Nonlinear Hydrodynamic Stability Analysis of Gravity-Driven Non-Newtonian Liquid Film Flows

• Main Authors: Po-Jen Cheng, 鄭博仁
• Other Authors: Cha''o-Kuang Chen
• Format: Others
• Language: zh-TW
• Published: 2001
• Online Access: http://ndltd.ncl.edu.tw/handle/21488992840751674269

博士 === 國立成功大學 === 機械工程學系 === 89 === The paper investigates the stability of thin non-Newtonian liquid film flowing down on a vertical wall or cylinder using a long-wave perturbation method to solve for generalized nonlinear kinematic equations with free film interface. To begin with a normal mode approach is employed to obtain the linear stability solution for the film flow. The threshold conditions, the linear growth rate of the amplitudes and the linear wave speeds are obtained subsequently as the by-products of linear solutions. To further investigate practical flow stability conditions, the weak nonlinear dynamics of a film flow is presented by using the method of multiple scales. It is shown that the necessary condition for the existence of such a solution is governed by the Ginzburg-Landau equation. The subcritical stability, subcritical instability, supercritical stability and supercritical explosive state will be obtained from the nonlinear film flow system. Some practical examples will be shown in the present thesis in order to illustrate the effectiveness on stability of the viscoelastic coefficient, the flow index of pseudoplastic liquid, the yield stress of Bingham liquid, the micropolar parameter and the cylinder size on the conclusive results. (1)Stability analysis of a thin viscoelastic film flow When a viscoelastic liquid film flow is modeled as a non-Newtonian flow, it possesses the characteristics of the so-called cross-viscosity and elastic properties. As the gravity-driven fluid is in motion, the flow energy is partially consumed by internal viscous forces and dissipated as heat to the environment, and partially stored as strain energy and the elastic stresses cannot be relaxed at a certain frequency. The degree of stability of the viscoelastic film flow decreases as the value of k increases. (2)Stability analysis of a thin pseudoplastic film flow When a pseudoplastic liquid film flow is modeled as a non-Newtonian flow, it possesses the characteristic of shear thinning effect. Physically, the gravity-driven pseudoplastic fluid of thin film flow will decrease the effective viscosity, it can, therefore, increase the convective motion of flow. The decreasing flow index indeed plays a significant role in destabilizing the flow and is thus of great practical importance. (3)Stability analysis of a thin Bingham plastic film flow For the film flow in stable states, the larger yield stress of the Bingham fluid decreases the convective motion of flow and tends to stabilize the flow. However, the yield stress of the Bingham fluid increases the disturbance energy in unstable states. Therefore, the flow will become relatively unstable as the value of yield stress is increased. (4)Stability analysis of a thin micropolar film flow The effect of the microrotation and couple stress will be taken into account in the Non-Newtonian fluid with the suspension micro-particle. Because the vortex viscosity parameter of the microstructure in micropolar fluid will increase the effective viscosity, it can, therefore, reduce the convective motion of flow. The flow field becomes relatively stable for a larger . (5) Stability analysis of a thin film flowing down on a vertical cylinder When the film flows down the outer surface has a destabilizing effect as the cylinder with a smaller radius . This destabilizing effect occurs because the surface tension will produce large capillary pressure at a smaller radius of curvature. This will induce the capillary pressure and force the fluid trough to move upward to the crest. Thus, the amplitude of the wave is increased.