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Extensional rheology of a dilute particle-laden viscoelastic solution
Phys. Rev. Fluids 4, 091301(R) – Published 9 September, 2019
DOI: https://doi.org/10.1103/PhysRevFluids.4.091301
Abstract
Recent discoveries have allowed a mathematical and computational foundation for understanding the rheology of particles suspended in viscoelastic fluids. We employ these new tools to understand the extensional rheology of such suspensions. We accomplish this by first calculating the renormalized particle contribution to the extensional viscosity in such a suspension in the dilute particle limit over a wide range of extensional Weissenberg number and Hencky strain. The models we use for the suspending fluids are the simplest dumbbell models—the Oldroyd-B, FENE-P, and Giesekus models—such that our results are general for polymer solutions which exhibit strong strain hardening at values of the Weissenberg number above those which engender the coil-stretch transition, . We demonstrate that the effect of particles on the “extra elongational viscosity” relative to the fluid is nonmonotonic in strain (increasing for small strain and then decreasing for large strain). Thus at a fixed strain, the particle “extra viscosity” relative to the fluid may increase or decrease with Wi. We demonstrate that this interesting behavior is due to the interplay between the two contributions of the “particle-induced fluid stress” (PIFS) and the “stresslet” to the extra viscosity. The contribution of the particle-induced fluid stress to the suspension viscosity increases at small strain but plateaus and then decreases at higher values of the strain. Thus, at small strain the local velocity gradients near a particle increase the polymer stretch, while for greater strain, polymers which have undergone the coil-stretch transition collapse in the neighborhood of a given particle. On the other hand, the stresslet contribution to the viscosity relative to the fluid decreases monotonically as the polymer stretch surrounding a given particle “shields” the particle and thus reduces the local surface tractions. Beyond Hencky strain of approximately 2 the decreasing value of the stresslet coupled with the plateauing of the PIFS, causes the overall reduction in the particle-induced extra viscosity relative to that of the fluid.
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