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In biology, cells undergo deformations under the action of flow caused by the fluid surrounding them. These flows lead to shape changes and instabilities that have been explored in detail for single component vesicles. However, cell membranes are often multicomponent in nature, made up of multiple phospholipids and cholesterol mixtures that give rise to interesting thermodynamics and fluid mechanics. Our work analyses shear flow around a multicomponent vesicle using a small-deformation theory based on vector and scalar spherical harmonics. We set up the problem by laying out the governing momentum equations and the traction balance arising from the phase separation and bending. These equations are solved along with a Cahn–Hilliard equation that governs the coarsening dynamics of the phospholipid–cholesterol mixture. We provide a detailed analysis of the vesicle dynamics (e.g. tumbling, breathing, tank-treading and swinging/phase-treading) in two regimes – when flow is faster than coarsening dynamics (Péclet number$${\textit{Pe}} \gg 1$$) and when the two time scales are comparable ($$\textit{Pe} \sim O(1)$$) – and provide a discussion on when these behaviours occur. The analysis aims to provide an experimentalist with important insights pertaining to the phase separation dynamics and their effect on the deformation dynamics of a vesicle. 

Vesicles are important surrogate structures made up of multiple phospholipids and cholesterol distributed in the form of a lipid bilayer. Tubular vesicles can undergo pearling – i.e. formation of beads on the liquid thread akin to the Rayleigh–Plateau instability. Previous studies have inspected the effects of surface tension on the pearling instabilities of single-component vesicles. In this study, we perform a linear stability analysis on a multicomponent cylindrical vesicle. We solve the Stokes equations along with the Cahn–Hilliard equation to develop the linearized dynamic equations governing the vesicle shape and surface concentration fields. This helps us to show that multicomponent vesicles can undergo pearling, buckling and wrinkling even in the absence of surface tension, which is a significantly different result from studies on single-component vesicles. This behaviour arises due to the competition between the free energies of phase separation, line tension and bending for this multi-phospholipid system. We determine the conditions under which axisymmetric and non-axisymmetric modes are dominant, and supplement our results with an energy analysis that shows the sources for these instabilities. Lastly, we delve into a weakly nonlinear analysis where we solve the nonlinear Cahn–Hilliard equation in the weak deformation limit to understand how mode-mixing alters the late time dynamics of coarsening. We show that in many situations, the trends from our simulations qualitatively match recent experiments (Yanagisawaet al.,Phys. Rev. E, vol. 82, 2010, p. 051928).