Mixing of viscous fluids

The paper presents a new methodology for investigating and evaluating the basic properties of distributive laminar mixing in creeping flows. Our analysis is based upon conservation of some topological properties (e.g. connectedness and orientation) of the Lagrangian interface line under continuous transformations induced by an Eulerian velocity field. The principal advantage of our approach for line tracking is that despite complicated stretching and folding, the area of the blob, enclosed by the contour, is preserved. This gives possibility to develop three criteria for estimating the quality of mixing. The objective of this article is to expound the methodology of investigation of distributive laminar mixing of highly viscous materials by considering a typical example of two-dimensional Stokes flow in an annular wedge cavity.

Our methodology is based on the following steps: (1) determination of an analytical solution for the velocity field in the cavity; (2) observations on the deformation of the interface contour line of the stirring blob; (3) finding and classification of periodic points; (4) construction of statistical quantity measures for estimation of the quality of mixing at any given moment of time.