Abstract
The microscopic dynamics of objects suspended in a fluid determines the macroscopic rheology of a suspension. For example, as shown by Danker and Misbah [Phys. Rev. Lett., 2007, 98, 088104], the viscosity of a dilute suspension of fluid-filled vesicles is a non-monotonic function of the viscosity contrast (the ratio between the viscosities of the internal encapsulated and the external suspending fluids) and exhibits a minimum at the critical point of the tank-treading-to-tumbling transition. By performing numerical simulations, we recover this effect and demonstrate that it persists for a wide range of vesicle parameters such as the concentration, membrane deformability, or swelling degree. We also explain why other numerical and experimental studies lead to contradicting results. Furthermore, our simulations show that this effect even persists in non-dilute and confined suspensions, but that it becomes less pronounced at higher concentrations and for more swollen vesicles. For dense suspensions and for spherical (circular in 2D) vesicles, the intrinsic viscosity tends to depend weakly on the viscosity contrast.
Highlights
Rheological properties of complex uids are not yet fully understood
We validated our computational method against the case of a single isolated vesicle (N 1⁄4 1) which corresponds to the limit of a very dilute suspension (f / 0)
We compute the instantaneous intrinsic viscosity h(t) of the uid suspending each of these two vesicles using eqn (4) and we show in Fig. 1b how h(t) evolves in time
Summary
Vesicles undergo mainly two states of motion under shear ow: either tank-treading (the particle assumes a steady angle with the ow direction, while its membrane undergoes a tanktreading-like motion) or tumbling (the particle rotates around its center of mass).[5]. There is an apparent contradiction between different studies regarding the dependency of the vesicle suspension viscosity on the viscosity contrast. We capture the non-monotonic behavior of the viscosity as proposed by Danker and Misbah and nd that it persists even when varying f, Ca or D. It only becomes less pronounced for denser suspensions or for very swollen vesicles, but it does not show a monotonically increasing/decreasing behavior with L as reported in ref. We explain this disagreement and provide insight into the origins that lead to this apparent contradiction
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