Dynamical regimes and hydrodynamic lift of viscous vesicles under shear

Abstract

The dynamics of two-dimensional viscous vesicles in shear flow, with different fluid viscosities etain and etaout inside and outside, respectively, is studied using mesoscale simulation techniques. Besides the well-known tank-treading and tumbling motions, an oscillatory swinging motion is observed in the simulations for large shear rate. The existence of this swinging motion requires the excitation of higher-order undulation modes (beyond elliptical deformations) in two dimensions. Keller-Skalak theory is extended to deformable two-dimensional vesicles, such that a dynamical phase diagram can be predicted for the reduced shear rate and the viscosity contrast etain/etaout. The simulation results are found to be in good agreement with the theoretical predictions, when thermal fluctuations are incorporated in the theory. Moreover, the hydrodynamic lift force, acting on vesicles under shear close to a wall, is determined from simulations for various viscosity contrasts. For comparison, the lift force is calculated numerically in the absence of thermal fluctuations using the boundary-integral method for equal inside and outside viscosities. Both methods show that the dependence of the lift force on the distance ycm of the vesicle center of mass from the wall is well described by an effective power law ycm(-2) for intermediate distances 0.8Rp< approximately ycm< approximately 3Rp with vesicle radius Rp. The boundary-integral calculation indicates that the lift force decays asymptotically as 1/[ycm ln(ycm)] far from the wall.

Dynamics and rheology of vesicle suspensions in wall-bounded shear flow

“…The data also show that it is difficult to reach the low shearrate plateau in simulations. This is due to the importance of thermal motion at low shear rates, but may also be related to the broad TT-to-TU transition in 2D [24] where some tumbling events already appear in the TT regime. This shear-thinning is mainly due to the formation of cellfree layers near the walls, as expected from the Fåhraeus-Lindqvist effect [27].…”

“…In two dimensions, the TT-to-TU transition is predicted to occur at λ c ≃ 3.7 for A * = 0.8 in the Keller-Skalak (KS) theory [2]. However, thermal vesicle undulations, which are neglected in KS theory, produce a continuous crossover from TT to TU for bending rigidities around κ = 6.4k B T R 0 [24], with A * = 0.7 and γ * 6. Thus, our simulation results of increasing η I (λ) are in qualitative agreement with the experimental results of ref.…”

“…For red blood cells (RBCs) in capillary flow, it was first found by Fåhraeus and Lindqvist [27] that cells are depleted from a layer near the vessel wall. It is now well understood that this is a consequence of the wall-induced hydrodynamic lift force on the cells [24]. For concentrated systems with φ = 0.28, we have measured the average thickness δ of the cell-free boundary layers near the walls.…”

“…Scattering occurs only when a fluid particle j and a membrane disk i overlap and move towards each other, so that the conditions |r i − r j | < r p and (r i − r j ) · (v i − v j ) < 0 are satisfied. A second disk k = i ± 1 in the same membrane, with min k=i±1 |r k − r j |, is selected to perform a three-body collision which conserves linear and angular momenta [24]. The MPC collision step is then performed only for those fluid particles which did The intrinsic viscosity ηI = (η − ηout)/(ηoutφ) as a function of the viscosity contrast λ for reduced shear rate γ * = 2.0, reduced area A * = 0.8, and concentrations φ = 0.05 (•), 0.09 (△), and 0.14 (⋆).…”

“…The radius r p of the disks is chosen large enough to ensure mutual overlap and a complete coverage of the membrane to prevent fluid particles from crossing the membrane. Since it is very important to conserve linear and angular momentum for vesicles with viscosity contrast [21,24], we employ the following scattering rule between fluid particles and membrane disks. Scattering occurs only when a fluid particle j and a membrane disk i overlap and move towards each other, so that the conditions |r i − r j | < r p and (r i − r j ) · (v i − v j ) < 0 are satisfied.…”