Double-diffusive two-fluid flow in a slippery channel: A linear stability analysis

Abstract

The effect of velocity slip at the walls on the linear stability characteristics of two-fluid three-layer channel flow (the equivalent core-annular configuration in case of pipe) is investigated in the presence of double diffusive (DD) phenomenon. The fluids are miscible and consist of two solute species having different rates of diffusion. The fluids are assumed to be of the same density, but varying viscosity, which depends on the concentration of the solute species. It is found that the flow stabilizes when the less viscous fluid is present in the region adjacent to the slippery channel walls in the single-component (SC) system but becomes unstable at low Reynolds numbers in the presence of DD effect. As the mixed region of the fluids moves towards the channel walls, a new unstable mode (DD mode), distinct from the Tollman Schlichting (TS) mode, arises at Reynolds numbers smaller than the critical Reynolds number for the TS mode. We also found that this mode becomes more prominent when the mixed layer overlaps with the critical layer. It is shown that the slip parameter has nonmonotonic effect on the stability characteristics in this system. Through energy budget analysis, the dual role of slip is explained. The effect of slip is influenced by the location of mixed layer, the log-mobility ratio of the faster diffusing scalar, diffusivity, and the ratio of diffusion coefficients of the two species. Increasing the value of the slip parameter delays the first occurrence of the DD-mode. It is possible to achieve stabilization or destabilization by controlling the various physical parameters in the flow system. In the present study, we suggest an effective and realistic way to control three-layer miscible channel flow with viscosity stratification.

Absolute and convective instabilities in double-diffusive two-fluid flow in a slippery channel

“…In this case, eventually the entire flow regime becomes unstable and the system behaves as a self-sustained Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/ces resonator, oscillating at an intrinsic frequency. In contrast, disturbances amplify as they advect downstream, away from their initial location in a convectively unstable flow (Sahu and Govindarajan, 2012;Govindarajan and Sahu, 2014). The instabilities observed at relatively low Reynolds numbers in Ghosh et al (2014b) for a miscible two-fluid flow system with viscosity decreasing towards the walls are convective in nature.…”

“…The instabilities observed at relatively low Reynolds numbers in Ghosh et al (2014b) for a miscible two-fluid flow system with viscosity decreasing towards the walls are convective in nature. However, the configuration with the highly viscous fluid adjacent to the slippery channel walls is unstable due to total viscosity stratification, and in this case velocity slip at the wall destabilizes the DD system (see Ghosh et al, 2014b).…”

“…For example, if a PDMS (polydimethylsiloxane) channel is hosting a two-fluid flow of cold water and hot glycerol solution (where R s 4 0, R f o 0; R s , R f are log-mobility ratios of the slower and faster diffusing scalars, namely temperature and glycerol, defined later in Section 2), then the present study addresses the spatio-temporal linear stability analysis of a DD flow system with a configuration where highly viscous fluid is near the wall (which implies R f þ R s 4 0). A temporal linear stability analysis by Ghosh et al (2014b) shows that there is a large unstable region for a wide range of wave numbers due to total viscosity stratification. The present study attempts (i) to find the boundaries of convectively and absolutely unstable regions for this configuration under wall slip, and (ii) to answer the questions: are there parameter regimes where the DD system in a rigid channel is not absolutely or convectively unstable but it is so in a slippery channel and vice versa.…”

“…Also the bandwidth of parameters for which the DD flow is unstable is much wider than that for SC flow. The recent review article by Govindarajan and Sahu (2014) extensively discussed instabilities in viscosity stratified flows.…”

“…The linear stability characteristics of a double-diffusive twofluid three-layer channel flow (the equivalent core-annular configuration in the case of a pipe) with velocity slip at the walls of the channel have been recently investigated by Ghosh et al (2014b). The flow system has two miscible fluids with two species having different diffusivity coefficients.…”