Nonlinear stability characterization of thin Newtonian film flows traveling down on a vertical moving plate

Stability Analysis of Thin Power-Law Fluid Film Flowing down a Moving Plane in a Vertical Direction

“…The multiple scales method is used to characterize the weakly nonlinear behaviors of the fluid. The resulting Ginburg-Landau equation [24] can be derived following the same procedure as Cheng [9] and Lai [8]:…”

“…Tsai [8] discussed the linear stability problem of thin magnetic fluid films condensing on a flat plane. Lai [9] discussed the stability of Newtonian fluid films on a vertical moving plane. Naganthran [10,11] focused on the Carreau thin film flow over an unsteady stretching sheet and provided several different numerical solutions.…”

Weakly nonlinear stability analysis of a falling film with countercurrent gas flow

“…These properties are of primary importance for the design of process devices, and it is therefore desirable to have a better understanding of these mechanisms that occur under various conditions and to develop a theoretical behavior that allows nonlinear effects. Apart from a detailed analysis by Chang [22], Chang et al [23], and Cheng and Chang [24] on the nonlinear stability of falling films, there have been many investigations on the weakly nonlinear stability analysis of the falling film flow system (down an inclined/vertical wall or on the surface of the cylinder) which include the investigations by Usha and Uma [25], Uma and Usha [26], Chen et al [27], Lai et al [28], Ünsal and Thomas [29] and Hung et al [30]. These investigations have examined the growth of an initially unstable periodic surface perturbation and its nonlinear interaction with the higher harmonics.…”