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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.