Stability of plane poiseuille flow of a viscous anisotropic fluid

Abstract

Experimental investigations show that the presence in a fluid of fibers and rigid asymmetric particles leads to a greater stability of flow in tubes and lowers the turbulent frictional resistance in a certain range of Reynolds numbers [1]. In the present paper, the anisotropic structure of a fluid with additives is described by Ericksen's rheological model [2]. The parameters of the model are particularized in accordance with the paper [3] of Pilipenko, Kalinichenko, and Lemak, and in the limiting case of weak Brownian motion allowance is made for the effect of the predominant orientation of the particles and the influence of additives on the longitudinal and shear viscosity. The stability of the Poiseuille flow is considered in the linear formulation. In an anisotropic viscous fluid, an equation of Orr-Sommerfeld type has a singular point. A rule for choosing the path of integration avoiding the singular point is obtained on the basis of a generalization of the method of Dikii [4] proposed in an investigation of the stability of the flow of an ideal fluid. The results of numerical calculations of the neutral stability curve for two-dimensional perturbations are given.