Dynamics and rheology of a dilute suspension of vesicles: higher order theory
Gerrit Danker, Thierry Biben, Thomas Podgorski, Claude Verdier, Chaouqi Misbah
Abstract
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
C
a
≡τ
γ
˙
is small enough (
τ
= vesicle relaxation time towards equilibrium shape,
γ
˙
=shear rate). At larger
C
a
the
tb
is preceded by the
vb
mode. For
C
a
≫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.