Shear-induced chaos in nonlinear Maxwell-model fluids

Abstract

A generalized model for the behavior of the stress tensor in non-Newtonian fluids is investigated for spatially homogeneous plane Couette flow, showing a variety of nonlinear responses and deterministic chaos. Mapping of chaotic solutions is achieved through the largest Lyapunov exponent for the two main parameters: The shear rate and the temperature and/or density. Bifurcation diagrams and stability analysis are used to reveal some of the rich dynamics that can be found. Suggested mechanisms for stability loss in these complex fluids include Hopf, saddle-node, and period-doubling bifurcations.

Flow Properties Inferred from Generalized Maxwell Models

“…The stability of solutions as discussed here was studied for the isotropic potential function [45], a bifurcation analysis for the anisotropic potential case has been performed recently [44]. These aspects are outside the scope of article.…”

Shear-stress-controlled dynamics of nematic complex fluids

“…Examples are the tumbling or wagging behavior observed both by theory [12] and in experiments of sheared tobacco viruses [9]. Further issues receiving much attention are the appearance of rheochaos (chaotic stressstrain curves and/or orientational dynamics) [12][13][14][16][17][18][19][20], and, sometimes combined with that, spontaneous spatial-symmetry breaking associated to shear-banding [8,21]. In the latter situation, the system separates into domains characterized by different local shear rates.…”

“…As a consequence of this non-linearity, the (five-dimensional) dynamical system involving the independent components of a generates complex orientational dynamics and associated rheological properties, even if the analysis is restricted to simple (Couette) shear geometries and to spatially homogeneous systems (for extensions of the Hess-Doi approach towards inhomogeneous systems see, e.g., [26][27][28][29]). Another class of mesoscopic theories focusses directly on the shear stress σ xy as a dynamic variable [8,19,20,30,31], an example being the non-local Johnson-Segalman model [18,32]. These models are capable of describing, on a quite general level, complex rheological behavior such as shear-banding [8], a drawback being that they reflect the (orientational and/or translational) dynamics within the underlying liquid only indirectly.…”

Feedback control of flow alignment in sheared liquid crystals

“…The nonlinear orientational dynamics also has direct implications for the rheological behavior of the system as reflected, e.g., by non-monotonic stress-strain curves ("constitutive relations") [17][18][19][20][21][22][23] and a non-Newtonian behavior of the viscosity. Understanding the dynamics is thus a prerequisite for the deliberate design of materials with specific rheological properties, which are tunable by parameters such as particle geometry, concentration (temperature) and external fields.…”