Boundary Slip And Hydrodynamics Of Fluid Flow In A Micro/Nano-Gap

In the classical fluid mechanics and lubrication mechanics, it is assumed that no relative velocity exists between the fluid molecular and the solid molecular at the solid/liquid interface. This is the so-called no-slip boundary condition. During the recent years, with the rapid development of science and technology in micro- and nano-measuring technologies and the related area, it has been found that there are many significant differences between fluid flow at macro-scale and that at micro/nano-scale. Among of them, boundary slip (wall slip) is one of the most important problems. Boundary slip means that there is a finite relative velocity between the fluid and the solid molecular at the interface. It has been shown that boundary slip often plays an important or dominant role in the micro/nano-gap fluid flow. Researchers are now paying more attention to reveaI the boundary slip evidences and to search the physical principle of the boundary slip through experimental observation and molecular dynamics simulation (MDS). However, few studies are available on the numerical analysis of the effect of boundary slip on the hydrodynamics in a micro/nano-gap fluid flow. Furthermore, there are mainly two problems in the numerical analysis of the boundary slip. The first one is that the constant slip length model fails to predict many experimental results, especially at a large shear rate. The second one is that, due to the unknown amplitude and direction of the boundary slip, there are some numerical difficulties when the limiting shear stress slip model (LSSM) is used. The iterative solution technique based on the finite difference method meets problems in both the consuming time and the numerical convergence. In fact the iterative technique is impossible in the two-dimensional gap flow with boundary slip. The main work of the present dissertation is summarized as follows:In this dissertation, the limiting shear stress model proposed originally in rheological study is introduced to describe the boundary slip, and then, based on the parametric variational principle and the corresponding finite element parametric quadratic programming method (PVP and FEPQPM), the numerical solving process of a boundary slip problem is given. For a spherical squeeze film system often used in experimental studies of boundary slip phenomena, we propose a fitting formula of the hydrodynamic force. Further numerical analyses on a parallel plate system and a spherical squeeze film system show that our predictions are in good agreement with the existing experimental observations. This indicates that the LSSM is applicable to describe the boundary slip, and the PVP and FEPQPM can be used to effectively solve the boundary slip problem. Due to avoiding a time-consuming iteration process, the PVP and FEPQPM give rise to a high computational efficiency. The corresponding numerical results show that the boundary slip can make a decrease in hydrodynamic force of a spherical squeeze film system. Furthermore, it is found that the hydrodynamic response of the squeeze sphere system is controlled by the surface slippage properties. When a large slip occurs at both the upper and the down surface, the hydrodynamic load support may vanish entirely. However, as long as One of the surfaces has the limiting shear strength high enough to suppress any slip, even if the other surface has a null limiting shear stress, a finite hydrodynamic force can be obtained. Moreover, the value of this hydrodynamic force is just one quarter of that without boundary slip.Based on the MDS of Troian et al., a nonlinear slip model (NSM) is presented here. It can be regarded as a combination of the SLM and the LSSM. When the shear rate is low, the NSM gives an approximate constant slip length, which is the same as what is predicted by the SLM. However, when the shear rate is high, the NSM is almost the same as the LSSM. Based on the NSM, this paper obtains the numerical solutions of the boundary slip problems for a parallel plate system and a sphere squeeze system. A good agreement occurs between the numerical result and experimental observation.Taking advantage of the LSSM, PVP and FEPQPM, this paper gives the detailed numerical analyses of the boundary slip and hydrodynamics of one-dimensional gap flow with different gap geometries. It is found that, when the surface has a homogenous slip property, i.e., the surface limiting shear stress has the same value on the entire surface, the boundary slip always decreases the hydrodynamics of the fluid system. Furthermore, this effect depends on what a surface is a moving. If a large slip occurs on the moving surface orboth the stationary and the moving surface, the hydrodynamic response of the fluid system decrease dramatically, even lose totally. It is also found that boundary slip can be induced or enhanced with the decrease in the fluid film thickness or the surface limiting shear stress, and the increase in shear rate or viscosity of fluid. From these results, we can know why a sliding bearing often fails to work for a thin gap film and a high sliding velocity. For a sliding-rolling gap fluid flow system, no load support is expected only in the case of large sliding/rolling ratio. This explains why the bearing failure occurs more easily in the case of pure sliding than in the case of pure rolling. It should be pointed out that the boundary slip always results in a low friction force.When the stationary surface has heterogeneous slip property (a complicated slip surface), the boundary slip has a complex influence on the hydrodynamics of the fluid system. This effect is controlled by such parameters as the location, the geometry shape, the geometry size and the limiting shear stress of the slip zone as well as the geometry of the fluid gap. In general, the larger the boundary slip at the slip zone, the more excellent hydrodynamic effect the fluid system has. Taking example for one-dimensional slider bearing and journal bearing, this paper shows theoretically that a "complicated slip bearing system" (CSBS) can give higher hydrodynamic load support capacity and lower friction coefficient than those of the corresponding traditional no-slip bearing system (TNBS). Moreover, it is found that a convergent geometry gap, the necessary condition for a TNBS to acquire hydrodynamic load capacity, will not be required for the CSBS. The CSBS can get a very high hydrodynamic load support with a parallel fluid gap or a slight divergence gap. Consequently, these effects induced by the complicate boundary slip can help us to design and manufacture some new types of bearing system.When the LSSM is used to solve the boundary slip problem in a two-dimensional flow, it is difficult to determine the slip velocity because both the amplitude and the direction of the slip velocity are not known a priori. A multi-linearity method is developed to approach the non-linear control equation of the two-dimensional slip gap flow. Then, based on the PVP and FEPQPM, a new numerical method is proposed to solve the two-dimensional slip gap flow problem with boundary slip. Making use of this method, the present paper analyzes the boundary slip problem in a two-dimensional gap flow. It is found that the fluid system exhibits an excellent hydrodynamic response when the stationary surface has heterogeneous slip property. Through simple numerical optimizations, it is found that boundary slip on a trapezoid slip zone at the stationary surface makes the fluid system obtain an excellent hydrodynamic response. When the gap is parallel, comparing with the TNBS, the hydrodynamic load support of the complex slip slider bearing system is increased by about 150%, but the corresponding surface friction coefficient is decreased over 50%. Based on the numerical analyses of a rotor-bearing system with the heterogeneous slip surface, it is found that, comparing with the no-slip rotor-bearing system, the rotor-bearing system with the heterogeneous boundary slip gives rise to a high load support capacity, a very low surface friction coefficient as well as an excellent operation stability. Moreover, numerical results show that the rotor-bearing system with the heterogeneous slip surface is a self-stable operation system. Perhaps this finding will be useful for us to design a new bearing system with outstanding properties. However, when the stationary surface has a homogenous slip property, the boundary slip always decreases the operation stability of the rotor-bearing system.Finally, in chapter 9, the enhancement of the mechanical behavior of the NiAl alloy by strong magnetic treatment under high temperature of 900℃is introduced. Although this work has no straightforward relationship with the other parts of the present dissertation, a simple introduction is also given here due to its novelty and challenge. This work shows that the NiAl alloy treated with the strong magnetic field under high temperature gets a much better mechanical property than that without. The bending strength is increased by～75%, and the press strength and tensile strength are all increased more than 100%. Furthermore, the SEM observation of the fracture section shows that the magnetic field improves the alloy ductility, giving rise to a change in the fracture behavior.In conclusion, firstly, this dissertation proposes and develops the LSSM and the NSM to describe the boundary slip problem. Through the comparison between the LSSM, the NSM and the SLM, it is shown that the former two is more applicable than the latter at a wide range of the shear rate. Secondly, we successfully propose a new method to overcome the difficulty in solving the nonlinear equation of the two-dimensional slip system. Finally, this dissertation gives the detailed numerical analyses on the boundary slip and hydrodynamics for different gap flows. Some new physical phenomena and rules are revealed. Especially, it is theoretically found that a heterogeneous boundary slip improves the hydrodynamic effects and operation stability of the fluid flow system at micro/nano-scale. What is mentioned above will be very important for the computations, analyses and engineering applications of the boundary slip phenomena.