Structure development during chaotic mixing in the journal bearing flow

Laminar mixing in the two-dimensional time-periodic Stokes flows between eccentric cylinders [journal bearing flow (JBF)] is studied using the extended mapping method [Galaktionov , Int. J. Multiphase Flows 28, 497 (2002)] with the emphasis on the material stretching, e.g., the interface generation abilities, of the flow. With this flexible and computational advantageous method both, the macroscopic material transport and the evolution of the microstructure can be described. It enables a convenient way for studying the material stretching in the flow and moreover, it provides spatial distribution of locally averaged stretching values instead of pointwise statistics, which was typical for previous studies [Liu , AIChE J. 40, 1273 (1994); Muzzio , Phys. Fluids A 3, 822 (1991)]. The results clearly indicate how the total amount of stretching generated by the flow depends on the parameters of the flow protocol, and that this is not just proportional to the work done on the system, as was suggested earlier in Muzzio , Phys. Fluids A 3, 822 (1991). It was found that when self-similar patterns are established, distinctive zones in the flow, which we call "microstructural demixing zones," are observed, where interfaces are contracted during a typical period of the mixing process. Spatial nonuniformity of stretching in chaotic flows calls for additional mixing measures that reflect the nonuniformity of self-similar stretching patterns, created by time-periodic mixing flows. (C) 2002 American Institute of Physics.