Usha R

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.

Long waves on a viscoelastic film flow down a wavy inclined plane is investigated. The analysis is performed to see how long non-linear waves on viscoelastic film down an uneven inclined wall are deformed due to the non-uniformity of the basic flow. The results are then compared with those corresponding to Newtonian film down a wavy inclined wall as well as viscoelastic film down a plane inclined wall. © 2004 Elsevier Ltd. All rights reserved.

A qualitative study of the effect of Poiseuille flow on the peristaltic transport of a particle-fluid suspension has been investigated in a two-dimensional mathematical model of peristalsis for the case when the wall of the channel executes a sinusoidal motion of small amplitude. The method of Frobenius series solution has been used to obtain a series solution for arbitrary values of Reynolds number and Poiseuille flow parameter. It is observed that the mean reversal flow is strongly dependent on the Poiseuille flow. Also, the effect of interaction is that the point of flow reversal is shifted from the center of the channel towards the boundaries.

The thermal effects on the dynamics of an axisymmetric flow of a non-volatile incompressible viscous thin liquid film on a rotating disk due to viscosity variation depending exponentially on temperature are considered. The nonlinear evolution equation is solved numerically. The numerical results reveal that heating the film from below enhances the rate of thinning. The increase in Biot number increases the film thickness, when the film is heated from below. Further, the relative amount of fluid retained on the substrate decreases as the film is heated from below. The results are reversed for the case of a film which is cooled from below. The rate of thinning of the film is more (less) for the case of temperature dependent viscosity when the film is heated (cooled) from below than for the case of constant viscosity of the fluid. © Springer-Verlag 2005.

Spatio-temporal instability of miscible two-fluid symmetric flow in a horizontal slippery channel is considered. Both fluids have the same density but different viscosity. A smooth viscosity stratification is created by a thin mixed layer between the fluids due to the presence of two species/scalars, which are diffusing at different rates. Our study suggests the existence of a rapidly growing absolute unstable mode for higher viscosity ratio with a highly viscous fluid close to the slippery channel wall. This instability is less stronger in the case of the equivalent single component two-fluid flow. The viscosity stratified single component (SC) and double-diffusive (DD) slippery flows are absolutely unstable for a wide range of parameter values, when a highly viscous fluid is adjacent to the slippery wall and the mixed layer is close to the channel wall with slip. The instability can be either enhanced or suppressed by wall slip and this is dependent on the location of mixed layer, inertial effects, diffusivity and the log-mobility ratios of the faster and slower diffusing species. This suggests that one can achieve early transition to turbulence due to the absolute instability in a viscosity stratified channel flow by making the channel walls hydrophobic/rough/porous with small permeability, which can be modelled by the Navier-slip condition.

A numerical solution is obtained for the development of a conducting fluid film on the surface of a spinning disc, in the presence of a magnetic field applied perpendicular to the disc. A finite-difference method is employed to obtain the solution of Navier-Stokes equations modified to include magnetic forces due to MHD interactions. The combined effects of film inertia, acceleration of the disc and magnetic forces are analysed. The numerical results reveal that the rate of thinning of the fluid film is strongly influenced by the inertial and magnetic forces when the Reynolds number is large and that the existing asymptotic theory by Ray and Dandapat [24] is inadequate for predicting transient film thickness. When the disc has a finite acceleration at the start-up, the magnetic and inertia effects are important even at low Reynolds numbers and the thinning rate is reduced. It is observed that for both low and high Reynolds number flows, the film thickness increases with Hartmann number M for a fixed time and the rate of depletion is less for large M than for small M.

This study is motivated by the preliminary direct numerical simulations in double-diffusive (DD) core-annular flows with slip at the wall which displayed elliptical shaped instability patterns as in a rigid pipe case; however, slip at the pipe wall delays the onset of instability for a range of parameters and increases the phase speed. This increased our curiosity to have a thorough understanding of the linear stability characteristics of the miscibleDDtwo-fluid flowin a pipe with slip at the pipewall. The present study, therefore, addresses the linear stability of viscosity-stratified core-annular Poiseuille flow of miscible fluids with matched density in a slippery pipe in the presence of two scalars diffusing at different rates. The physical mechanisms responsible for the occurrence of instabilities in the DD system are explained through an energy budget analysis. The differences and similarities between core-annular flow in a slippery pipe and in a plane channel with velocity slip at the walls are explored. The stability characteristics are significantly affected by the presence of slip. The diffusivity effect is non-monotonic in a DD system. A striking feature of instability is that only a band of wavenumbers is destabilized in the presence of moderate to large inertial effects. Both the longwave and shortwave are stabilized at small Reynolds numbers. Slip exhibits a dual role of stabilizing or destabilizing the flow. The preliminary direct numerical simulations confirm the predictions of the linear stability analysis. The present study reveals that it may be possible to control the instabilities in core-annular pressure driven pipe flows by imposing a velocity slip at the walls.

We revisit the problem of the weakly nonlinear stability analysis of an immiscible two-fluid viscosity-stratified, density-matched, plane Poiseuille flow (PPF) in a rigid channel. A formal amplitude expansion method, in which the flow variables are expanded in terms of a small amplitude function, is employed to examine the nonlinear development of the uniform wave trains. By employing the Chebyshev spectral collocation method, the linear growth rate and the first Landau coefficient, which determine the weakly nonlinear temporal evolution of a finite amplitude disturbance in the vicinity of linear instability, are computed. The focus is on the parameter regime where the long-waves are stable. The present analysis reveals the existence of both subcritical unstable and supercritical stable bifurcations. It is found that similar to the single fluid PPF, the two-fluid flow remains subcritically unstable at the onset of linear instability. There is a transition from subcritical bifurcation at higher wave numbers to supercritical bifurcation at lower wave numbers. The feedback of the mean flow correction onto the wave is responsible for the subcritical bifurcation. The equilibrium amplitude increases (decreases) as a function of the Reynolds number at a fixed wave number, where the bifurcation is supercritical (subcritical). Similar to the single fluid PPF, there is a reduction in the critical Reynolds number due to even extremely weak but finite amplitude disturbances. Moreover, as the disturbance intensity increases, the percentage reduction in the critical Reynolds number increases. The study helps one to have a better understanding and perspective of the bifurcations that occur close to criticality in the two-fluid interface dominated PPF system. In addition, it calls for devoted experiments supplemented with numerical and theoretical predictions on Poiseuille flow of viscosity and/or density stratified systems that would shed light on the nature of transition.

Linear instability analysis of a thin layer of viscoelastic fluid flowing down a non-uniformly heated inclined plane is considered. The study is based on the assumption of constant temperature gradient (positive or negative) along the plane. The film flow system is influenced by gravity, mean surface tension, thermocapillary forces acting along the free surface and viscoelastic forces. The role of these forces is investigated by seeking a solution of the stability problem in a series in small wave number. The results show that the critical Reynolds number is influenced by the Reynolds number, the ratio of Marangoni number to Prandtl number, the Biot number, the viscoelastic parameter and the angle of inclination. © 2005 Elsevier Ltd. All rights reserved.

Weakly nonlinear stability analysis of a falling film with countercurrent gas-liquid flow has been investigated. A normal mode approach and the method of multiple scales are employed to carry out the linear and nonlinear stability solutions for the film flow system. The results show that both supercritical stability and subcritical instability are possible for a film flow system when the gas flows in the countercurrent direction. The stability characteristics of the film flow system are strongly influenced by the effects of interfacial shear stress when the gas flows in the countercurrent direction. The effect of countercurrent gas flow in a falling film is to stabilize the film flow system. © 2007 Springer Science+Business Media, Inc.