Nonlinear Rupture of Thin Micropolar Liquid Film Under a Magnetic Field

2016 ◽  
Vol 33 (2) ◽  
pp. 249-256
Author(s):  
P.-J. Cheng ◽  
C.-K. Chen ◽  
Y.-C. Wang ◽  
M.-C. Lin ◽  
C.-K. Yang
Keyword(s):  
Magnetic Field ◽  
Liquid Film ◽  
Evolution Equations ◽  
Film Flow ◽  
Nonlinear Evolution Equations ◽  
Rupture Time ◽  
Initial Disturbance ◽  
Horizontal Plate ◽  
Film Rupture ◽  
Micropolar Liquid

AbstractThis paper investigates the rupture problem of a thin micropolar liquid film under a magnetic field on a horizontal plate, using long-wave perturbation to resolve nonlinear evolution equations with a free film interface. The governing equation is resolved using a finite difference method as part of an initial value problem for spatial periodic boundary conditions. The effect of a micropolar liquid under a magnetic field on the nonlinear rupture mechanism is studied in terms of the micropolar parameter, R, the Hartmann constant, m and the initial disturbance amplitude, H0. Modeling results indicate that the R, m and H0 parameters strongly affect the film flow. Enhancing the micropolar and magnetic effects is found to delay the rupture time. In addition, the results show that the film rupture time increases as the values of initial disturbance magnitude decrease. The micropolar and magnetic parameters indeed play a significant role in the film flow on a horizontal plate. Moreover, the optimum conditions can be found to alter stability of the film flow by controlling the applied magnetic field.

Nonlinear Rupture Theory of a Thin Liquid Film With Insoluble Surfactant

1998 ◽  
Vol 120 (3) ◽  
pp. 598-604 ◽  
Author(s):  
Chi-Chuan Hwang ◽  
Chaur-Kie Lin ◽  
Da-Chih Hou ◽  
Wu-Yih Uen ◽  
Jenn-Sen Lin
Keyword(s):  
Liquid Film ◽  
Evolution Equations ◽  
Thin Liquid Film ◽  
Quantitative Difference ◽  
Marangoni Effect ◽  
Nonlinear Evolution Equations ◽  
Rupture Time ◽  
Diffusion Effect ◽  
Dynamic Rupture ◽  
Insoluble Surfactant

Effects of insoluble surfactant on the dynamic rupture of a thin liquid film coated on a flat plate are studied. The strong nonlinear evolution equations derived by the integral method are solved by numerical method. The results show that enhancing (weakening) the Marangoni effect (the surface diffusion effect) will delay the rupture process. Furthermore, the rupture time predicted by the integral theory is shorter than that predicted by the long-wave expansion method. In addition, the quantitative difference in the rupture time predicted by two models enlarges with the increase of Marangoni effect, however, without obvious change as the diffusion effect increases.

scholarly journals Nanofluid thin film flow of Sisko fluid and variable heat transfer over an unsteady stretching surface with external magnetic field

2019 ◽  
Vol 13 ◽  
pp. 174830181983245 ◽  
Author(s):  
Muhammad Jawad ◽  
Zahir Shah ◽  
Saeed Islam ◽  
Waris Khan ◽  
Aurang Zeb Khan
Keyword(s):  
Magnetic Field ◽  
Thin Film ◽  
Brownian Motion ◽  
Liquid Film ◽  
Film Flow ◽  
Thin Film Flow ◽  
Sisko Fluid ◽  
Variable Heat ◽  
Liquid Film Flow ◽  
Optimal Approach

This research paper investigates two dimensional liquid film flow of Sisko nanofluid with variable heat transmission over an unsteady stretching sheet in the existence of uniform magnetic field. The basic governing time-dependent equations of the nanofluid flow phenomena with Sisko fluid are modeled and reduced to a system of differential equations with use of similarity transformation. The significant influence of Brownian motion and thermophoresis has been taken in the nanofluids model. An optimal approach is used to obtain the solution of the modeled problems. The convergence of the Homotopy Analysis Method (HAM) method has been shown numerically. The variation of the skin friction, Nusselt number and Sherwood number, their influence on liquid film flow with heat and mass transfer have been examined. The influence of the unsteadiness parameter [Formula: see text] over thin film is explored analytically for different values. Moreover for comprehension, the physical presentation of the embedded parameters, like [Formula: see text], magnetic parameter [Formula: see text], stretching parameter [Formula: see text] and Sisko fluid parameters [Formula: see text], Prandtl number Pr, thermophoretic parameter [Formula: see text], Brownian motion parameter [Formula: see text], Schmidt number [Formula: see text] have been represented by graph and discussed.

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

1996 ◽  
Vol 118 (3) ◽  
pp. 498-505 ◽  
Author(s):  
Chen-I Hung ◽  
Jung-Shun Tsai ◽  
Cha’o-Kuang Chen
Keyword(s):  
Angular Momentum ◽  
Liquid Film ◽  
Nonlinear Stability ◽  
Vertical Plate ◽  
Film Flow ◽  
Flow System ◽  
Kinematic Equation ◽  
Stability Behavior ◽  
The Stability ◽  
Micropolar Liquid

A perturbation method is used to investigate analytically the nonlinear stability behavior of a thin micropolar liquid film flowing down a vertical plate. In this analysis, the conservation of mass, momentum, and angular momentum are considered and a corresponding nonlinear generalized kinematic equation for the film thickness is thereby derived. Results show that both the supercritical stability and the subcritical instability can be found in the micropolar film flow system. This analysis shows that the effect of the micropolar parameter R(=κ/μ) is to stabilize the film flow, that is, the stability of the flowing film increases with the increasing magnitude of the micropolar parameter R. Also, the present analysis shows that the micropolar coefficients, Δ(=h02/j) and Λ(=γ/μj), have very little effects on the stability of the micro-polar film.

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.

The Stability of Evaporating Thin Liquid Film Containing Insoluble Surfactant on Heated Substrate

2012 ◽  
Vol 614-615 ◽  
pp. 191-194
Author(s):  
Chun Xi Li ◽  
Bing Lu ◽  
Xue Min Ye
Keyword(s):  
Liquid Film ◽  
Evolution Equations ◽  
Thin Liquid Film ◽  
Nonlinear Evolution Equations ◽  
Linear Stability Theory ◽  
Film Stability ◽  
Heated Substrate ◽  
Insoluble Surfactant ◽  
The Stability ◽  
Evaporation Number

Flow of evaporating thin liquid film containing insoluble surfactant on a uniformally heated substrate is considered in this paper. Coupled nonlinear evolution equations for the film thickness and surfactant concentration are derived on the base of lubrication theory and reasonable boundary conditions. The flow stability of the thin liquid film has been studied using normal mode method according to the linear stability theory. The results show that the film stability is promoted by increasing the Capillary number and the surfactant Peclet number, while increasing the Marangoni number, the interface resistance number, the vapor recoil number and the evaporation number can reduce the stability of the system.

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