Laminar mixing and chaotic mixing in several cavity flows

Abstract

The objective of this work is an experimental study of laminar mixing in several kinds of two-dimensional cavity flows by means of material line and blob deformation in a new experimental system consisting of two sets of roller pairs connected by belts. The apparatus can be adjusted to produce a range of aspect ratios (0.067–10), Reynolds numbers (0.1–100), and various kinds of flow fields with one or two moving boundaries. Flow visualization is conducted by marking underneath the free surface of the flow with a tracer solution of low diffusivity and of approximately the same density and viscosity as the flowing fluid. The effects of the initial location of the material blob, relative motion of the two bands, and minor changes in the geometry of the flow region are investigated experimentally.The alternate periodic motion of two bands in a cavity flow is an example of a laminar flow which might lead to chaotic mixing. The governing parameter is the dimensionless frequency of oscillation of the walls f which, under the proper conditions, is able to produce horseshoe functions of various types. The deformation of blobs is central to the understanding of mixing and can be studied to identify horseshoe functions. It is found that the efficiency of mixing depends strongly on the value of f and that there exists an optimal value of f that produces the best mixing in a given time.