Effect of miscibility on the linear instability of two-fluid channel flow Rama Govindarajan Engineering Mechanics Unit, Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur, Bangalore 560 064, India Received 14 August 2003; received in revised form 27 June 2004 Abstract This study provides an extension into the finite-miscibility regime of theories for interfacial instabilities in two-fluid channel flow. When the two fluids are of high mass diffusivity, a new mode of instability, called here the overlap mode, appears when the critical layer of the dominant disturbance overlaps the viscosity- stratified layer. For poor diffusivity, the instability is qualitatively different: broadband and at low Reynolds number, beginning to resemble the Yih mode for immiscible interfaces. The results lend themselves to ver- ification by experiment and direct numerical simulation. Ó 2004 Elsevier Ltd. All rights reserved. Keywords: Instability of two-fluid flow; Miscibility; Viscosity-stratification 1. Introduction We consider here the symmetric flow through a channel of two miscible fluids of equal densities but different viscosities separated by a mixed layer of viscosity-stratified fluid, as shown in Fig. 1. The stability analysis presented may be used for any level of miscibility and for any (non-zero) thickness of the mixed layer. The limiting case of immiscible fluids separated by a sharp interface has been studied extensively (e.g. Yih, 1955, 1967; Renardy, 1987; Joseph and Renardy, 1993; 0301-9322/$ - see front matter Ó 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijmultiphaseflow.2004.06.006 E-mail address: rama@jncasr.ac.in www.elsevier.com/locate/ijmulflow International Journal of Multiphase Flow 30 (2004) 1177–1192