Bottom reconstruction in thin-film flow over topography: Steady solution and linear stability

2009 ◽  
Vol 21 (8) ◽  
pp. 083605 ◽  
Author(s):  
C. Heining ◽  
N. Aksel
Keyword(s):  
Thin Film ◽  
Linear Stability ◽  
Film Flow ◽  
Steady Solution ◽  
Thin Film Flow ◽  
Flow Over Topography

scholarly journals Hydromagnetic thin film flow: Linear stability

2013 ◽  
Vol 88 (2) ◽  
Author(s):  
Mustapha Amaouche ◽  
Hamid Ait Abderrahmane ◽  
Lamia Bourdache
Keyword(s):  
Thin Film ◽  
Linear Stability ◽  
Film Flow ◽  
Thin Film Flow

Nonlinear Stability Analysis of Thin Film Flow from a Liquid Jet Impinging on a Circular Concentric Disk

2006 ◽  
Vol 22 (2) ◽  
pp. 115-124 ◽  
Author(s):  
P.-J. Cheng ◽  
H.-Y. Lai
Keyword(s):  
Thin Film ◽  
Linear Stability ◽  
Film Flow ◽  
Multiple Scales ◽  
Impinging Jet ◽  
Jet Flow ◽  
Liquid Jet ◽  
Conditional Stability ◽  
Thin Film Flow ◽  
Potential Core

AbstractThe paper investigates the stability of thin film flow from a liquid jet impinging on a circular concentric disk using a long-wave perturbation method to solve for the generalized nonlinear kinematic equations of free film interface. To begin with a normal mode approach is employed to obtain the linear stability solution for the film flow. In the linear stability solutions only subcritical region can be resolved. In other words, no solution of supercritical region can be obtained in linear domain. Furthermore, the role that the forces of gravitation and surface tension play in the flow is nothing but to stabilize the system. To further investigate the realistic impinging jet flow stability conditions, the weak nonlinear dynamics of a film flow is studied by using the method of multiple scales. Various subcritical nonlinear behaviors expressed in terms of absolute stability, conditional stability and explosive instability can be characterized by solving the Ginzburg-Landau equation. It is found that the jet flow will become relatively unstable for an increasing Reynolds number, a relative smaller distance from the center of the impinging jet on the disk and a smaller diameter of the exit jet. It is also concluded that the flow will always stay in a subcritical instability region if the characteristic diameter of the potential core at nozzle exit is less than 0.01mm for the numerical conditions given in this paper. In such a case when the amplitude of external flow disturbance is smaller than the threshold amplitude a stable jet flow can be ensured.

scholarly journals Inertial two- and three-dimensional thin film flow over topography

2011 ◽  
Vol 50 (5-6) ◽  
pp. 537-542 ◽  
Author(s):  
S. Veremieiev ◽  
H.M. Thompson ◽  
Y.C. Lee ◽  
P.H. Gaskell
Keyword(s):  
Thin Film ◽  
Film Flow ◽  
Three Dimensional ◽  
Thin Film Flow ◽  
Flow Over Topography

scholarly journals Optimal Homotopy Asymptotic Method for a thin film flow of a pseudo plastic fluid draining down or lifting up on a cylindrical surface

2013 ◽  
Vol 19 (4) ◽  
pp. 513-527
Author(s):  
Kamran Alam ◽  
M.T. Rahim ◽  
S. Islam ◽  
A.M. Sidiqqui
Keyword(s):  
Thin Film ◽  
Asymptotic Method ◽  
Cylindrical Surface ◽  
Film Flow ◽  
Vertical Cylinder ◽  
Stokes Number ◽  
Velocity Shear ◽  
Thin Film Flow ◽  
Fluid Velocities ◽  
Optimal Homotopy Asymptotic Method

In this study, the pseudo plastic model is used to obtain the solution for the steady thin film flow on the outer surface of long vertical cylinder for lifting and drainage problems. The non-linear governing equations subject to appropriate boundary conditions are solved analytically for velocity profiles by a modified homotopy perturbation method called the Optimal Homotopy Asymptotic method. Expressions for the velocity profile, volume flux, average velocity, shear stress on the cylinder, normal stress differences, force to hold the vertical cylindrical surface in position, have been derived for both the problems. For the non-Newtonian parameter ?=0, we retrieve Newtonian cases for both the problems. We also plotted and discussed the affect of the Stokes number St, the non-Newtonian parameter ? and the thickness ? of the fluid film on the fluid velocities.

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