Elastic capsules in shear flow: Analytical solutions for constant and time-dependent shear rates

摘要

We investigate the dynamics of microcapsules in linear shear flow within a reduced model withtwo 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 thispaper, we integrate the equations of motion in the quasi-spherical limit analytically for time-constant andtime-dependent shear flow using matched asymptotic expansions. Using this method, we find analyticalexpressions for the mean tumbling rate in general time-dependent shear flow. The capsule dynamics isstudied in more detail when the inverse shear rate is harmonically modulated around a constant mean valuefor which a dynamic phase diagram is constructed. By a judicious choice of both modulation frequency andphase, 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 modulationfrequency.