Showing papers by "R. Usha published in 2015"

Effects of velocity slip on the inertialess instability of a contaminated two-layer film flow

Abstract: This manuscript provides a theoretical stability analysis for the configuration of two-layer immiscible flow down an inclined plane with velocity slip along the incline in the limit of zero Reynolds number. Surfactants may be present at the air–liquid interface, liquid–liquid interface, or both. In addition to an Orr–Sommerfeld analysis (again at zero Reynolds number), a long wavelength stability analysis is performed and the results are shown to be consistent. The interface mode, namely the mode of instability that arises because of viscosity stratification, is examined. Stability results (growth rates as a function of slip parameter and neutral stability boundaries) for various configurations of viscosity, surfactant placement, and layer thickness are compared with those of the previous literature and found to agree. It is found that velocity slip along the inclined plane reduces the maximum growth rate of instabilities in configurations where they occur, and the range of unstable wave numbers shrinks as well, indicating that slip has a promise for stabilization. This suggests that there is a possibility of using this favourably as a control option for two-layer flows in the absence or presence of surfactants, in relevant applications by designing the substrate to be a porous substrate with small permeability or a slippery substrate or a rough substrate or a hydrophobic substrate which can be modelled as substrates with velocity slip.

Experimental determination of the viscosity at very low shear rate for shear thinning fluids by electrocapillarity

Abstract: Non-Newtonian fluids can present a complex rheological behaviour involving shear-thinning, viscoelastic or thixotropic effects. We focus here on the characterization of generalized Newtonian fluids as shear-thinning fluids. Rotational rheometers are torque-sensitive, which makes the measurement of viscosity at low shear-rates very difficult, in particular for low viscosity fluids. An accurate knowledge of this value is, however, particularly important for the characterization of several types of flows, in particular those featuring a free surface, a symmetry axis or a symmetry plane. The experimental determination of viscosity and surface tension is enabled from the propagation of attenuated capillary waves. An optical technique has been implemented in order to determine the shear-thinning viscosity at values of the shear-rate as small as 10 −3 s −1 from measurements of the spatial attenuation and wavelength. We have performed measurements on two different polymer solutions; we show that this technique is complementary to the classical rotational rheometer techniques since it gives access to the zero shear viscosity, which could not be measured by using rotational rheometers. The present technique is thus used to characterize the Newtonian plateau, while a rotational rheometer is used to characterize the fluid behaviour at moderate to high shear rates.

Steady solution of an inverse problem in gravity-driven shear-thinning film flow: Reconstruction of an uneven bottom substrate

Abstract: We consider a thin film of a power-law fluid flowing over an undulated substrate under the action of gravity. Instead of determining the free surface position as in the case of a direct problem, we focus on the inverse problem, where for a specific free surface shape, we find the corresponding bottom topography which causes the free surface profile. As an asymptotic approach for thin films and moderate Reynolds numbers, we apply the weighted-residual integral boundary-layer method (WRIBL) which enables us to derive a set of two evolution equations for the film thickness h and the flow rate q. We obtain the steady solutions of the above model equation for the inverse problem for weakly undulated free surface profile by a perturbation method. We examine the influence of viscosity of fluid, inertia, film thickness, hydrostatic pressure and surface tension on the reconstructed bottom topography for a shear-thinning fluid. For a moderately undulated free surface shape, we solve the model equation numerically and obtain the bottom topography. We perform spatial linear stability analysis of the corresponding direct problem using Floquet theory. The results show that the critical Reynolds number is influenced by the shear-thinning rheology, surface tension effects and the amplitude of the free surface of the target profile. The analysis provides a strategy for control of free surface instabilities that arise in gravity-driven shear-thinning films over inclined undulated substrates and it corresponds to reconstruction of bottom undulated substrate that causes a target free surface.

Etude expérimentale de la stabilité de l'écoulement de films de fluide non Newtonien sur plan incliné

Abstract: We study the stability of shear-thinning (pseudoplastic) fluid films flow down an inclined plane. We focus on fluids obeying the Carreau law. An optical technique called electrocapillarity has been implemented in order to determine the surface tension and viscosity, at values of the shear rate as small as 10 -3 s -1 , by studying the damping of propagating capillary waves. The main objective of this work is to experimentally study the linear stability of shear-thinning fluid films flow. For a fixed inclination angle, the experimental study essentially consists in measuring the cutoff frequency and wavelength of primary waves, and then determining the critical Reynolds number. The experimental results presented in the (Re, f) and (Re, k) planes are in good agreement with the numerical results, and confirm the destabilizing effect of the shear-thinning properties in comparison with the Newtonian case. Mots clefs : Stabilite ; Rheologie ; Films minces ; Surface libre. 22 eme Congres Francais de Mecanique Lyon, 24 au 28 Aout 2015