Simple Shear Flow of Suspensions of Elastic Capsules

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The simple shear flow of homogeneous suspensions of two-dimensional capsules enclosed by elastic membranes is studied in the limit of vanishing Reynolds number, in the special case where the viscosity of the fluid enclosed by the capsules is equal to the viscosity of the ambient fluid. The deformation of capsules with circular, elliptical, and biconcave unstressed shapes, and the rheological and statistical properties of their infinitely dilute and moderately dense suspensions are investigated by dynamical simulation using the method of interfacial dynamics for Stokes flow. In a preliminary investigation, the behavior of solitary capsules suspended in an infinite fluid is studied as a function of the dimensionless membrane elasticity number expressing the capsule deformability or the strength of the shear flow. It is found that a critical elasticity number above which a capsule exhibits continued elongation does not exist, and an equilibrium configuration is reached no matter how large the shear rate, in agreement with previous results for three-dimensional flow. A correspondence is established between the elasticity numbers for two- and three-dimensional flow at which the capsules undergo the same degree of deformation. Simulations of pairwise capsule interceptions reveal behavior similar to that exhibited by liquid drops with uniform surface tension. Because of strong hydrodynamic interactions in two-dimensional Stokes flow, the concept of hydrodynamic diffusivity in the limit of infinite dilution is ill-defined in the absence of fluid inertia. Dynamical simulations of doubly periodic monodisperse suspensions with up to 50 capsules distributed in each periodic cell at areal fractions of 0.25 and 0.40 provide information on the effective rheological properties of the suspension and on the nature of the statistical properties of the particle motion. The character of the flow is found to be intermediate between that of liquid drops and rigid particles, and this is attributed to the membrane deformability and to the ability of the interfaces to perform tank-treading motion. The results are compared with rheological measurements of blood flow with good agreement.