Stability Analysis of A Thin Micropolar Fluid Flowing on A Rotating Circular Disk

2011 ◽  
Vol 27 (1) ◽  
pp. 95-105 ◽  
Author(s):  
C. K. Chen ◽  
M. C. Lin ◽  
C. I. Chen
Keyword(s):  
Stability Analysis ◽  
Linear Stability ◽  
Micropolar Fluid ◽  
Film Flow ◽  
Multiple Scales ◽  
Landau Equation ◽  
Kinematic Model ◽  
Circular Disk ◽  
Necessary Condition ◽  
Thin Film Flow

ABSTRACTThe stability analysis of a thin micropolar fluid flowing on a rotating circular disk is investigated numerically. The target is restricted to some neighborhood of critical value in the linear stability analysis. First, a generalized nonlinear kinematic model is derived by the long wave perturbation method. The method of normal mode is applied to the linear stability. After the weakly nonlinear dynamics of a film flow is studied by using the method of multiple scales, the Ginzburg-Landau equation is determined to discuss the necessary condition in terms of the various states of subcritical stability, subcritical instability, supercritical stability, and supercritical explosion for the existence of such flow pattern. The modeling results indicate that the rotation number and the radius of circular disk play the significant roles in destabilizing the flow. Furthermore, the micropolar parameter K serves as the stabilizing factor in the thin film flow.

scholarly journals Weakly Nonlinear Hydrodynamic Stability of the Thin Newtonian Fluid Flowing on a Rotating Circular Disk

2009 ◽  
Vol 2009 ◽  
pp. 1-15 ◽  
Author(s):  
Cha'o-Kuang Chen ◽  
Ming-Che Lin
Keyword(s):  
Stability Analysis ◽  
Newtonian Fluid ◽  
Rotation Number ◽  
Hydrodynamic Stability ◽  
Stability Region ◽  
Multiple Scales ◽  
Landau Equation ◽  
Circular Disk ◽  
Necessary Condition ◽  
Weakly Nonlinear

The main object of this paper is to study the weakly nonlinear hydrodynamic stability of the thin Newtonian fluid flowing on a rotating circular disk. A long-wave perturbation method is used to derive the nonlinear evolution equation for the film flow. The linear behaviors of the spreading wave are investigated by normal mode approach, and its weakly nonlinear behaviors are explored by the method of multiple scales. The Ginzburg-Landau equation is determined to discuss the necessary condition for the existence of such flow pattern. The results indicate that the superctitical instability region increases, and the subcritical stability region decreases with the increase of the rotation number or the radius of circular disk. It is found that the rotation number and the radius of circular disk not only play the significant roles in destabilizing the flow in the linear stability analysis but also shrink the area of supercritical stability region at high Reynolds number in the weakly nonlinear stability analysis.

scholarly journals Weakly Nonlinear Stability Analysis of a Thin Magnetic Fluid during Spin Coating

2010 ◽  
Vol 2010 ◽  
pp. 1-17 ◽  
Author(s):  
Cha'o-Kuang Chen ◽  
Dong-Yu Lai
Keyword(s):  
Spin Coating ◽  
Film Flow ◽  
Multiple Scales ◽  
Landau Equation ◽  
Kinematic Model ◽  
Circular Disk ◽  
Nonlinear Stability Analysis ◽  
Weakly Nonlinear ◽  
The Stability ◽  
Magnetic Filed

This paper investigates the stability of a thin electrically conductive fluid under an applied uniform magnetic filed during spin coating. A generalized nonlinear kinematic model is derived by the long-wave perturbation method to represent the physical system. After linearizing the nonlinear evolution equation, the method of normal mode is applied to study the linear stability. Weakly nonlinear dynamics of film flow is studied by the multiple scales method. The Ginzburg-Landau equation is determined to discuss the necessary conditions of the various critical flow states, namely, subcritical stability, subcritical instability, supercritical stability, and supercritical explosion. The study reveals that the rotation number and the radius of the rotating circular disk generate similar destabilizing effects but the Hartmann number gives a stabilizing effect. Moreover, the optimum conditions can be found to alter stability of the film flow by controlling the applied magnetic field.

Weakly Nonlinear Stability Analysis of a Thin Liquid Film With Condensation Effects During Spin Coating

2009 ◽  
Vol 131 (10) ◽  
Author(s):  
C. K. Chen ◽  
M. C. Lin
Keyword(s):  
Liquid Film ◽  
Spin Coating ◽  
Multiple Scales ◽  
Landau Equation ◽  
Thin Liquid Film ◽  
Kinematic Model ◽  
Circular Disk ◽  
Nonlinear Stability Analysis ◽  
Weakly Nonlinear ◽  
The Stability

This paper investigates the stability of a thin liquid film with condensation effects during spin coating. A generalized nonlinear kinematic model is derived by the long-wave perturbation method to represent the physical system. The weakly nonlinear dynamics of a film flow are studied by the multiple scales method. The Ginzburg–Landau equation is determined to discuss the necessary conditions of the various states of the critical flow states, namely, subcritical stability, subcritical instability, supercritical stability, and supercritical explosion. The study reveals that decreasing the rotation number and the radius of the rotating circular disk generally stabilizes the flow.

Nonlinear Stability Analysis of Thin Film Flow from a Liquid Jet Impinging on a Circular Concentric Disk

2006 ◽  
Vol 22 (2) ◽  
pp. 115-124 ◽  
Author(s):  
P.-J. Cheng ◽  
H.-Y. Lai
Keyword(s):  
Thin Film ◽  
Linear Stability ◽  
Film Flow ◽  
Multiple Scales ◽  
Impinging Jet ◽  
Jet Flow ◽  
Liquid Jet ◽  
Conditional Stability ◽  
Thin Film Flow ◽  
Potential Core

AbstractThe paper investigates the stability of thin film flow from a liquid jet impinging on a circular concentric disk using a long-wave perturbation method to solve for the generalized nonlinear kinematic equations of free film interface. To begin with a normal mode approach is employed to obtain the linear stability solution for the film flow. In the linear stability solutions only subcritical region can be resolved. In other words, no solution of supercritical region can be obtained in linear domain. Furthermore, the role that the forces of gravitation and surface tension play in the flow is nothing but to stabilize the system. To further investigate the realistic impinging jet flow stability conditions, the weak nonlinear dynamics of a film flow is studied by using the method of multiple scales. Various subcritical nonlinear behaviors expressed in terms of absolute stability, conditional stability and explosive instability can be characterized by solving the Ginzburg-Landau equation. It is found that the jet flow will become relatively unstable for an increasing Reynolds number, a relative smaller distance from the center of the impinging jet on the disk and a smaller diameter of the exit jet. It is also concluded that the flow will always stay in a subcritical instability region if the characteristic diameter of the potential core at nozzle exit is less than 0.01mm for the numerical conditions given in this paper. In such a case when the amplitude of external flow disturbance is smaller than the threshold amplitude a stable jet flow can be ensured.

Non-Linear Stability Analysis of a Thin Newtonian Film Flowing Down an Infinite Vertical Rotating Cylinder

2005 ◽  
Vol 219 (9) ◽  
pp. 911-923 ◽  
Author(s):  
C-I Chen ◽  
C-K Chen ◽  
Y-T Yang
Keyword(s):  
Linear Stability ◽  
Film Flow ◽  
Multiple Scales ◽  
Kinematic Model ◽  
Rotating Cylinder ◽  
Second Step ◽  
Step Procedure ◽  
Non Linear ◽  
Mode Method

Non-linear stability theories for the characterization of Newtonian film flow down an infinite vertical rotating cylinder is given. A generalized non-linear kinematic model is derived to represent the physical system and is solved by the long-wave perturbation method in a two-step procedure. In the first step, the normal mode method is used to characterize the linear behaviours. In the second step, an elaborated non-linear film flow model is solved by using the method of multiple scales to characterize flow behaviours at various states of subcritical stability, subcritical instability, supercritical stability, and supercritical explosion. The modelling results indicate that by increasing the rotation speed, ω, and decreasing the radius of cylinder, R, the film flow becomes less stable, generally.

Non-linear stability analysis of micropolar fluid lubricated journal bearings with turbulent effect

2019 ◽  
Vol 71 (1) ◽  
pp. 31-39
Author(s):  
Subrata Das ◽  
Sisir Kumar Guha
Keyword(s):  
Stability Analysis ◽  
Linear Stability ◽  
Micropolar Fluid ◽  
Journal Bearing ◽  
Journal Bearings ◽  
Turbulent Regime ◽  
Content Type ◽  
Non Linear ◽  
The Stability ◽  
Bearing System

Purpose The purpose of this paper is to investigate the effect of turbulence on the stability characteristics of finite hydrodynamic journal bearing lubricated with micropolar fluid. Design/methodology/approach The non-dimensional transient Reynolds equation has been solved to obtain the non-dimensional pressure field which in turn used to obtain the load carrying capacity of the bearing. The second-order equations of motion applicable for journal bearing system have been solved using fourth-order Runge–Kutta method to obtain the stability characteristics. Findings It has been observed that turbulence has adverse effect on stability and the whirl ratio at laminar flow condition has the lowest value. Practical implications The paper provides the stability characteristics of the finite journal bearing lubricated with micropolar fluid operating in turbulent regime which is very common in practical applications. Originality/value Non-linear stability analysis of micropolar fluid lubricated journal bearing operating in turbulent regime has not been reported in literatures so far. This paper is an effort to address the problem of non-linear stability of journal bearings under micropolar lubrication with turbulent effect. The results obtained provide useful information for designing the journal bearing system for high speed applications.

Stability Analysis of a Thin Pseudoplastic Fluid with Condensation Effects Flowing on a Rotating Circular Disk

2013 ◽  
Vol 699 ◽  
pp. 413-421
Author(s):  
Ming Che Lin
Keyword(s):  
Linear Stability ◽  
Kinematic Model ◽  
Circular Disk ◽  
Vital Role ◽  
Linear Growth Rate ◽  
Flow Index ◽  
Neutral Stability ◽  
Pseudoplastic Fluid ◽  
Linear Solution ◽  
By Products

This paper investigates the linear stability of a thin axisymmetric pseudoplastic fluid with condensation effects flowing on a rotating circular disk. Long-wave perturbation analysis is proposed to derive a generalized kinematic model of the physical system with a small Reynolds number. The method of normal mode is applied to study the linear stability. The neutral stability curve and the linear growth rate are obtained subsequently as the by-products of linear solution. The study reveals that the rotation number generates a destabilizing effect in pseudoplastic fluid. The degree of the flow index n plays a vital role in stabilizing the film flow.

scholarly journals Hydromagnetic thin film flow: Linear stability

2013 ◽  
Vol 88 (2) ◽  
Author(s):  
Mustapha Amaouche ◽  
Hamid Ait Abderrahmane ◽  
Lamia Bourdache
Keyword(s):  
Thin Film ◽  
Linear Stability ◽  
Film Flow ◽  
Thin Film Flow
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