A note on transient stress calculation via numerical simulations

We revisit the experiments of start-up shear of an immiscible dilute polymer blend presented in [J. Non-Newtonian Fluid Mech. 99 (2001) 167] and calculate the transient stresses via numerical simulations. As part of this investigation, we validate a stress-relaxation experimental technique [J. Non-Newtonian Fluid Mech. 99 (2001) 167; J. Non-Newtonian Fluid Mech. 93 (2000) 153] for the measurement of the interfacial contribution. The simulations assume Newtonian behavior, thus, not including bulk viscoelastic effects, and are performed using an adaptive boundary-integral method [Phys. Fluids 10 (8) (1998) 1781; J. Comput. Phys. 168 (2001) 445] to describe highly deformed drops and the effect of breakup events on the stresses. When viscoelasticity is negligible, we find agreement between simulations and experiments for the total stress and interface contribution at both subcritical and supercritical capillary numbers, and demonstrate that no existing analytical models are capable of describing correctly the stress evolution. Interestingly, we find that the breakup time is independent of the capillary number at high capillary number, and depends on the viscosity ratio only. When viscoelasticity is important, the comparison between the simulation results and the experimental data allows us to quantify the effect of viscoelasticity on the stresses by isolating correctly the Newtonian contribution.