Vesicles under shear flow exhibit various dynamics: tank-treading (tt),
tumbling (tb) and vacillating-breathing (vb). A consistent higher order
theory reveals a direct bifurcation from tt to tb if Ca​≡τγ˙​ is small enough (τ= vesicle relaxation time towards
equilibrium shape, γ˙​=shear rate). At larger Ca​ the tb is
preceded by the vb mode. For Ca​≫1 we recover the leading order original
calculation, where the vb mode coexists with tb. The consistent calculation
reveals several quantitative discrepancies with recent works, and points to new
features. We analyse rheology and find that the effective viscosity exhibits a
minimum at tt−tb and tt−vb bifurcation points.Comment: 4 pages, 5 figure