R. Usha

Bio: R. Usha is an academic researcher from Indian Institute of Technology Madras. The author has contributed to research in topics: Reynolds number & Instability. The author has an hindex of 17, co-authored 85 publications receiving 1061 citations. Previous affiliations of R. Usha include University of Hyderabad & Anna University.

Electrified film on a porous inclined plane: dynamics and stability.

Abstract: The time evolution of a thin conducting liquid film flowing down a porous inclined substrate is investigated when an electric field acts normal to the substrate. It is assumed that the flow through the porous medium is governed by Darcy's law together with Beavers-Joseph condition. Under the assumption of small permeability relative to the thickness of the overlying fluid layer, the flow is decoupled from the filtration flow through the porous medium. A slip condition at the bottom is used to incorporate the effects of the permeability of the substrate. From the set of exact averaged equations derived using integral boundary method for the film thickness and for the flow rate, a nonlinear evolution equation for the film thickness is derived through a long-wave approximation. A linear stability analysis of the base flow is performed and the critical Reynolds number is obtained. The results reveal that the substrate porosity in general destabilizes the liquid film flow and the presence of the electric field enhances this destabilizing effect. A weakly nonlinear stability analysis divulges the existence of supercritical stable and subcritical unstable zones in the wave number/Reynolds number parameter space and the results demonstrate how the neutral curves change as the intensity of the electric filed or the permeability of the porous medium is varied. The numerical solution of the nonlinear evolution equation in a periodic domain reveals that the base flow yields to surface structures that are either time independent waves of permanent form that propagate or time-dependent modes that oscillate slightly in the amplitude. Further, it is observed that the shape and amplitude of long-time waveforms are influenced by the permeability of the porous medium as well as by the applied electric field. The results reveal that the destabilization induced by the electric field in an otherwise stable film over a porous medium is exhibited in the form of traveling waves of finite amplitude. The presence of the porous substrate promotes the oscillatory behavior of the long-time waveform; however, the electric field has a tendency to suppress this oscillatory behavior.

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.

Numerical study of concentrated fluid–particle suspension flow in a wavy channel

Abstract: The particle migration effects and fluid–particle interactions occurring in the flow of highly concentrated fluid–particle suspension in a spatially modulated channel have been investigated numerically using a finite volume method. The mathematical model is based on the momentum and continuity equations for the suspension flow and a constitutive equation accounting for the effects of shear-induced particle migration in concentrated suspensions. The model couples a Newtonian stress/shear rate relationship with a shear-induced migration model of the suspended particles in which the local effective viscosity is dependent on the local volume fraction of solids. The numerical procedure employs finite volume method and the formulation is based on diffuse-flux model. Semi-implicit method for pressure linked equations has been used to solve the resulting governing equations along with appropriate boundary conditions. The numerical results are validated with the analytical expressions for concentrated suspension flow in a plane channel. The results demonstrate strong particle migration towards the centre of the channel and an increasing blunting of velocity profiles with increase in initial particle concentration. In the case of a stenosed channel, the particle concentration is lowest at the site of maximum constriction, whereas a strong accumulation of particles is observed in the recirculation zone downstream of the stenosis. The numerical procedure applied to investigate the effects of concentrated suspension flow in a wavy passage shows that the solid particles migrate from regions of high shear rate to low shear rate with low velocities and this phenomenon is strongly influenced by Reynolds numbers and initial particle concentration. Copyright © 2008 John Wiley & Sons, Ltd.

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

Abstract: 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.

Arbitrary squeeze flow between two disks

Abstract: A viscous incompressible fluid is contained between two parallel disks with arbitrarily shrinking width h(τ). The solution is obtained as a power series in a single nondimensional parameter (squeeze number) S, for small values of S in contrast to the “multifold” series solution obtained by Ishizawa in terms of an infinite set of nondimensional parameters. The gap width h(τ) is obtained for different states: when the top disk moves with constant velocity, constant force or constant power.

Dynamics and stability of thin liquid films

Abstract: The dynamics and stability of thin liquid films have fascinated scientists over many decades: the observations of regular wave patterns in film flows down a windowpane or along guttering, the patterning of dewetting droplets, and the fingering of viscous flows down a slope are all examples that are familiar in daily life. Thin film flows occur over a wide range of length scales and are central to numerous areas of engineering, geophysics, and biophysics; these include nanofluidics and microfluidics, coating flows, intensive processing, lava flows, dynamics of continental ice sheets, tear-film rupture, and surfactant replacement therapy. These flows have attracted considerable attention in the literature, which have resulted in many significant developments in experimental, analytical, and numerical research in this area. These include advances in understanding dewetting, thermocapillary- and surfactant-driven films, falling films and films flowing over structured, compliant, and rapidly rotating substrates, and evaporating films as well as those manipulated via use of electric fields to produce nanoscale patterns. These developments are reviewed in this paper and open problems and exciting research avenues in this thriving area of fluid mechanics are also highlighted.

Viscous flow due to a shrinking sheet

Abstract: The viscous flow induced by a shrinking sheet is studied. Existence and (non)uniqueness are proved. Exact solutions, both numerical and in closed form, are found.

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