Non-modal instabilities of two-dimensional disturbances in plane Couette flow of a power-law fluid

Instabilities of fluid flows have traditionally been investigated by normal mode analysis, i.e. by linearizing the equations of flow and testing for unstable eigenvalues of the linearized problem. However, the results of eigenvalue analysis agree poorly in many cases with experiments, especially for shear flows. In this paper we study the instabilities of two-dimensional Couette flow of a polymeric fluid in the framework of non-modal stability theory rather than normal mode analysis. A power-law model is used to describe the polymeric liquid. We focus on the response to external excitations and initial conditions by examining the pseudospectra structures and the transient energy growths. For both Newtonian and non-Newtonian flows, the results show that there can be a rather large transient growth even though the linear operator of Couette flow has no unstable eigenvalue. The effects of non-Newtonian viscosity on the transient behaviors are examined in this study. The results show that the "shear-thinning/shear-thickening" effect increases/decreases the amplitude of responses to external excitations and initial conditions. (C) 2010 Elsevier B.V. All rights reserved.

Indentation of power law creep solids by self-similar indenters

For creep solids obeying the power law under tension proposed by Tabor, namely sigma = b(epsilon) over dot(m), it has been established through dimensional analysis that for self-similar indenters the load F versus indentation depth h can be expressed as F(t) = bh(2)(t)[(h) over dot(t)/h(t)](m)Pi(alpha) where the dimensionless factor Pi(alpha) depends on material parameters such as m and the indenter geometry. In this article, we show that by generalizing the Tabor power law to the general three dimensional case on the basis of isotropy, this factor can be calculated so that indentation test can be used to determine the material parameters b and m appearing in the original power law. Hence indentation test can replace tension test. This could be a distinct advantage for materials that come in the form of thin films, coatings or otherwise available only in small amounts. To facilitate application values of this constant are given in tabulated form for a range of material parameters. (C) 2010 Elsevier B.V. All rights reserved.