A linear stability analysis of a gravity-driven miscible two-fluid flow with matched density and different viscosities, containing a thin mixed layer between the two fluids, down a slippery inclined plane is considered. Results reveal the stabilizing effects on the surface (S), the overlap (O1 and O2) and the TS (not shown) modes that exist for a configuration with more viscous fluid adjacent to the free surface under overlap conditions. There is a possibility of destabilizing the overlap mode (O1) when the mixed layer is very close to the slippery wall, indicating the dual role played by the wall slip. The stabilizing characteristics of slip can be favourably used to suppress the nonlinear breakdown that may happen due to the coexistence of the unstable modes in a flow over a substrate with no slip. © 2015 The Authors. Published by Elsevier B.V.

Usha R

Department of Mathematics

Linear stability analysis

Multiphase flow

Plasma stability

Viscosity

Inclined planes

Stability analysis

Stabilizing effects

TWO-FLUID FLOW

UNSTABLE MODES

VELOCITY SLIPS

Viscosity stratification

Viscous fluids

Flow of fluids

Fulltext

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IIT Madras

Procedia IUTAM

The linear stability characteristics of pressure-driven miscible two-fluid flow with same density and varying viscosities in a channel with velocity slip at the wall are examined.Aprominent feature of the instability is that only a band ofwave numbers is unstable whatever the Reynolds number is, whereas shorter wavelengths and smaller wave numbers are observed to be stable. The stability characteristics are different from both the limiting cases of interface dominated flows and continuously stratified flows in a channel with velocity slip at the wall. The flow system is destabilizing when a more viscous fluid occupies the region closer to the wall with slip. For this configuration a new mode of instability, namely the overlap mode, appears for high mass diffusivity of the two fluids. This mode arises due to the overlap of critical layer of dominant instability with the mixed layer of varying viscosity. The critical layer contains a location in the flowdomain atwhich the base flowvelocity equals the phase speed of themost unstable disturbance. Such amode also occurs in the corresponding flow in a rigid channel, but absent in either of the above limiting cases of flow in a channel with slip. The flow is unstable at low Reynolds numbers for a wide range of wave numbers for low mass diffusivity, mimicking the interfacial instability of the immiscible flows. A configuration with less viscous fluid adjacent to the wall is more stable at moderate miscibility and this is also in contrast with the result for the limiting case of interface dominated flows in a channel with slip, where the above configuration ismore unstable. It is possible to achieve stabilization or destabilization of miscible two-fluid flow in a channel with wall slip by appropriately choosing the viscosity of the fluid layer adjacent to the wall. In addition, the velocity slip at the wall has a dual role in the stability of flow system and the trend is influenced by the location of the mixed layer, the location of more viscous fluid and the mass diffusivity of the two fluids. It is well known that creating a viscosity contrast in a particularway in a rigid channel delays the occurrence of turbulence in a rigid channel. The results of the present study show that the flow system can be either stabilized or destabilized by designing the walls of the channel as hydrophobic surfaces, modeled by velocity slip at the walls. The study provides another effective strategy to control the flow system. © 2014 AIP Publishing LLC.

Physics of Fluids

Linear stability analysis of miscible two-fluid flow in a channel with velocity slip at the walls

We show that miscible two-layer free-surface flows of varying viscosity down an inclined substrate are different in their stability characteristics from both immiscible two-layer flows, and flows with viscosity gradients spanning the entire flow. New instability modes arise when the critical layer of the viscosity transport equation overlaps the viscosity gradient. A lubricating configuration with a less viscous wall layer is identified to be the most stabilizing at moderate miscibility (moderate Peclet numbers). This also is in contrast with the immiscible case, where the lubrication configuration is always destabilizing. The co-existence that we find under certain circumstances, of several growing overlap modes, the usual surface mode, and a Tollmien-Schlichting mode, presents interesting new possibilities for nonlinear breakdown. © 2013 AIP Publishing LLC.

Linear stability of miscible two-fluid flow down an incline

Annual Review of Fluid Mechanics

Instabilities in Viscosity-Stratified Flow

Journal of Fluid Mechanics

A falling film down a slippery inclined plane

A note on the stability of slip channel flows

Stability Analysis of a Gravity Driven Miscible Two-fluid Flow: Role of Wall Slip

Journal	Data powered by TypesetProcedia IUTAM
Publisher	Data powered by TypesetElsevier B.V.
ISSN	22109838
Open Access	Yes