Long waves on a viscoelastic film flow down a wavy incline
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.
Electrified film on a porous inclined plane: Dynamics and stability
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. © 2010 The American Physical Society.
Flow of thin liquid film over a rough rotating disk in the presence of a transverse magnetic field
The development of a flow of a viscous conducting fluid over a rough spinning disk in the presence of a transverse magnetic field has been analysed for different patterns of surface roughness of the disk and different initial distributions of the height of the liquid lubricant. The numerical solution of the governing equation of motion subject to initial and boundary conditions has been obtained by a finite-difference method. The temporal evolution of the free surface of the fluid and the rate of retention of the liquid lubricant on the spinning disk have been obtained for different values of the two parameters M, the Hartmann number and Nratio, the ratio of the surface tension effect to the centrifugation effect. In the absence of the magnetic field, the results have been observed to agree with those of [6]. It has been observed that the effect of surface roughness is to enhance the relative volume of the fluid retained on the spinning disk and this is further enhanced by the presence of the magnetic field.
Interfacial phase change effects on the stability characteristics of thin viscoelastic liquid film down a vertical wall
Weakly nonlinear stability analysis of thin viscoelastic liquid film flowing down a vertical wall including the phase change effects at the interface has been investigated. A normal mode approach and the method of multiple scales are employed to carry out the linear stability solution and the nonlinear stability solution for the film flow system. The results show that both the supercritical stability and subcritical instability are possible for condensate, evaporating and isothermal viscoelastic film flow system. The stability characteristics of the viscoelastic film flow are strongly influenced by the phase change parameter. The condensate (evaporating) viscoelastic film is more stable (unstable) than the isothermal viscoelastic film and the effect of viscoelasticity is to destabilize the film flowing down a vertical wall. © 2004 Elsevier Ltd. All rights reserved.
Dynamics of a thin film with temperature-dependent viscosity on a rotating disk
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.
A thin conducting liquid film on a spinning disk in the presence of a magnetic field: Dynamics and stability
A theoretical analysis of the effects of a magnetic field on the dynamics of a thin nonuniform conducting film of an incompressible viscous fluid on a rotating disk has been considered. A nonlinear evolution equation describing the shape of the film interface has been derived as a function of space and time and has been solved numerically. The temporal evolution of the free surface of the fluid and the rate of retention of the liquid film on the spinning disk have been obtained for different values of Hartmann number M, evaporative mass flux parameter E, and Reynolds number Re. The results show that the relative volume of the fluid retained on the spinning disk is enhanced by the presence of the magnetic field. The stability characteristics of the evolution equation have been examined using linear theory. For both zero and nonzero values of the nondimensional parameter describing the magnetic field, the results show that (a) the infinitesimal disturbances decay for small wave numbers and are transiently stable for larger wave numbers when there is either no mass transfer or there is evaporation from the film surface, and although the magnitude of the disturbance amplitude is larger when the magnetic field is present, it decays to zero earlier than for the case when the magnetic field is absent, and (b) when absorption is present at the film surface, the film exhibits three different domains of stability: disturbances of small wave numbers decay, disturbances of intermediate wave numbers grow transiently, and those of large wave numbers grow exponentially. The range of stable wave numbers increases with increase in Hartmann number. © 2009 by ASME.
A thin conducting viscous film on an inclined plane in the presence of a uniform normal electric field: Bifurcation scenarios
A theory for two dimensional long and stationary waves of finite amplitude on a thin viscous liquid film down an inclined plane in the presence of uniform electric field at infinity is investigated. A set of exact averaged equations for the film flow system is described and linearized stability analysis of the uniform flow is performed using normal-mode formulation and the critical condition for linear instability is obtained. The linearized instability for the permanent wave equation, consistent to the second order in ε, is examined and the eigenvalue properties of the fixed points are classified in various parametric regimes. Numerical integration of the permanent wave equation as a third-order dynamical system is carried out. Different bifurcation scenarios leading to multiple-hump solitary waves or leading to chaos are exhibited in the parametric space. © 2008 American Institute of Physics.
Weakly nonlinear stability analysis of a falling film with countercurrent gas flow
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.
Dynamics and stability of a thin liquid film on a heated rotating disk film with variable viscosity
A theoretical analysis of the thermal effects on the dynamics of a thin nonuniform film of a nonvolatile incompressible viscous fluid on a heated rotating disk has been considered and the effects of temperature-dependent viscosity and surface tension have been analyzed. A nonlinear evolution equation describing the shape of the film interface has been derived as a function of space and time and its stability characteristics have been examined using linear theory. It has been observed that the infinitesimal disturbances decay for small wave numbers and are transiently stable for large wave numbers, for both zero and nonzero values of Biot number. © 2005 American Institute of Physics.
Nonlinear stability analysis of a falling film in the presence of gas flow
A viscous liquid film flows down along the interior of an annular region under gravity with a countercurrent/cocurrent stream of gas phase adjoining the free surface. The interfacial shear stress effects on the stability of the film flow system in the presence of gas flow has been analyzed for the model that describes the motion for the annular countercurrent/cocurrent gas-liquid two-dimensional falling film. A nonlinear evolution of Benney type describing the film thickness in the presence of gasflow has been derived using long wave theory and lubrication approximation. Linear and weakly nonlinear stability analysis of the evolution equation show that both supercritical stability and subcritical instability are possible for the film flow system in the presence of gas flow. The nonlinear equation has been solved numerically in a periodic domain and the results show that the shape and amplitude of the permanent wave are greatly influenced by the countercurrent/cocurrent gas flow. Copyright © 2007 by ASME.