Wrinkling instability of vesicles in steady linear flow

We present experimental observations and numerical simulations of a wrinkling instability that occurs at sufficiently high strain rates in the trembling regime of vesicle dynamics in steady linear flow. Spectral and statistical analysis of the data shows similarities and differences with the wrinkling instability observed earlier for vesicles in transient elongation flow. The critical relevance of thermal fluctuations for this phenomenon is revealed by a simple model using coupled Langevin equations that reproduces the experimental observations quite well. Introduction. – Wrinkling is a well-known phenomenon frequently observed in nature and everyday life on widely different spatial scales [1,2]. It bridges mechanics, geometry, physics, and biology. It usually occurs either in extensible materials due to external stretching, or as a result of compression of inextensible materials, in which case it reduces to the Euler buckling instability [3]. In contrast to the wrinkling instability in films and structures such as micro-capsules, where it occurs due to stretching elasticity [4], in vesicles with unstretchable lipid membranes it takes place under compression due to negative surface tension [5, 6]. Vesicles are fluid droplets encapsulated by a phospholipid-bilayer membrane and suspended in either the same or another fluid [7]. They are considered as simple model objects to simulate red-blood-cell dynamics in a first step towards understanding blood rheology. Two constraints, namely the conservation of both vesicle volume V and surface area A, result in rather involved non-linear dynamics in flow (for a review, see [8]). In transient plane elongation (hyperbolic) flow, the wrinkling instability happening during the relaxation of a vesicle towards a new stationary state was studied experimentally [5]. There, the flow direction was reversed faster than the vesicle’s relaxation time scale τ ∼ ηoutR 0/κ, where κ is the bending elasticity, ηout outer fluid viscosity, and R0 = (3V/4π) 1/3 the effective vesicle radius defined via the volume V . This sudden reversal causes a switching from vesicle stretching to vesicle compression, see Fig. 1 top. The next reversal then takes Figure 1: Schematic presentation of flow reversal and vesicle compression in elongation (top) and linear (bottom) flows. place after full relaxation. For strain rates χ lower than a critical value χc, this flow reversal leads to an almost smooth transition from an elliptical vesicle with long axis in the direction of compression to one with long axis perpendicular to it. During this transient transformation, only deformations with wave number k = 2 are induced by the flow. Higher-order deformations are only excited thermally, and the deformation power spectrum Pk ∼ k is observed since bending deformations enter as κk in the membrane energy [7]. For χ > χc, higher-order deformation modes, coined wrinkles, are generated on top of an almost elliptical vesicle. A spectral analysis of the shape distortions easily identifies the wrinkling onset due to a sharp growth of higher-order harmonics (see Fig. 3 in [5]). In this Letter, we explore another mechanism to observe wrinkling caused by the interplay of thermal fluctuations