(95d) Spatio-Temporal Pattern Formation in Viscoelastic Taylor-Couette Flow: Dynamical Simulation and Mechanism

We report spatio-temporal pattern formation in Taylor-Couette flow (i.e. flow between rotating cylinders) of viscoelastic dilute polymer solutions obtained for the first time from first principle dynamical simulations using a parallel, fully spectral time-splitting algorithm [1, 2]. Experimental investigations of pattern formation in viscoelastic TCF have uncovered a variety of intriguing flow transitions including rotating standing waves (RSW), disordered oscillations (DO) and solitary vortex solutions which can be time-dependent (oscillatory strips (OS)) or time-invariant (diwhirls (DW)). However, to date, theoretical investigations have been limited to weakly nonlinear analysis or computation of axisymmetric steady states. This has limited the understanding of the mechanisms of flow-microstructure coupling underlying the pattern formation process which, as shown by experiments, inherently includes creation/destruction of spatial (i.e. axisymmetry vs. non-axisymmetry, periodicity in the direction of the cylinder axis) and temporal (i.e. stationary, time-periodic or disordered) symmetries which can be captured only by means of a fully 3-dimensional dynamical simulations. In this presentation, we will report, the principal findings of such dynamical explorations and discuss the pattern formation mechanisms. Solution structures with varying spatial and temporal symmetries, such as rotating standing waves, flames, disordered oscillations, and solitary vortex solutions which include diwhirls (stationary and axisymmetric) and oscillatory strips (axisymmetric or non-axisymmetric) are observed, depending on the ratio of fluid relaxation time to the time period of inner cylinder rotation. The flow-microstructure coupling mechanisms underlying the pattern formation process will be also discussed.

1. D.G. Thomas, U.A. Al-Mubaiyedh, R. Sureshkumar & B. Khomami, Time-dependent simulation of non-axisymmetric patterns in viscoelastic Taylor-Couette flow, accepted, J. Non-Newtonian Fluid Mech. (2006)

2. D.G. Thomas, R. Sureshkumar & B. Khomami, Pattern formation in Taylor-Couette flow of dilute polymer solutions: dynamical simulations and mechanism, submitted, (2006)