplet in viscoelastic matrix subject to oscillatory shear flow

The deformation and breakup of a Newtonian droplet in an Oldroyd-B or Giesekus matrix subject to oscillatory shear flow are investigated using a GPU-based lattice Boltzmann method. We first focus on droplet deformation at low capillary numbers (Ca), and explore how the maximum deformation parameter D_max, the inclination angle θ corresponding to D_max, and the phase lag in stable oscillations vary with Deborah number (De), oscillation period T* and mobility parameter α. Results show that D_max decreases with De due to the suppression of elastic stress caused by oscillatory shear. An increase in T* favours the development of elastic stress and thus leads to the increase of D_max. The phase lag is found to first increase and then decrease with De, with the former attributed to the increased relaxation time at low De and the latter to the increased suppression of viscoelasticity at high De. The parameter α rarely affects droplet deformation at low T*, whereas at moderate or large T*, the droplet deformation, rotation and phase lag all decrease as α increases. Then, we explore droplet breakup in a special oscillatory shear flow, where the magnitude of shear velocity periodically changes but the moving direction remains unchanged. By establishing Ca−De and Ca−α phase diagrams, we show that the critical capillary number for droplet breakup increases with increasing De or α. In addition, the droplet breakup is found to happen not only in the stretching stage but also in the retraction stage.