Showing papers by "R. Usha published in 2013"

Thin film flow down a porous substrate in the presence of an insoluble surfactant: Stability analysis

Abstract: The stability of a gravity-driven film flow on a porous inclined substrate is considered, when the film is contaminated by an insoluble surfactant, in the frame work of Orr-Sommerfeld analysis. The classical long-wave asymptotic expansion for small wave numbers reveals the occurrence of two modes, the Yih mode and the Marangoni mode for a clean/a contaminated film over a porous substrate and this is confirmed by the numerical solution of the Orr-Sommerfeld system using the spectral-Tau collocation method. The results show that the Marangoni mode is always stable and dominates the Yih mode for small Reynolds numbers; as the Reynolds number increases, the growth rate of the Yih mode increases, until, an exchange of stability occurs, and after that the Yih mode dominates. The role of the surfactant is to increase the critical Reynolds number, indicating its stabilizing effect. The growth rate increases with an increase in permeability, in the region where the Yih mode dominates the Marangoni mode. Also, the growth rate is more for a film (both clean and contaminated) over a thicker porous layer than over a thinner one. From the neutral stability maps, it is observed that the critical Reynolds number decreases with an increase in permeability in the case of a thicker porous layer, both for a clean and a contaminated film over it. Further, the range of unstable wave number increases with an increase in the thickness of the porous layer. The film flow system is more unstable for a film over a thicker porous layer than over a thinner one. However, for small wave numbers, it is possible to find the range of values of the parameters characterizing the porous medium for which the film flow can be stabilized for both a clean film/a contaminated film as compared to such a film over an impermeable substrate; further, it is possible to enhance the instability of such a film flow system outside of this stability window, for appropriate choices of the porous substrate characteristics.

Linear stability of miscible two-fluid flow down an incline

Abstract: 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.

Dynamics of a pre-lens tear film after a blink: Model, evolution, and rupture

Abstract: A mathematical model is developed to investigate the dynamics and rupture of a pre-lens tear film on a contact lens. The contact lens is modeled as a saturated porous medium of constant, finite thickness and is described by the Darcy-Brinkman equations with stress-jump condition at the interface. The model incorporates the influence of capillarity, gravitational drainage, contact lens properties such as the permeability, the porosity, and the thickness of the contact lens on the evolution and rupture of a pre-lens tear film, when the eyelid has opened after a blink. Two models are derived for the evolution of a pre-lens tear film thickness using lubrication theory and are solved numerically; the first uses shear-free surface condition and the second, the tangentially immobile free surface condition. The results reveal that life span of a pre-lens tear film is longer on a thinner contact lens for all values of permeability and porosity parameter considered. An increase in permeability of contact lens, poro...

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

Abstract: 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.

Instabilities of a free bilayer flowing on an inclined porous medium

Abstract: The instabilities of a free bilayer flowing on an inclined Darcy-Brinkman porous layer have been explored. The bilayer is composed of a pair of immiscible liquid films with a deformable liquid-liquid interface and a liquid-air free surface. An Orr-Sommerfeld analysis of the governing equations and boundary conditions uncovers that this configuration can be unstable by a pair of long-wave interfacial modes at the free surface and at the interface together with a couple of finite wave-number shear modes originating from the inertial influences at the liquid layers. In particular, one of the shear modes originates beyond a threshold flow rate owing to the slippage at the porous-liquid interface and is found to be the dominant one even when the porous medium is moderately thin, porous, and permeable. The strength of the porous media mediated mode (a) grows with increase in porosity, (b) grows and then remains invariant with increase in thickness, and (c) initially grows and then decays with increase in the permeability of the porous layer. Further, the presence of a lower layer with smaller viscosity and a thicker upper layer is found to facilitate the growth of this newly identified porous media mode. Importantly, beyond a threshold upper to lower thickness and viscosity ratios and the angle of inclination the porous media mode dominates over all the other interfacial or shear modes, highlighting its importance in the bilayer flows down an inclined porous medium. The study showcases the importance of a porous layer in destabilizing a free bilayer flow down an inclined plane, which can be of importance to improve mixing, emulsification, and heat and mass transfer characteristics in the microscale devices.