The effects of a hydrophobic surface on stability and transition in wall-bounded shear flows are investigated. The hydrophobic surface is represented by a slip-boundary condition on the surface. The linear stability analysis with slip-boundary conditions shows that the critical Reynolds number increases with streamwise slip. The effects of slip-boundary conditions on the transient growth of initial disturbances are investigated through the singular value decomposition (SVD) analysis of the linearized Navier–Stokes equations. The maximum transient growth (i.e., the amplification factor for the optimal disturbance) is reduced with streamwise slip, indicating that non-normality of the linearized Navier–Stokes equations is reduced with streamwise slip. Finally, it is shown that the transition to turbulence is delayed significantly with streamwise slip, whereas spanwise slip induces an earlier transition. The present results suggest that it is desirable to develop a hydrophobic surface with specified directional sensitivity in order to meet a particular need for specific applications.

Effects of hydrophobic surface on stability and transition

The effects of a hydrophobic surface on stability and transition in wall-bounded shear flows are investigated. The hydrophobic surface is represented by a slip-boundary condition on the surface. The linear stability analysis with slip-boundary conditions shows that the critical Reynolds number increases with streamwise slip. The effects of slip-boundary conditions on the transient growth of initial disturbances are investigated through the singular value decomposition SVD analysis of the linearized Navier–Stokes equations. The maximum transient growth i.e., the amplification factor for the optimal disturbance is reduced with streamwise slip, indicating that non-normality of the linearized Navier–Stokes equations is reduced with streamwise slip. Finally, it is shown that the transition to turbulence is delayed significantly with streamwise slip, whereas spanwise slip induces an earlier transition. The present results suggest that it is desirable to develop a hydrophobic surface with specified directional sensitivity in order to meet a particular need for specific applications. © 2005 American Institute of Physics. DOI: 10.1063/1.2126569

http://absimage.aps.org/image/DFD05/MWS_DFD05-2005-000546.pdf

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. A prominent feature of the instability is that only a band of wave 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 flow domain at which the base flow velocity equals the phase speed of the most unstable disturbance. Such a mode 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 is more 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 particular way 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.

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

We study a model for Poiseuille flow instability in a porous medium of Brinkman type. In particular, we analyse the effect of slip boundary conditions on the onset of instability. Due to numerous applications in micro-electro-mechanical-systems and other microfluidic devices, such a study is essential. We accurately analyse as to when instability will commence and determine the critical Reynolds number as a function of the slip coefficient.

Instability in Poiseuille flow in a porous medium with slip boundary conditions

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.

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

We investigate the linear stability of plane Poiseuille flow in 2D under slip boundary conditions. The slip s is defined by the tangential velocity at the wall in units of the maximal flow velocity. As it turns out, the critical Reynolds number depends smoothly on s but increases quite rapidly.

Heiko Buehring

Papers

Critical curves of plane Poiseuille flow with slip boundary conditions