Transient deformation of an Oldroyd-B drop in a Newtonian matrix (O∕N) after abrupt start of shear at . Overshoot in occurs at sufficiently large . N∕N runs with viscosity ratios and 0.5 are also shown for comparison.
Growth of the polymer normal stress at the tip and the tangential stress at the equator of the drop for O∕N, and being the local normal and tangent vectors. , and 1. The normal stress at the tip and the tangential stress at the equator are the major viscoelastic agents for suppressing drop deformation (Ref. 14). The apparent nonsmoothness of the curves is due to our sampling the solution at large time intervals.
The deformation of a Newtonian drop in an Oldroyd-B matrix (N∕O) at . overshoots only for intermediate values of .
Two-stage drop deformation for N∕O at high . N∕N cases with viscosity ratios and 2 are also shown for comparison. for all runs except the N∕N case with , for which the reduced matrix viscosity yields a smaller .
Comparison between N∕O simulations with the experiment of Sibillo et al. (Ref. 11). For the experimental data at , time has been scaled by a factor of . (a) Transient deformation ; (b) transient orientation angle .
Increase of the overshoot in with at a fixed . (a) Newtonian drop in Oldroyd-B matrix (N∕O); (b) Oldroyd-B drop in Newtonian matrix (O∕N).
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