Phase Diagram of Single Vesicle Dynamical States in Shear Flow

Abstract

We report the first experimental phase diagram of vesicle dynamical states in a shear flow presented in a space of two dimensionless parameters suggested recently by V. Lebedev et al. To reduce errors in the control parameters, 3D geometrical reconstruction and determination of the viscosity contrast of a vesicle in situ in a plane Couette flow device prior to the experiment are developed. Our results are in accord with the theory predicting three distinctly separating regions of vesicle dynamical states in the plane of just two self-similar parameters.

Dynamics of a vesicle in general flow

“…The experimental path across the phase diagram depends on the initial state and the way /s and s are varied. The possibility to observe all dynamical states with the same vesicle, even for ϭ 1 used in the current experiment, complements the previous views based on the shear flow dynamics (2)(3)(4)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19)(20). On the other hand, the experimental approach used here will be advantageous to study the dynamics of other flexible microobjects, including biological membranes and red blood cells, in flow.…”

“…Particle tracking velocimetry (PTV) measurements show fair agreement with numerical simulations and high flow uniformity ( Fig. 2 To reduce error bars on S and ⌳, the geometrical parameters R and ⌬ of each vesicle were measured in situ from a 3D reconstruction of its shape (20) in TT motion at low S, with mean errors of 1.7% on R and of 6.1% on ⌬ within the range [0.3, 2.5]. Since only vesicles with ϭ 1 were used in this work, there is no error contribution from this parameter (20).…”

“…2 To reduce error bars on S and ⌳, the geometrical parameters R and ⌬ of each vesicle were measured in situ from a 3D reconstruction of its shape (20) in TT motion at low S, with mean errors of 1.7% on R and of 6.1% on ⌬ within the range [0.3, 2.5]. Since only vesicles with ϭ 1 were used in this work, there is no error contribution from this parameter (20). Errors from non-uniformity of the velocity field were below 2%; that cumulates to overall mean errors of 8.7% on S and of 2% on ⌳.…”

“…As we have verified recently, only the 1 of them presented in ref. 5 describes adequately the experimental data (20). The main result of this model, which is based on the approximation of ⌬Ͻ Ͻ1, second order spherical harmonics, and neglecting thermal noise, is a self-similar solution, which reduces the number of the dimensionless control parameters to just 2: S ' 7␥ out R 3 / ͌ 3⌬ and ⌳ ' 4(1 ϩ 23/32) ͌ ⌬/ ͌ 30, where is the bending elasticity [taken further as ϭ 25 k B TϷ10…”

“…To scan all 3 regimes of motion and to trace transitions among them in a shear flow, one should vary both ␥ and , that is change the viscosities of inner and outer fluids, which is an impossible task to realize on an individual vesicle. Because of topology of the phase diagram (5,20), the only remaining possibility with a single vesicle is to scan transitions from TU to TR by varying ␥.…”