Capsule dynamics and rheology in shear flow: Particle pressure and normal stress

摘要

In this paper, we examine the dynamics of an isolated capsule using a hybrid lattice-Boltzmann/finite-element method, with a focus on how the capsule dynamics affects the rheology of capsule suspensions. We study initially spherical capsules undergoing a "tank-treading" behavior in which the particle assumes an ellipsoidal shape at a steady orientation while the capsule's membrane rotates. Of particular interest is the calculation of the particle pressure and a full characterization of the normal stresses. To date, results on capsule rheology only consider normal stress differences, which are insufficient to explain particle migration using the suspension balance model [P. R. Nott and J. F. Brady, "Pressure-driven suspension flow: Simulation and theory," J. Fluid Mech.275, 157 (1994)]. We also extend the results of R. Roscoe ["On the rheology of a suspension of viscoelastic spheres in a viscous liquid," J. Fluid Mech.28, 273 (1967)] using the solution for ellipsoidal particles of G. B. Jeffery ["The motion of ellipsoidal particles immersed in a viscous fluid," Proc. R. Soc. London, Ser. A102, 161 (1922)] to predict the particle-phase pressure of deformable particles. Both analytical modeling and numerical results show a negative (tensile) particle pressure, in contrast with the case of an isolated sphere, which shows no particle pressure.