Stability of a binary mixture of a chemically reacting incompressible fluid in a plane couette flow

Abstract

The stability of a binary mixture of a chemically reacting incompressible fluid in plane couette flow is considered with respect to a two-dimensional infinitesimal disturbance. The eighenvalues are found with the aid of microcomputer. Neutral stability curves for various Schmidt numbers at Reynolds numbers up to 150 are obtained by Gallagher method. It is found that the principle of the exchange of stabilities holds for this problem. Thus, using the basic orthogonal functions, the differential equations are reduced to a set of paired matrix equations with the conclusion that all fluids are unstable at different values of stability parameter C=1.40 x 10 to 2.0 x 10 for wave number (a) = 0.2 to 2 (based on half-channel width and half the relative velocity of the plates).

Keywords: Incompressible fluid, binary mixture, wave number, couette flow and stability parameter.

Nigerian Journal of Physics Vol. 18 (2) 2006: pp. 155-160