Keller-Skalak theory

However, the vesicle shape in shear flow is often not as constant as assnmed by Keller and Skalak. In these situations, it is very helpful to compare simulation results with a generalized KeUer-Skalak theory, in which shape deformation and thermal fluctuations are taken into account. Therefore, a phenomenological model has been suggested in [180], in which in addition to the inclination angle 9 a second parameter is introduced to characterize the vesicle shape and deformation, the asphericity [207]... 

The theory of Keller and Skalak [194] describes the hydrodynamic behavior of vesicles of fixed ellipsoidal shape in shear flow, with the viscosities t)in and qo of the internal and external fluids, respectively. Despite of the tqtproximations needed to derive the equation of motion for the inclinalion angle 6, which measures the deviation of the symmetry axis of the ellipsoid from the flow direction, this theory describes vesicles in flow surprisingly well. It has been generalized later [197] to describe the effects of a membrane viscosity Tjmb-... 

The main result of the theory of Keller and Skalak is the equation of motion for the inclination angle [194],... 

The theory of Keller and Skalak [194] predicts for fluid vesicles a transition from tank-treading to tumbling with increasing viscosity contrast rjm/Tjo- This has been confirmed in recent simulations based on a phase-field model [203],... 

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