Oscillatory motion of sheared nanorods beyond the nematic phase

Abstract

We study the role of the control parameter triggering nematic order (temperature or concentration) on the dynamical behavior of a system of nanorods under shear. Our study is based on a set of mesoscopic equations of motion for the components of the tensorial orientational order parameter. We investigate these equations via a systematic bifurcation analysis based on a numerical continuation technique, focusing on spatially homogeneous states. Exploring a wide range of parameters we find, unexpectedly, that states with oscillatory motion can exist even under conditions where the equilibrium system is isotropic. These oscillatory states are characterized by a wagging motion of the paranematic director, and they occur if the tumbling parameter is sufficiently small. We also present full nonequilibrium phase diagrams in the plane spanned by the concentration and the shear rate.

Binary mixtures of rod-like colloids under shear: microscopically-based equilibrium theory and order-parameter dynamics

“…Finally, we notice the small "islands" of KT regions within the T state (A-species) or W-state (B-species). This indicates a bi-stability of the solutions which may be interpreted as a coexistence of in-shear-plane and out-of-shear plane oscillations (as already mentioned in [34]). At this point, it would be very interesting to extend the present analysis to spatially inhomogeneous systems: Indeed, as previously shown for a one-component system [37,71], bistability in the homogeneous system can translate to spatially separated dynamical coexistence of different states, when one allows for inhomogeneity.…”

“…The simplest one is a (supercritical) Hopf bifurcation occurring at the boundary between alignment (A) and wagging (W). In [34] we have presented a complete continuation analysis revealing the complexity of the dynamical behavior already in the one-component case (where one has already five dynamical variables). Performing such an analysis for the mixture would have been beyond the scope for the present paper.…”

“…Indeed, experience with one-component systems [34] shows that the nature of the underlying equilibrium state is crucial for the dynamical behavior under shear. The equilibrium mixtures considered here were characterized by particles with equal diameters and different length.…”

“…Therefore, all numerical integrations have been repeated several times. To characterize the resulting dynamical states, we use an algorithm that recognizes the periodicity and sign change of the calculated time-dependent order parameters q i k (t) [68,32,35,65,69,34].…”

Time-delayed feedback control of shear-driven micellar systems

“…The Pyragas scheme has been applied to a broad variety of non-linear systems from various fields (see [30,31] for overviews) including semiconductor nanostructures, lasers, neural systems and general reaction-diffusion systems [32,33]. There are also recent applications to the flow of soft-matter systems, both from the experimental [34] and from the theoretical side [35], an example being the stabilization of steady shear-aligned states in sheared liquid crystals [36]. Within the present study, we focus on a non-diagonal control scheme which targets the average total stress or shear rate, respectively, yielding a Pyragas term involving only the viscoelastic stress.…”