PRINCIPAL DIRECTIONS AS A BASIS FOR THE EVALUATION OF MIXING

Measures of mixing for laminar flow are developed from basic principles of continuum mechanics for infinitesimal rates of stretch. The entire analysis is performed from the basis of the eigenvalues and principal directions of the appropriate flow tensors. Measuring the rate of line growth, where the line marks the interface between two miscible fluids, in terms of the major eigenvalue provides a direct measure of the maximum rate of mixing. Two efficiency measures for mixing are derived in terms of the eigenvalues and their directions. The creation efficiency of the magnitude of the major eigenvalue as a function of the energy input into the flow field is evaluated. The orientation of the interface to the principal direction qualifies the mixing efficiency in laminar flow. The new theory is used to analyze two-dimensional and three-dimensional channels. The results demonstrate not only the continuum measures for mixing but also extend our present understanding on mixing and provide future directions.