Long-wave Perturbation Method Research Articles

Surface waves on viscoelastic magnetic fluid film flow down a vertical column

Long-wave perturbation method is employed to solve the nonlinear hydromagnetic stability of a thin electrically conductive viscoelastic fluid film flowing down on the outside surface of a vertical cylinder. As the viscoelastic effect and the magnetic force are introduced into governing equation, the results are more compatible with the practice situation. The modeling results display that the degree of instability in the film flow is further intensified by the lateral curvature of cylinder. It is also observed that by increasing the effect of the magnetic field and by decreasing the viscoelastic effect tends to enhance the stability as traveling down along the vertical cylinder. Moreover, the instability state could be neutralized by controlling the applied magnetic field. The optimum conditions can be found through the use of a system to alter stability of the film flow by controlling the applied magnetic field.

Stability Analysis on Viscous Magnetic Fluid Film Flowing Down Along a Vertical Cylinder

AbstractThe paper investigates the hydromagnetic stability theory of a thin electrically conductive fluid film flowing down along the outside surface of a vertical cylinder. The long-wave perturbation method is employed to solve for generalized kinematic equations with free film interface. The normal mode approach is used to compute the stability solution for the film flow. The modeling results display that 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. It is also observed that by increasing the effect of the magnetic field and increasing the radius of the cylinder the film flow can become relatively more stable as traveling down along the vertical cylinder.

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

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.

STABILITY ANALYSIS OF THE THIN POWER LAW LIQUID FILM FLOWING DOWN ON A VERTICAL CYLINDER

The paper investigates the stability theory of a thin power law liquid film flowing down along the outside surface of a vertical cylinder. The long-wave perturbation method is employed to solve for generalized linear kinematic equations with free film interface. The normal mode approach is used to compute the stability solution for the film flow. 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 analysis results also indicate that by increasing the flow index and increasing the radius of the cylinder the film flow can become relatively more stable as traveling down along the vertical cylinder.

Nonlinear stability analysis of thin micropolar film flows travelling down a vertical moving plate

This paper employs linear and nonlinear stability theories to conduct a numerical characterization of thin micropolar film flows travelling down a vertical moving plate. Having applied the long-wave perturbation method to derive the generalized kinematic equations for a free film surface condition, the multiple scales method is used to solve the micropolar film flow in the cases of a stationary vertical plate, a vertical plate moving in the downward direction and a vertical plate moving in the upward direction. The numerical results indicate that both subcritical instability and supercritical stability conditions may occur in the micropolar film flow system. No obvious change in the supercritical stability condition is observed when the plate moves vertically in the upward or downward direction. The numerical results indicate that a downward motion of the vertical plate tends to enhance the stability of the film flow.

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

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.

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

The paper presents both the linear and nonlinear stability theories for the characterization of thin Newtonian film flows traveling down along a vertical moving plate. The linear model is first developed to characterize the flow behavior. After showing the inadequacy of the linear model in representing certain flow characteristics, the nonlinear kinematics model is then developed to represent the system. The long-wave perturbation method is employed to derive the generalized kinematic equations with free film surface condition. The linear model is solved by using the normal mode method for three different, namely, the quiescent, up-moving and down-moving, moving conditions. Subsequently, the elaborated nonlinear film flow model is solved by the method of multiple scales. The modeling results clearly indicate that both subcritical instability and supercritical stability conditions are possible to occur in the film flow system. The effect of the down-moving motion of the vertical plate tends to enhance the stability of the film flow.

Perturbation analysis to the nonlinear stability characterization of thin condensate falling film on the outer surface of a rotating vertical cylinder

The linear and nonlinear stability theories for characterization of condensate film flow down on the outer surface of a rotating infinite vertical cylinder is investigated analytically. A generalized nonlinear 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 behaviors. The amplitude growth rates and the threshold conditions are characterized subsequently and summarized as the by-products of the linear solutions. In the second step, an elaborated nonlinear film flow model is solved by using the method of multiple scales to characterize flow behaviors at various states of sub-critical stability, sub-critical instability, supercritical stability and supercritical explosion. The modeling results indicate that by increasing the rotation speed, Ω, and decreasing the radius of cylinder, R, the film flow becomes less stable, generally.

Nonlinear stability analysis of the thin pseudoplastic liquid film flowing down along a vertical wall

This article investigates the weakly nonlinear stability theory of a thin pseudoplastic liquid film flowing down on a vertical wall. The long-wave perturbation method is employed to solve for generalized nonlinear kinematic equation with free film interface. The normal mode approach is 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. It is shown that the necessary condition for the existence of such a solution is governed by the Ginzburg–Landau equation. The modeling results indicate that both subcritical instability and supercritical stability conditions are possible to occur in a pseudoplastic film flow system. The results also reveal that the pseudoplastic liquid film flows are less stable than Newtonian’s as traveling down along the vertical wall. The degree of instability in the film flow is further intensified by decreasing the flow index n.

Nonlinear Stability Analysis of Thin Viscoelastic Film Flow Traveling Down along a Vertical Cylinder

This paper investigates the weakly nonlinear stability theoryof a thin viscoelastic liquid film flowing down along the outsidesurface of a vertical cylinder. The long-wave perturbation method isemployed to solve for generalized nonlinear kinematic equations withfree film interface. The normal mode approach is first used to computethe linear stability solution for the film flow. The method of multiplescales is then used to obtain the weak nonlinear dynamics of the filmflow for stability analysis. The modeling results indicate that both thesubcritical instability and supercritical stability conditions arepossible to occur in a viscoelastic film flow system. The degree ofinstability in the film flow is further intensified by the lateralcurvature of cylinder. This is somewhat different from that of theplanar flow. The modeling results also indicate that by increasing theviscoelastic effect and decreasing the radius of the cylinder the filmflow can become less stable as traveling down along the verticalcylinder.

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

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.

Stability analysis of thin viscoelastic liquid film flowing down on avertical wall

This paper investigates the stability of thin viscoelastic liquid filmflowing down on a vertical wall using a long-wave perturbation method to findthe solution for generalized nonlinear kinematic equations with a free filminterface. To begin with, a normal mode approach is employed to obtain the linearstability solution for the film flow. The linear growth rate of the amplitudes,the wave speeds and the threshold conditions are obtained subsequently as theby-products of linear solutions. The results of linear analysis indicate thatthe viscoelastic parameter k = k0/(ρh0*2}) destabilizes the film flow asits magnitude increases. To further investigate practical flow stabilityconditions, the weak nonlinear dynamics of a film flow are presented by usingthe method of multiple scales. It is shown that the necessary condition for theexistence of such a solution is governed by the Ginzburg-Landau equation.Modelling results indicate that both the subcritical instability and thesupercritical stability conditions are possible in a viscoelastic film flowsystem. The results of nonlinear modelling further indicate that the thresholdamplitude εa0 in the subcritical instability region becomessmaller as the viscoelastic parameter k increases. If the initial finiteamplitude of disturbance is greater than the value of threshold amplitude, thesystem becomes explosively unstable. It is also interesting to note that boththe the threshold amplitude and the nonlinear wave speed in the supercriticalstability region increase as the value of k increases. Therefore, the flowbecomes unstable when the value of k increases. The viscoelastic parameter kindeed plays a significant role in destabilizing the film flow travelling downalong a vertical plate.