Studies on the chaotic rheological parameters of periodically forced suspensions of weak brownian slender bodies in simple shear flow

Abstract

We consider the technologically important problem of the rheology of periodically forced suspensions of slender rods in simple shear flow. We present a novel technique to calculate rheological parameters and other properties of such suspensions when the orientations of the suspended particles evolve chaotically. We demonstrate for the first time that the rheological parameters like the apparent viscosities and the first and second normal stress differences of suspensions of orientable particles can show chaotic behavior when the orientation vector evolves chaotically. We also demonstrate that the range of the Poincare section points of the rheological parameters is increased by about five to six orders of magnitude when the orientations of the suspended particles evolve chaotically than when the orientations evolve non-chaotically in certain chaotic regimes. This suggests that a wide range of properties may be obtained by small variations in controllable parameters. When coupled with suitable control of chaos algorithms, a wide range of suspension behavior is thus possible since a chaotic solution can be considered as an unlimited reservoir of unstable periodic solutions of arbitrary period. We examine the consequences of the chaotic evolution of the orientable particles on the dynamics and rheology of suspensions starting off with uniform initial orientation distributions as well as aligned initial distributions. We provide numerical evidence for the existence of riddled and intermingled basins of attractions in the system. Consequently, small changes in the preparation of aligned suspensions can lead to dramatically different rheological behavior in some parametric regimes. In other parametric regimes differences in the dynamical behavior do not translate into differences in the rheological behavior of aligned suspensions. In this work we also show that the chaotic rheological parameters can be controlled to oscillate in a desired periodic orbit with an algorithm which is easy to implement experimentally. Further, the possibility of obtaining novel rheological properties such as the second normal stress difference being greater in magnitude than the first normal stress difference and the first normal stress difference being positive is also demonstrated through control of chaos. It is also demonstrated that complex non-sinusoidal periodic behavior can be obtained through the above technique. The results of this work may be applicable to the development of computer controlled intelligent rheology.