Rheology of a dense suspension of spherical capsules under simple shear flow

Abstract

We present a numerical analysis of the rheology of a dense suspension of spherical capsules in simple shear flow in the Stokes flow regime. The behaviour of neo-Hookean capsules is simulated for a volume fraction up to φ = 0.4 by graphics processing unit computing based on the boundary element method with a multipole expansion. To describe the specific viscosity using a polynomial equation of the volume fraction, the coefficients of the equation are calculated by least-squares fitting. The results suggest that the effect of higher-order terms is much smaller for capsule suspensions than rigid sphere suspensions; for example, O(φ 3 ) terms account for only 8 % of the specific viscosity even at φ = 0.4 for capillary numbers Ca 0.1. We also investigate the relationship between the deformation and orientation of the capsules and the suspension rheology. When the volume fraction increases, the deformation of the capsules increases while the orientation angle of the capsules with respect to the flow direction decreases. Therefore, both the specific viscosity and the normal stress difference increase with volume fraction due to the increased deformation, whereas the decreased orientation angle suppresses the specific viscosity, but amplifies the normal stress difference.

Haemorheology in dilute, semi-dilute and dense suspensions of red blood cells

“…To counter the computational costs, we set Re = ρU c a/µ 0 = 0.2, where ρ is the plasma density. This value well represents capsule dynamics in unbounded shear flows solved by the boundary integral method in Stokes flow (Omori et al 2012;Matsunaga et al 2016) (see also Appendix §A.1 and §A.3). In this study, the range of Ca = 0.05-1.2 is considered covering typical venule wall-shear rates of 333 s −1 (Koutsiaris et al 2013), corresponding to Ca = 0.4, and arteriole wall shear rate of 670 s −1 (Koutsiaris et al 2007) corresponding to Ca = 0.8.…”

“…At the single cell level, the effect of viscosity ratio λ on steady motions has been well investigated Mauer et al 2018). In suspensions, numerical studies of the behaviors of deformable particles modeled as neo-Hookean spherical capsules (Clausen et al 2011;Kumar et al 2014;Matsunaga et al 2016) or as viscoelastic materials ) have been conducted, while numerical studies of the behaviors of RBCs modeled as deformable biconcave capsules are still limited (Fedosov et al 2011;Reasor Jr et al 2013;Gross et al 2014;Lanotte et al 2016), where the shear-thinning behaviors of a suspension of RBCs was systematically investigated. However, it remains unclear how the viscosity ratio λ affects the bulk suspension rheology of RBCs.…”

Numerical simulations of vorticity banding of emulsions in shear flows

“…This confirms that the initial banded strucutres, when coalescence is prohibited, tend to distribute homogeneously inside the domain. When the collision force is applied to prevent the coalescence, the system behaves similarly to a suspension of deformable particles 32,34,35 . Rosti et al 34 show that the effective viscosity of a suspension of deformable particles can be estimated with the Eilers formula, valid for rigid spheres, by computing an effective volume fraction based on the mean deformation of the par-ticles.…”

Injection of Deformable Capsules in a Reservoir: A Systematic Analysis

“…Numerical simulations provide a fine spatial and temporal resolution of physical variables, which enable for a quantitative analysis and allow for different mathematical models and hypotheses to be tested. Some fundamental studies of cells or capsules have been undertaken using computational simulations, investigating the importance of cell shape and deformability, concentration and apparent viscosity, transport and migration, providing important insight into micro-circulation dynamics [4][5][6][7][8][9][10][11].…”

“…While inertial effects have been predominantly used to sort cells in micro-fluidic devices, it is known that cell deformability and shape play important roles in their transport dynamics [7, 27-30, 8, 19]. The volumetric concentration of suspended particles in flow is also known to affect the apparent viscosity [9,5,11] of the medium, and the resulting inter-cellular flow interactions have been observed to affect transport of the cells through different microchannel configurations [31][32][33][34][35]. The motion of suspended particles in micro-channels are also known to induce a pattern of wall shear stress variation along the wall [36,37,31], which is not only important in mechanotransduction and signalling pathways, but also in cell adhesion mechanics [38].…”