Dynamic modes of microcapsules in steady shear flow: Effects of bending and shear elasticities

Abstract

The dynamics of microcapsules in steady shear flow was studied using a theoretical approach based on three variables: The Taylor deformation parameter αD, the inclination angle θ, and the phase angle φ of the membrane rotation. It is found that the dynamic phase diagram shows a remarkable change with an increase in the ratio of the membrane shear and bending elasticities. A fluid vesicle (no shear elasticity) exhibits three dynamic modes: (i) Tank-treading (TT) at low viscosity ηin of internal fluid (αD and θ relaxes to constant values), (ii) Tumbling (TB) at high ηin (θ rotates), and (iii) Swinging (SW) at middle ηin and high shear rateγ (θ oscillates). All of three modes are accompanied by a membrane (φ) rotation. For microcapsules with low shear elasticity, the TB phase with no φ rotation and the coexistence phase of SW and TB motions are induced by the energy barrier of φ rotation. Synchronization of φ rotation with TB rotation or SW oscillation occurs with integer ratios of rotational frequencies. At high shear elasticity, where a saddle point in the energy potential disappears, intermediate phases vanish, and either φ or θ rotation occurs. This phase behavior agrees with recent simulation results of microcapsules with low bending elasticity.

Intermittency and synchronized motion of red blood cell dynamics in shear flow

“…Additional cases of synchronized motion and coexistence of TT and tumbling are presented in figures 4(b) and (c) in which the membrane rotation progressively slows down, resulting in increasing values of f θ /f φ = 2 and 3, respectively. Similarly to the prediction made by Noguchi (2009Noguchi ( , 2010, integer values of f θ /f φ are observed, which in the present simulations vary from 1 to 6. These additional cases of synchronized motion are presented in the supplementary materials (figures S17-S32 and two animations).…”

“…The bending energy has the opposite trend to the elastic energy: it is maximum near the dimple and minimum around the rim. However, bending energy alone does not provide a barrier to membrane rotation, as noted by Noguchi (2010) and also illustrated in our previous study by Yazdani & Bagchi (2011), where we observed that the TB-TT transition border at low λ remained nearly unchanged with increasing bending stiffness.…”

“…Figure 7(a) shows f θ /f φ obtained from our simulations as a function of Ca and λ. The frequency ratio varies from 1 to 6 in the parameter range considered in the simulations, resembling a Devil's staircase as predicted by the reduced model of Noguchi (2009Noguchi ( , 2010. The figure shows that f θ /f φ increases with increasing λ, but decreases with increasing Ca.…”

“…Following the discovery of the intermittent dynamics, several theoretical and computational studies emerged that either supported or rejected the possibility of such dynamics (Abkarian et al 2007;Skotheim & Secomb 2007;Kessler, Finken & Seifert 2008;Noguchi 2009Noguchi , 2010 Email address for correspondence: pbagchi@jove.rutgers.edu Intermittency in red blood cell dynamics 473 2011; Vlahovska et al 2011;Abreu & Seifert 2012). The theoretical models that predicted the intermittent motion are the reduced-order models which assume that the cell maintains its resting shape while in the flow (Abkarian et al 2007;Skotheim & Secomb 2007;Noguchi 2009Noguchi , 2010Abreu & Seifert 2012). Additionally, the reduced model of Noguchi (2009Noguchi ( , 2010 also predicted a synchronized motion characterized by simultaneous cell tumbling and membrane rotation with integer ratios of the rotational frequencies.…”

“…The theoretical models that predicted the intermittent motion are the reduced-order models which assume that the cell maintains its resting shape while in the flow (Abkarian et al 2007;Skotheim & Secomb 2007;Noguchi 2009Noguchi , 2010Abreu & Seifert 2012). Additionally, the reduced model of Noguchi (2009Noguchi ( , 2010 also predicted a synchronized motion characterized by simultaneous cell tumbling and membrane rotation with integer ratios of the rotational frequencies. Later, however, a small-deformation model developed by Vlahovska et al (2011) concluded that the intermittency is a result of the shape preservation assumed in the reduced models and is suppressed if the cell is allowed to deform along the vorticity direction (the so-called breathing motion).…”