Effects of viscosity ratio on deformation of a viscoelastic drop in a Newtonian matrix under steady shear

摘要

Deformation of an Oldroyd B drop in a Newtonian matrix under steady shear is simulated using a front tracking finite difference method for varying viscosity ratio. For drop viscosity lower than that of the matrix, the long-time steady deformation behavior is similar to that of the viscosity matched system-the drop shows reduced deformation with increasing Deborah number due to the increased inhibiting viscoelastic normal stress inside the drop. However for higher viscosity ratio systems, the drop response is non-monotonic-the steady drop deformation first decreases with increasing Deborah number but above a critical Deborah number, it increases with further increase in Deborah number, reaching higher than the viscous case value for some viscosity ratios. We explain the increase in deformation with Deborah number by noting that at higher viscosity ratios, strain rate inside the drop is reduced, thereby reducing the inhibiting viscoelastic stress. Furthermore, similar to the viscosity matched system, the drop inclination angle increases with increasing Deborah number. A drop aligned more with the maximum stretching axis at 45 degree of the imposed shear, experiences increased viscous stretching. With increased ratio of polymeric viscosity to total drop viscosity, the drop deformation decreases and the inclination angle increases. Our simulation results compare favorably with a number of experimental and computational results from other researchers.