The mechanism of shape instability for a vesicle in extensional flow

Abstract

When a flexible vesicle is placed in an extensional flow (planar or uniaxial), it undergoes two unique sets of shape transitions that to the best of the authors' knowledge have not been observed for droplets. At intermediate reduced volumes (i.e. intermediate particle aspect ratio) and high extension rates, the vesicle stretches into an asymmetric dumbbell separated by a long, cylindrical thread. At low reduced volumes (i.e. high particle aspect ratio), the vesicle extends symmetrically without bound, in a manner similar to the breakup of liquid droplets. During this 'burst' phase, 'pearling' occasionally occurs, where the vesicle develops a series of periodic beads in its central neck. In this paper, we describe the physical mechanisms behind these seemingly unrelated instabilities by solving the Stokes flow equations around a single, fluid-filled particle whose interfacial dynamics is governed by a Helfrich energy (i.e. the membranes are inextensible with bending resistance). By examining the linear stability of the steady-state shapes, we determine that vesicles are destabilized by curvature changes on its interface, similar to the Rayleigh-Plateau phenomenon. This result suggests that the vesicle's initial geometry plays a large role in its shape transitions under tension. The stability criteria calculated by our simulations and scaling analyses agree well with available experiments. We hope that this work will lend insight into the stretching dynamics of other types of biological particles with nearly incompressible membranes, such as cells.

Measuring Cell Viscoelastic Properties Using a Microfluidic Extensional Flow Device

“…In our study, although we did observe rolling of cells with visible defects in the entrance channels of the cross-slot device (shear dominant Poiseuille flow), we never observed tumbling or rolling in the stagnation-point region (pure extensional flow), only stretching. The existence of one deformation mode in extensional flow-stretching-is expected from cell-mimetic vesicle simulations (60,61) and experiments (37,62). Thus, the differences in our observation of one deformation mode compared to the previous four modes of deformation are a result of the different flow fields.…”

Asymmetric shapes and pearling of a stretched vesicle

“…Membrane inextensibility engenders nonlinearity that gives rise to unexpected behaviours: multiple dynamical states of vesicles in shear flow, slipper-like shapes in Poiseuille flow, and asymmetric shapes in straining flows. Narsimhan et al (2014) highlights the importance of forcing-dependent tension and non-spherical rest shape in destabilizing the symmetric dumbbell in extensional flows, both uniaxial and planar. It would be interesting to study whether other soft particles that can develop non-uniform surface tensions in response to applied flow, e.g.…”

“…In contrast, the surface tension of surfactant-free fluid surfaces is a constant material property and the surface area is allowed to change. The unique interfacial mechanics of vesicles, in particular their non-spherical rest shape, fixed area, and forcing-dependent tension, give rise to the multiple steady states in shear, asymmetric slipper shapes in Poiseuille flow (Kaoui & Misbah 2009;Farutin & Misbah 2011) and underlie the observed instabilities as explained by Narsimhan et al (2014).…”

“…A somewhat similar situation arises with the 'pearling' of elongated drops in an electric field shown in figure 1(c): in this case, the applied electric pressure acts as tension. Narsimhan et al (2014) analyse the dynamics of ellipsoidal (intermediate aspect ratio) and tubular (high aspect ratio) vesicles both theoretically and numerically. In the case of vesicle with intermediate aspect ratio, the analytical theory considers a small perturbation around a spheroidal shape, while the base shape for a tubular vesicle is a cylinder.…”

“…Numerical simulations by Zhao & Shaqfeh (2013) discovered that a vesicle can transition to pear-like shapes. Narsimhan, Spann & Shaqfeh (2014) explain the mechanism of this counterintuitive symmetry breaking and provide a comprehensive analysis of vesicle instabilities in straining flows.…”