Stability Analysis of a Film Flow Down an Incline in the Presence of a Floating Flexible Membrane

2020 ◽  
pp. 253-263
Author(s):  
M. Sani ◽  
H. Behera ◽  
S. Ghosh
Keyword(s):  
Stability Analysis ◽  
Film Flow ◽  
Flexible Membrane

Nonlinear hydromagnetic stability analysis of a pseudoplastic film flow

2009 ◽  
Vol 13 (4-5) ◽  
pp. 247-255 ◽  
Author(s):  
Po-Jen Cheng ◽  
I-Peng Chu
Keyword(s):  
Stability Analysis ◽  
Film Flow

Stability analysis of non-inertial thin film flow over a heterogeneously heated porous substrate

2016 ◽  
Vol 28 (2) ◽  
pp. 022104 ◽  
Author(s):  
Tara Chand Kumawat ◽  
Naveen Tiwari
Keyword(s):  
Thin Film ◽  
Stability Analysis ◽  
Film Flow ◽  
Porous Substrate ◽  
Thin Film Flow

Stability analysis of thin film flow along a heated porous wall

2009 ◽  
Vol 21 (1) ◽  
pp. 014103 ◽  
Author(s):  
Uwe Thiele ◽  
Benoît Goyeau ◽  
Manuel G. Velarde
Keyword(s):  
Thin Film ◽  
Stability Analysis ◽  
Film Flow ◽  
Porous Wall ◽  
Thin Film Flow

Long-Wave Instabilities in a Non-Newtonian Film on a Nonuniformly Heated Inclined Plane

2009 ◽  
Vol 131 (3) ◽  
Author(s):  
I. Mohammed Rizwan Sadiq ◽  
R. Usha
Keyword(s):  
Stability Analysis ◽  
Evolution Equation ◽  
Nonlinear Evolution Equation ◽  
Film Flow ◽  
Nonlinear Evolution ◽  
Flow System ◽  
Nonuniform Heating ◽  
Inclined Plane ◽  
Long Wave ◽  
Wave Instabilities

A thin liquid layer of a non-Newtonian film falling down an inclined plane that is subjected to nonuniform heating has been considered. The temperature of the inclined plane is assumed to be linearly distributed and the case when the temperature gradient is positive or negative is investigated. The film flow is influenced by gravity, mean surface tension, and thermocapillary forces acting along the free surface. The coupling of thermocapillary instability and surface-wave instabilities is studied for two-dimensional disturbances. A nonlinear evolution equation is derived by applying the long-wave theory, and the equation governs the evolution of a power-law film flowing down a nonuniformly heated inclined plane. The linear stability analysis shows that the film flow system is stable when the plate temperature decreases in the downstream direction while it is less stable for increasing temperature along the plate. Weakly nonlinear stability analysis using the method of multiple scales has been investigated and this leads to a secular equation of the Ginzburg–Landau type. The analysis shows that both supercritical stability and subcritical instability are possible for the film flow system. The results indicate the existence of finite-amplitude waves, and the threshold amplitude and nonlinear speed of these waves are influenced by thermocapillarity. The nonlinear evolution equation for the film thickness is solved numerically in a periodic domain in the supercritical stable region, and the results show that the shape of the wave is influenced by the choice of wave number, non-Newtonian rheology, and nonuniform heating.

Nonlinear Stability Analysis of the Thin Micropolar Liquid Film Flowing Down on a Vertical Cylinder

2000 ◽  
Vol 123 (2) ◽  
pp. 411-421 ◽  
Author(s):  
Po-Jen Cheng ◽  
Cha’o-Kuang Chen ◽  
Hsin-Yi Lai
Keyword(s):  
Stability Analysis ◽  
Liquid Film ◽  
Nonlinear Stability ◽  
Film Flow ◽  
Multiple Scales ◽  
Vertical Cylinder ◽  
Nonlinear Stability Analysis ◽  
Weakly Nonlinear ◽  
Free Film ◽  
Micropolar Liquid

This paper investigates the weakly nonlinear stability theory of a thin micropolar liquid film flowing down along the outside surface of a vertical cylinder. The long-wave perturbation method is employed to solve for generalized nonlinear kinematic equations with free film interface. The normal mode approach is first used to compute the linear stability solution for the film flow. The method of multiple scales is then used to obtain the weak nonlinear dynamics of the film flow for stability analysis. The modeling results indicate that both subcritical instability and supercritical stability conditions are possible to occur in a micropolar film flow system. The degree of instability in the film flow is further intensified by the lateral curvature of cylinder. This is somewhat different from that of the planar flow. The modeling results also indicate that by increasing the micropolar parameter K=κ/μ and increasing the radius of the cylinder the film flow can become relatively more stable traveling down along the vertical cylinder.

Linear stability analysis of thin liquid film flow over a heterogeneously heated substrate

2014 ◽  
Vol 26 (4) ◽  
pp. 042105 ◽  
Author(s):  
Naveen Tiwari ◽  
Anmol Awasthi ◽  
Jeffrey M. Davis
Keyword(s):  
Stability Analysis ◽  
Liquid Film ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Film Flow ◽  
Thin Liquid Film ◽  
Heated Substrate ◽  
Liquid Film Flow
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