Fluid vesicles, shear flow

H. Noguchi and G. Gompper, Dynamics of fluid vesicles in shear flow effect of membrane viscosity and thermal fluctuations, Phys. Rev. E 72, 011901 (2005). 

The imposition of shear flow can have quite dramatic consequences on the structure and phase behavior of complex fluids. Steady shearing of binary amphiphilic systems can lead to a completely new phase of densely packed onionlike vesicles [140]. Shear flow also strongly affects the stability of the lamellar phase [141-145]. We want to discuss here the role of shear in the microemulsion-to-lamellar transition. 

Noguchi H, Gompper G (2004) Fluid vesicles with viscous membranes in shear flow. Phys Rev Lett 93(25) 258102... 

Red blood cells have a biconcave disc shape, which can hardly be distinguished from the discocyte shape of fluid vesicles with reduced volume V 0.6, compare Fig. 23. However, the membrane of red blood cells is more complex, since a spectrin network is attached to the plasma membrane [181], which helps to retain the integrity of the cell in strong shear gradients or capillary flow. Because of the spectrin network, the red blood cell membrane has a non-zero shear modulus ju. 

The dynamical behavior of fluid vesicles in simple shear flow has been stodied experimentally [190-193], theoretically [194-201], numerically with the boundary-integral technique [202,203] or the phase-field method [203,204], and with meso-scale solvents [37,180,205]. The vesicle shape is now determined by the competition of the curvature elasticity of the membrane, the constraints of constant volume V and constant surface area S, and the external hydrodynamic forces. 

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-... 

Shear flow does not only induce different dynamical modes of prolate and oblate fluid vesicles, it can also induce phase transformations. The simplest case is a oblate fluid vesicle with Tjn,b = 0 and viscosity contrast rjin/rjo = 1- When the reduced shear rate reaches 1, the discocyte vesicles are stretched by the flow forces into a prolate shape [37,180,202], A similar transition is found for stomatocyte vesicles, except that in this case a larger shear rate 3 is required. In the case of non-zero membrane viscosity, a rich phase behavior appears, see Fig. 29. 

Fig. 32 Snapshots of vesicles in capillary flow, with bending rigidity K/k T = 20 and capillary radius / cap = 1-4/fo- a Fluid vesicle with discoidal shape at the mean fluid velocity v T/ffcap =41, both in side and top views, b Elastic vesicle (RBC model) with parachute shape at t m r/Rcap — 218 (with shear modulus nRl/ksT = 110). The blue arrows represent the velocity field of the solvent, c Elastic vesicle with shpper-like shape at v r/Rcap = 80 (with iiRl/k T = 110). The inside and outside of the membrane are depicted in red and green, respectively. The upper front quarter of the vesicle in (b) and the front half of the vesicle in (c) are removed to allow for a look into the interior, the black circles indicate the lines where the membrane has been cut in this procedure. Thick black lines indicate the walls of the cylindrical capillary. From [187]...

Fig. 33 Critical flow velocity Vm of the discocyte-to-parachute transition of elastic vesicles and of the discocyte-to-prolate transition of fluid vesicles, as a function of the bending rigidity for IdRl/ksT =110 (left), and of the shear modulus ju for k/UbT = 10 (right). From [187]...

The fundamental difference between the flow behaviors of fluid vesicles and red blood cells at high flow velocities is due to the shear elasticity of the spectrin network. Its main effect for jiRq/ k > 1 is to suppress the discocyte-to-prolate transition, because the prolate shape would acquire an elastic energy of order fiR. In comparison, the shear stress in the parachute shape is much smaller. 

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