Stability of Parallel Non-Newtonian Flows

Abstract

De-/anti-icing fluids are sprayed on aircraft wings to prevent dangerous loss of performance due to ice formation. The residual layers of such fluids which may either be of newtonian or non-newtonian character could also adversely effect the performance of the aircraft. Therefore it is important to investigate the stability characteristics of such fluids. Stability problem for non-newtonian fluids (power-law fluids in particular) has been solved using the linear stability theory for the case of nearly parallel flows. Orr-Sommerfeld equation for power-law fluids has been obtained. The linear stability theory yields an eigenvalue problem which is solved by the so called shooting method. In this method, two asymptotical solutions for the eigenfunctions are constructed at the edge of the boundary layer and Orr-Sommerfeld equation is integrated towards the wall using these two solutions as the initial values of the integral. At the wall, no slip boundary conditions have to be satisfied and the eigenvalues are computed by the Newton iteraction method. The parameter sets defining the stable and unstable regimes have thus been distinctly identified. The same method is also shown to be applicable to two-layer Couette flow and semi-infinite configurations in which either both or at least one layer is constituted by a power-law fluid