2015-10-30

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.