Linear Stability of Double-sided Symmetric Thin Liquid Film by Integral-theory
Mathematics and Statistics
(Issue : 1)
(Volume : 11)
The Integral Theory approach is used to
explore the stability and dynamics of a free double-sided
symmetric thin liquid film. For a Newtonian liquid with
non-variable density and moving viscosity, the flowing in a
thinning liquid layer is analyzed in two dimensions. To
construct an equation that governs such flow, the Navier
and Stokes formulas are utilized with proper boundary
conditions of zero shear stress conjointly of normal stress
on the bounding free surfaces with dimensionless variables.
After that, the equations that are a non-linear evolution
structure of layer thickness, local stream rate, and the
unknown functions can be solved by using straight stability
investigation, and the normal mode strategy can moreover
be connected to these conditions to reveal the critical
condition. The characteristic equation for the growth rate
and wave number can be analyzed by using MATLAM
programming to show the region of stable and unstable
films. As a result of our research, we are able to
demonstrate that the effect of a thin, free, double-sided
liquid layer is an unstable component
Linear Stability of Thin Liquid Films Flows Down on an Inclined Plane Using Long-Wave Theory
General Letters in Mathematics (GLM)
(Issue : 4)
(Volume : 12)
The Long-Wave Theory is applied to investigate the dynamic stability of free thin fluid films flowing down
an inclined plane. We assume that thin supported films have a thickness of 𝐻̅ and less than or equal to one
hundred nm. Equations of Navier and Stokes, continuity-equation, and related boundary conditions are used to
represent a two-dimensional stream demonstrated as a continuum. Under long-wave approximation, the
governing equations for the film interface have been rescaled and simplified to obtain a highly non-linear
condition of development for the film interface. A procedure for evaluating the magnitude of the effects of the
high-order effects is also used to formulate simplified governing equations. In the future, we can study this problem
by adding heat transfer over the stretching plate. In addition, we can also study the stability analysis to twodimension flow of a viscous liquid within a horizontal thin liquid film with neglecting the inertia terms of NavierStokes equations.
In this paper, we consider the unsteady flow within a double-sided symmetric thin liquid film with negligible inertia. We apply the Navier-Stokes equations in two dimensional flows for incompressible fluid. The similarity method is used in which the explicit time dependence can be isolated and thus the shape of the film will depend on one variable only. The differential equation of the film thickness is obtained analytically and the solution of equation that represents the film thickness is obtained numerically by using Rung-Kutta method.
stability and dynamics of a free double-sided symmetric thin liquid film are investigated by using the long-wave method. The flow in thin liquid film is considered in two dimensions for Newtonian liquid with constant density and dynamic viscosity. The Navier-stokes equations is used with appropriate boundary conditions of zero shear stress and also of normal stress on the bounding free surfaces with non-dimensional variables to obtain an equation that governs such flow.
This thesis deals with the unsteady flow within a double-sided symmetric thin liquid film with negligible inertia. The Navier-Stokes equations are applied in two dimensions for incompressible fluid with appropriate boundary conditions of zero shear stress. Also, for normal stress on the bounding free surfaces with non-dimensional variables to obtain an equation that governs such flow. The similarity method is used by which the explicit time dependence can be isolated and thus the shape of the film will depend on one variable only. The differential equation of the film thickness is obtained analytically and the solution of equation that represents the film thickness is obtained numerically by using Rung-Kutta method with the aid of Matlab (ode45). In addition, the stability and dynamics of a free double-sided symmetric thin liquid film are investigated by using the long-wave method. The flow in thin liquid film is considered in two dimensions for Newtonian liquid with constant density and dynamic viscosity. Moreover, the stability of the evolution equation of the thickness of the horizontal thin liquid film is studied, where the convective terms are neglected by using disturbance.
