Mathematics and Statistics Vol. 11(1), pp. 13 - 21
DOI: 10.13189/ms.2023.110102
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Linear Stability of Double-sided Symmetric Thin Liquid Film by Integral-theory

Ibrahim S. Hamad *
Department of Mathematics, Faculty of Science, University of Zakho, Kurdistan Region, Iraq


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.

Thinning Liquid Layers, Navier and Stokes Equations, Continuity-formulas

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Ibrahim S. Hamad , "Linear Stability of Double-sided Symmetric Thin Liquid Film by Integral-theory," Mathematics and Statistics, Vol. 11, No. 1, pp. 13 - 21, 2023. DOI: 10.13189/ms.2023.110102.

(b). APA Format:
Ibrahim S. Hamad (2023). Linear Stability of Double-sided Symmetric Thin Liquid Film by Integral-theory. Mathematics and Statistics, 11(1), 13 - 21. DOI: 10.13189/ms.2023.110102.