Dynamical regimes and hydrodynamic lift of viscous vesicles under shear

TL;DR

This study explores the complex dynamics of viscous vesicles in shear flow, revealing a new oscillatory swinging motion, extending theoretical models, and analyzing the hydrodynamic lift force near walls through simulations and boundary-integral methods.

Contribution

The paper introduces the observation of oscillatory swinging motion in viscous vesicles and extends Keller-Skalak theory to predict their dynamical phase diagram.

Findings

Identification of oscillatory swinging motion at high shear rates.

Good agreement between simulations and extended theoretical predictions.

Lift force on vesicles follows a power law decay with distance from the wall.

Abstract

The dynamics of two-dimensional viscous vesicles in shear flow, with different fluid viscosities $\eta_{\rm in}$ and $\eta_{\rm out}$ 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 $\eta_{\rm in}/\eta_{\rm out}$. 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 $y_{\rm {cm}}$ of the vesicle center of mass from the wall is well described by an effective power law $y_{\rm {cm}}^{-2}$ for intermediate distances $0.8 R_{\rm p} \lesssim y_{\rm {cm}} \lesssim 3 R_{\rm p}$ with vesicle radius $R_{\rm p}$. The boundary-integral calculation indicates that the lift force decays asymptotically as $1/[y_{\rm {cm}}\ln(y_{\rm {cm}})]$ far from the wall.