PRINCIPAL DIRECTIONS AS A BASIS FOR THE EVALUATION OF MIXING

Measures of mixing for laminar flow are developed from basic principle s of continuum mechanics for infinitesimal rates of stretch. The entir e analysis is performed from the basis of the eigenvalues and principa l directions of the appropriate flow tensors. Measuring the rate of li ne growth, where the line marks the interface between two miscible flu ids, in terms of the major eigenvalue provides a direct measure of the maximum rate of mixing. Two efficiency measures for mixing are derive d in terms of the eigenvalues and their directions. The creation effic iency of the magnitude of the major eigenvalue as a function of the en ergy input into the flow field is evaluated. The orientation of the in terface to the principal direction qualifies the mixing efficiency in laminar flow. The new theory is used to analyze two-dimensional and th ree-dimensional channels. The results demonstrate not only the continu um measures for mixing but also extend our present understanding on mi xing and provide future directions.