Elastic capsules in shear flow: Analytical solutions for constant and time-dependent shear ratesS. Kessler, R. Finken and U. Seifert
II. Institut für Theoretische Physik, Universität Stuttgart, Pfaffenwaldring 57, 70550, Stuttgart, Germany
Received 25 February 2009 / Revised version 25 May 2009 / Published online 9 August 2009
We investigate the dynamics of microcapsules in linear shear flow within a reduced model with two degrees of freedom. In previous work for steady shear flow, the dynamic phases of this model, i.e. swinging, tumbling and intermittent behaviour, have been identified using numerical methods. In this paper, we integrate the equations of motion in the quasi-spherical limit analytically for time-constant and time-dependent shear flow using matched asymptotic expansions. Using this method, we find analytical expressions for the mean tumbling rate in general time-dependent shear flow. The capsule dynamics is studied in more detail when the inverse shear rate is harmonically modulated around a constant mean value for which a dynamic phase diagram is constructed. By a judicious choice of both modulation frequency and phase, tumbling motion can be induced even if the mean shear rate corresponds to the swinging regime. We derive expressions for the amplitude and width of the resonance peaks as a function of the modulation frequency.PACS
87.16.D- - Membranes, bilayers, and vesicles.
47.15.G- - Low-Reynolds-number (creeping) flows. Correspondence: email@example.com
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag 2009