The behavior of closed inextensible membranes in linear and quadratic shear flows

Olla, Piero

doi:10.1016/s0378-4371(99)00563-4

Cited by 32 publications

(36 citation statements)

References 24 publications

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“…In analogous way, vesicles are able to migrate transverse to a wall bounded shear flow thanks to tank-treading (Olla 1997;Sukumaran & Seifert 2001;Abkarian et Al. 2002), and similar behavior have been observed in quadratic shear flows as well (Olla 2000;Coupier et Al. 2008;Danker et Al.…”

Section: P Ollasupporting

confidence: 79%

“…The choice Ca = O(ǫ 1/2 ) allows us to circumvent such difficulties. Forκ = 0, these equations correspond to the ones obtained in Seifert (1999) and Olla (2000). They differ only for the expression of the coefficient of the time derivative, that, to the order considered in ǫ, due to the ordering in Eq.…”

Section: P Ollamentioning

confidence: 83%

“…We shall determine the bending rigidity profile that would generate such behavior, and investigate the possibility that the required bending rigidity profiles be obtained as a direct response of the membrane to the external environment, without the need of an "intelligent", internal control system. An analytical treatment of the problem is possible only in the case of quasi-spherical vesicles, and, for this purpose, the analysis in Seifert (1999) and Olla (2000) will be generalized to the case of an inhomogeneous membrane. As discussed in Farutin et Al.…”

Section: P Ollamentioning

confidence: 99%

“…It is possible to see that local inextensibility leads to the following relation between velocity components on the membrane (Seifert 1999;Olla 2000):…”

Section: P Ollamentioning

confidence: 99%

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Tank-treading as a means of propulsion in viscous shear flows

Olla

2011

J. Fluid Mech.

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The use of tank-treading as a means of propulsion for microswimmers in viscous shear flows is taken into exam. We discuss the possibility that a vesicle be able to control the drift in an external shear flow, by varying locally the bending rigidity of its own membrane. By analytical calculation in the quasi-spherical limit, the stationary shape and the orientation of the tank-treading vesicle in the external flow, are determined, working to lowest order in the membrane inhomogeneity. The membrane inhomogeneity acts in the shape evolution equation as an additional force term, that can be used to balance the effect of the hydrodynamic stresses, thus allowing the vesicle to assume shapes and orientations that would otherwise be forbidden. The vesicle shapes and orientations required for migration transverse to the flow, together with the bending rigidity profiles that would lead to such shapes and orientations, are determined. A simple model is presented, in which a vesicle is able to migrate up or down the gradient of a concentration field, by stiffening or softening of its membrane, in response to the variations in the concentration level experienced during tank-treading.

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Section: P Ollasupporting

confidence: 79%

Section: P Ollamentioning

confidence: 83%

Section: P Ollamentioning

confidence: 99%

“…It is possible to see that local inextensibility leads to the following relation between velocity components on the membrane (Seifert 1999;Olla 2000):…”

Section: P Ollamentioning

confidence: 99%

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Tank-treading as a means of propulsion in viscous shear flows

Olla

2011

J. Fluid Mech.

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“…Experimental studies 7,8,9,10 of vesicle behavior in unbounded shear flow observe that in weak flows, and when the inner and outer fluids are the same, the vesicle deforms into a tanktreading stationary prolate ellipsoid with an inclination angle close to π/4 with respect to the flow direction; however, in striking contrast to drops, when the fluid inside is more viscous than outside the vesicle undergoes a tumbling motion. Numerical simulations 11,12,13 and analytical theories 14,15,16 of vesicle microhydrodynamics attempt to elucidate such experimental observations. In their classic paper Keller and Skalak 17 analyzed the motion of a tank-treading ellipsoid in unbounded shear flow.…”

Section: Introductionmentioning

confidence: 99%

Dynamics of a viscous vesicle in linear flows

2007

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An analytical theory is developed to describe the dynamics of a closed lipid bilayer membrane (vesicle) freely suspended in a general linear flow. Considering a nearly spherical shape, the solution to the creeping-flow equations is obtained as a regular perturbation expansion in the excess area. The analysis takes into account the membrane fluidity, incompressibility and resistance to bending. The constraint for a fixed total area leads to a non-linear shape evolution equation at leading order. As a result two regimes of vesicle behavior, tank-treading and tumbling, are predicted depending on the viscosity contrast between interior and exterior fluid. Below a critical viscosity contrast, which depends on the excess area, the vesicle deforms into a tank-treading ellipsoid, whose orientation angle with respect to the flow direction is independent of the membrane bending rigidity. In the tumbling regime, the vesicle exhibits periodic shape deformations with a frequency that increases with the viscosity contrast. Non-Newtonian rheology such as normal stresses is predicted for a dilute suspension of vesicles. The theory is in good agreement with published experimental data for vesicle behavior in simple shear flow.

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