Vesicles in a Poiseuille flow

Vesicle dynamics in unbounded Poiseuille flow is analyzed using a small-deformation theory. Our analytical results quantitatively describe vesicle migration and provide new physical insights. At low ratio between the inner and outer viscosity $\lambda$ (i.e. in the tank-treading regime), the vesicle always migrates towards the flow centerline, unlike other soft particles such as drops. Above a critical $\lambda$, vesicle tumbles and cross-stream migration vanishes. A novel feature is predicted, namely the coexistence of two types of nonequilibrium configurations at the centreline, a bullet-like and a parachute-like shapes.Comment: 4 pages and 5 figure

Dynamics and rheology of a dilute suspension of vesicles: higher order theory

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 $C_a\equiv \tau \dot\gamma$ is small enough ($\tau$= vesicle relaxation time towards equilibrium shape, $\dot\gamma$=shear rate). At larger $C_a$ the $tb$ is preceded by the $vb$ mode. For $C_a\gg 1$ 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

Vesicles in Poiseuille Flow

Blood microcirculation critically depends on the migration of red cells towards the flow centerline. We identify theoretically the ratio of the inner over the outer fluid viscosities λ as a key parameter. At low λ, the vesicle deforms into a tank-treading ellipsoid shape far away from the flow centerline. The migration is always towards the flow centerline, unlike drops. Above a critical λ, the vesicle tumbles or breaths and migration is suppressed. A surprising coexistence of two types of shapes at the centerline, a bulletlike and a parachutelike shape, is predicted

Rheology and dynamics of vesicle suspension in comparison with droplet emulsion

International audienceThis paper deals with the study of dynamics and rheology of a dilute suspension of vesicles. The study is analytical and is based on the small deformation theory. Vesicles in the small deformation limit exhibit, under shear flow, rich dynamics in comparison to droplets (in the regime where the droplet maintains its integrity). For example, droplets only assume a fixed orientation with respect to the flow, while vesicles undergo three types of motions: (i) tank-treading (tt, where the vesicle assumes a fixed orientation with respect to the flow, while the membrane makes a tanktreading motion, (ii) tumbling (tb), which occurs as a saddle-node bifurcation from the tank-treading motion for a certain critical viscosity ratio, (iii) vacillating-breathing (vb), where the vesicle long axis undergoes oscillations around the shear direction whereas its shape executes a breathing-like motion. This mode is found to coexist with tumbling in the high shear rate limit (or high capillary number Ca =gdot tau , where gdot is the shear rate and tau is the relaxation time towards equilibrium shape of the vesicle). After analyzing these modes and comparing dynamics to droplets, we study rheology. It is found that the constitutive law, written in the co-moving frame, is nonlinear even to leading order. This markedly contrasts with droplet emulsion where the equation is linear to leading order. We make a link between rheology and the above three dynamical states. It is found that the effective viscosity undergoes a cusp singularity at the tumbling bifurcation (which happens at small enough Ca), while the normal stress differences collapse in the tumbling and VB regimes. At high enough Ca the tb transition is preceded by the vb mode. We also report on shear thinning and the behavior of the normal stress difference as a function of gdot