%0 Journal Article %1 vlahovska:2007pi %A Vlahovska, P M %A Gracia, R S %D 2007 %J Physical Review E %K BENDING MEMBRANE RED SHEAR-FLOW; SIMPLE STIFFNESS; %N 1 %P 16313 %T Dynamics of a viscous vesicle in linear flows %V 75 %X 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 nonlinear 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.

@article{vlahovska:2007pi, abstract = {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 nonlinear 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.}, added-at = {2013-11-08T00:45:00.000+0100}, author = {Vlahovska, P M and Gracia, R S}, bdsk-file-1 = {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}, biburl = {https://www.bibsonomy.org/bibtex/23d66bd33b7b1fbb19566f1b700fc89be/andresgm}, date-modified = {2012-03-09 13:51:27 +0000}, interhash = {238b0956d6f2903cd986fbd0c8ad11a3}, intrahash = {3d66bd33b7b1fbb19566f1b700fc89be}, issn = {1539-3755}, journal = {Physical Review E}, keywords = {BENDING MEMBRANE RED SHEAR-FLOW; SIMPLE STIFFNESS;}, month = jan, number = 1, pages = 16313, timestamp = {2013-11-08T00:45:00.000+0100}, title = {Dynamics of a viscous vesicle in linear flows}, volume = 75, year = 2007 }