Analytical solutions and classification of vesicle motion and deformation in shear flow: Uncovering new tank-treading...

Using a small deformation approach, a fractional ordinary differential system is proposed to investigate the motion and deformation of a vesicle in shear flow. Closed analytical expressions of the orientation angle and the ellipticity of the vesicle contour (shape deformation) are provided. Three different motions are identified, the classical tank-treading state, and two new types of motions, namely, the over-damped tank-treading mode, in which the vesicle's orientation angle ψ and its shape deformation R tend more slowly toward equilibrium, and the under-damped tank-treading mode, in which ψ oscillates all the time along the flow direction with decreasing amplitude, while R starts making a breathing motion and then tends to an attractive amplitude. The implications of our findings extend widely within the field of fluid dynamics, revealing the potential for further advancements and applications in understanding complex fluid systems.