J. Fluid Mech. (2012), vol. 711, pp. 122–146. c  Cambridge University Press 2012 122 doi:10.1017/jfm.2012.380 Reynolds number effects on lipid vesicles David Salac 1 † and Michael J. Miksis 2 1 Department of Mechanical and Aerospace Engineering, University at Buffalo SUNY, Buffalo, NY 14260, USA 2 Engineering Sciences and Applied Mathematics, Northwestern University, Evanston, IL 60208, USA (Received 10 November 2011; revised 7 May 2012; accepted 23 July 2012; first published online 31 August 2012) Vesicles exposed to the human circulatory system experience a wide range of flows and Reynolds numbers. Previous investigations of vesicles in fluid flow have focused on the Stokes flow regime. In this work the influence of inertia on the dynamics of a vesicle in a shearing flow is investigated using a novel level-set computational method in two dimensions. A detailed analysis of the behaviour of a single vesicle at finite Reynolds number is presented. At low Reynolds numbers the results recover vesicle behaviour previously observed for Stokes flow. At moderate Reynolds numbers the classical tumbling behaviour of highly viscous vesicles is no longer observed. Instead, the vesicle is observed to tank-tread, with an equilibrium angle dependent on the Reynolds number and the reduced area of the vesicle. It is shown that a vesicle with an inner/outer fluid viscosity ratio as high as 200 will not tumble if the Reynolds number is as low as 10. A new damped tank-treading behaviour, where the vesicle will briefly oscillate about the equilibrium inclination angle, is also observed. This behaviour is explained by an investigation on the torque acting on a vesicle in shear flow. Scaling laws for vesicles in inertial flows have also been determined. It is observed that quantities such as vesicle tumbling period follow square-root scaling with respect to the Reynolds number. Finally, the maximum tension as a function of the Reynolds number is also determined. It is observed that, as the Reynolds number increases, the maximum tension on the vesicle membrane also increases. This could play a role in the creation of stable pores in vesicle membranes or for the premature destruction of vesicles exposed to the human circulatory system. Key words: capsule/cell dynamics, membranes, multiphase flow 1. Introduction Vesicles have been proposed in various biotechnologies, such as drug delivery systems (Choon & Cullis 1995; Allen & Cullis 2004; Torchilin 2006). Vesicles used in such a technology would be exposed to all conditions in the circulatory system, from creeping flow (Fung & Zweifach 1971) to flows where inertia cannot be ignored (Ku et al. 1985). As a result, the behaviour of vesicles in external flows has been of great interest experimentally (Abkarian, Lartigue & Viallat 2002; Abkarian & Viallat 2005, 2008; Abkarian, Faivre & Viallat 2007; Coupier et al. 2008; Deschamps et al. 2009a; Deschamps, Kantsler & Steinberg 2009b), theoretically (Vlahovska & Gracia 2007; Lebedev, Turitsyn & Vergeles 2008; Danker, Vlahovska & Misbah 2009; Vlahovska, Podgorski & Misbah 2009; Schwalbe, Vlahovska & Miksis 2010) and † Email address for correspondence: davidsal@buffalo.edu