Mixing in internally stirred flows

Abstract

We consider mixing in a viscous fluid by the periodic rotation and translation of a stirrer, the Reynolds number being low enough that the Stokes approximation is valid in the unsteady, two-dimensional flow. Portions of the boundary of the container may also move to contribute to the mixing. The shapes of the stirrer and the container are arbitrary. It is shown that the recently developed embedding method for eigenfunction expansions in arbitrary domains is well suited to analyse the mixing properties of such mixers. This application depends crucially on the accurate analytical description of the complex, unsteady field. After carefully validating the proposed method against the recent results found in the literature, examples are given of how the method could be used in practice. A special advantage of the suggested method is that it can be extended to handle three-dimensional mixing flows with virtually no change in the procedure shown here.

How rotational vortices enhance transfers

“…Methods based on a discretization of the gradient operator are available for this purpose. [24][25][26][27][28] We chose an alternative simulation method, coined the tracer method to investigate the effective transfer properties of these systems. 21,[29][30][31][32] Its principle is to inject a large number of passive Brownian tracers into the flow.…”

Reactive strip method for mixing and reaction in two dimensions

“…The concentration field is, however, advected by the flowfield. We consider a domain of lengths L × H which, in a nondimensional sense, may be written as L × H where the pertinent characteristic lengthscale, L, is appropriately chosen as per the discussion after equation (7). In this domain we consider a strip of a given length l (nondimensional length l) and width s, (nondimensional width s).…”

“…We now use the information obtained through the previous step in order to solve the set of equations (7). The Chebyshev spectral collocation method provides an efficient methodology to compute the solutions in terms of linear combinations of Chebyshev polynomials.…”

“…For several important industrial and chemical processes such as plastic molding, paint processing, food and pharmaceutical processing, paper processing etc. which are inherently highly dissipative in nature owing to the relatively stronger viscous forces as compared to the inertial forces, it is often the best strategy to mechanically stir, stretch, and wrap the multiple species so as to amplify the concentration gradients [3,4,5,6,7,8,9].…”

Signature of coalescence during scalar mixing in heterogeneous flow fields

“…An accurate description of solute mixing is crucial in order to understand a host of geophysical processes (Pierrehumbert 1991;Fernando 1991). Scalar mixing is central to geological storage of carbon dioxide (Caldeira & Rau 2000), contaminant transport in groundwater (Zheng & Bennett 2002), growth of biofilms (Tél et al 2005), plastic and pharmaceutical processing (Mohr et al 1957;Nienow et al 1997) ozone layer dynamics and other chemical processes (Cerbelli et al 2002;Shankar & Kidambi 2009;Levenspiel & Bischoff 1964).…”