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.

Usha R

Department of Mathematics

Lubrication

Viscosity

CRITICAL LAYER

Free-surface flow

INSTABILITY MODES

Linear stability

TOLLMIEN-SCHLICHTING MODES

Transport equation

TWO-LAYER FLOWS

VISCOSITY GRADIENT

Flow of fluids

Fulltext

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IIT Madras

Linear stability of miscible two-fluid flow down an incline

Physics of Fluids

A linear stability analysis of a thin shear-thinning film with a deformable top surface flowing down an inclined porous substrate modelled as a smooth substrate with velocity slip at the wall is examined, and the physical mechanism for the long-wave instability is analysed. Through a phenomenological model, the influence of slip velocity and the shear-thinning rheology on the wave speed of long surface waves on a non-Newtonian shear-thinning film down a substrate with velocity slip is predicted. The viscosity disturbance plays a significant role in the destabilization of the flow system. Indeed, slip at the bottom that accounts for the characteristics of the porous/rough substrate does not affect the physical mechanism of the instability. However, it is shown that slip at the bottom enhances the inertia effects which in turn destabilizes the flow system at smaller Reynolds numbers. © 2019, Springer-Verlag GmbH Austria, part of Springer Nature.

Acta Mechanica

The mechanism of long-wave instability in a shear-thinning film flow on a porous substrate

The inviscid temporal stability analysis of two-fluid parallel shear flow with a free surface, down an incline, is studied. The velocity profiles are chosen as piecewise-linear with two limbs. The analysis reveals the existence of unstable inviscid modes, arising due to wave interaction between the free surface and the shear-jump interface. Surface tension decreases the maximum growth rate of the dominant disturbance. Interestingly, in some limits, surface tension destabilises extremely short waves in this flow. This can happen because of the interaction with the shear-jump interface. This flow may be compared with a corresponding viscous two-fluid flow. Though viscosity modifies the stability properties of the flow system both qualitatively and quantitatively, there is qualitative agreement between the viscous and inviscid stability analysis when the less viscous fluid is closer to the free surface. © 2016, Springer Science+Business Media Dordrecht.

Meccanica

Inviscid instability of two-fluid free surface flow down an incline

The effects of wall velocity slip on the linear stability of a gravity-driven miscible two-fluid flow down an incline are examined. The fluids have the matched density but different viscosity. A smooth viscosity stratification is achieved due to the presence of a thin mixed layer between the fluids. The results show that the presence of slip exhibits a promise for stabilizing the miscible flow system by raising the critical Reynolds number at the onset and decreasing the bandwidth of unstable wave numbers beyond the threshold of the dominant instability. This is different from its role in the case of a single fluid down a slippery substrate where slip destabilizes the flow system at the onset. Though the stability properties are analogous to the same flow system down a rigid substrate, slip is shown to delay the surface mode instability for any viscosity contrast. It has a damping/promoting effect on the overlap modes (which exist due to the overlap of critical layer of dominant disturbance with the mixed layer) when the mixed layer is away/close from/to the slippery inclined wall. The trend of slip effect is influenced by the location of the mixed layer, the location of more viscous fluid, and the mass diffusivity of the two fluids. The stabilizing characteristics of slip can be favourably used to suppress the non-linear breakdown which may happen due to the coexistence of the unstable modes in a flow over a substrate with no slip. The results of the present study suggest that it is desirable to design a slippery surface with appropriate slip sensitivity in order to meet a particular need for a specific application.

Stability of viscosity stratified flows down an incline: Role of miscibility and wall slip

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.

Procedia IUTAM

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

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.

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

Reviews of Modern Physics

Dynamics and stability of thin liquid films

Journal of Fluid Mechanics

Linear temporal and spatio-temporal stability analysis of a binary liquid film flowing down an inclined uniformly heated plate

Stability of miscible core–annular flows with viscosity stratification

Low-Reynolds-number instabilities in three-layer flow down an inclined wall

International Journal of Multiphase Flow

Effect of miscibility on the linear instability of two-fluid channel flow

Journal	Data powered by TypesetPhysics of Fluids
Publisher	Data powered by TypesetAmerican Institute of Physics Inc.
ISSN	10706631
Open Access	No