The mixing region between dissimilar fluids is investigated in the region where the similarity transformation is valid. The treatment is complete in that laminar and turbulent cases both with and without large density differences are considered. The Schmidt number is an arbitrary input to the problem and may be varied. The ordinary differential equation resulting from the similarity transformation is integrated numerically and some solutions are presented. The three boundary conditions are proper; the so-called arbitrary third boundary condition is treated as originally suggested by von Karman and extended to the case of large density difference. Illustrations of the effects of varying velocity ratio, density ratio, and Schmidt number are presented.
The Mixing of Two Parallel Streams of Dissimilar Fluids—Part I: Analytical Development
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Baker, R. L., Tao, L. N., and Weinstein, H. (June 1, 1971). "The Mixing of Two Parallel Streams of Dissimilar Fluids—Part I: Analytical Development." ASME. J. Appl. Mech. June 1971; 38(2): 301–309. https://doi.org/10.1115/1.3408776
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