Lattice Boltzmann Method For Multiphase Fluid Flows In Complex Microchannels

The multiphase fluid flows in complex microchannels are encountered in a variety of applications, such as energy, environment, chemical engineering, microfluidic chip, and so on. These flows are not only related to the complex interfacial dynamics including migra-tion/deformation/breakup/coalescence, but also are greatly influenced by many microscopic factors, such as channel structures, capillary force, interaction between fluid and solid wall. For this reason, the multiphase fluid flows in complex microchannels are very complicated, and the flow law and its influence mechanism are still not understood clearly. When study-ing these flow problems, the traditional numerical method will suffer from many difficulties including the complexity in treating boundary conditions, inconvenience in describing the interaction between different phases, low performance in parallel computing. However, the lattice Boltzmann method (LBM) based on the kinetic theory has been proven to be an ef-fective method in studying multiphase flows due to its microscopic nature and mesoscopic characteristic.Up to now, in the aspects of studies on LBM for multiphase flows in complex mi-crochannels, some key and fundamental problems have not been solved:on one hand, the exsiting LBM models for multiphase flows are imperfect; on the other hand, the transport laws of multiphase flows in complex microchnnels are not clear. Therefore, we aim to im-proving lattice Boltzmann models for mutiphase flows, and then applied them to study the multiphase fluid flows in complex microchannels. In addition, we also study the classical Rayleigh-taylor instability problem. This thesis is composed of the following parts:(1) Based on the phase-field theory, we present two-and three-dimensional multiphase lattice Boltzmann models for the interface capturing. Compared to existing lattice Boltz-mann models for multiphase flows, the present model can achieve an overall improvement in the accuracy and stability of the capturing interface, and the calculations of macroscopic pressure and velocity can be much easier. In addition, the present model can be applied to multiphase flow at a high Reynolds number or low viscosity. This work will provide a theoretical foundation for LBM to study multiphase fluid flows in complex microchannels.(2) Through modifying equilibrium distribution functions and introducing some proper source terms, we develop an accurate, simple and efficient lattice Boltzmann model for ax-isymmetric multiphase flows. This model can avoid some problems that exist in the previous axisymmetric multiphase lattice Boltzmann models, such as some complicated source terms included and poor performance in interface capturing. To test the performance of the present model, we simulated the classical Rayleigh-Plateau instability and drop dripping case, and numerical results agree well with experimental data and analytical solution.(3) We study the immiscible displacement processes of multiphase fluid in the mi-crochannel patterned with a cavity, and mainly focus on the effects of surface wettability, capillary number, density ratio and cavity size on the dynamics of the liquid and displace-ment efficiency. The results show that the wettability has a significant influence on dynamic behaviors of the liquid:for the nonwetting case, the liquid can be completely displaced out, and for the wetting case, the liquid will be pinched off, leading to part of the liquid remain-ing in the cavity. Besides, the relationships between the critical capillary number and some physical parameters including wettability, density ratio and cavity size are also discussed.(4) Based on the proposed model, we study the drop dynamics including migra-tion/deformation/breakup in the bifurcate microchannel, and mainly analyze the influencing mechanisms of surface wettability, capillary number and outflow flux ratio. The results show that the drop behaviors in the branch depend on the surface wettability:for the nonwetting case, the daughter drop completely suspends in the branch, and for the wetting case, the daughter drop takes on a secondary breakup, which results in part of drop adhering on the wall and the remaining flowing to the outlet. Furthermore, we observe that when the capil-lary number is large enough, the drop can symmetrically break up into two same daughter drops, and when the capillary number is small, the drop remains at bifurcate position. In addition, through adjusting the outflow flux ratio, the drop can take on asymmetric rupture or flow into the branch where the flow velocity is larger.(5) The propose model is applied to simulate the Rayleigh-Taylor instability prob-lem in the two-and three-dimensional microchannels. We mainly investigate the effect of Reynolds number on the development of the disturbance at several stages and the in-terfacial dynamics. The numerical results are summarized as follows:at a high Reynolds number, a sequence of growth stages can be obtained, including linear growth, terminal ve-locity, reacceleration, and chaotic mixing development, and numerical results quantitatively agree well with the theoretical predictions at early stages, while at late chaotic mixing stage, it is found that the instability takes on a quadratic growth; at a low Reynolds number, the flows are laminar, and some late growth stages can no longer be reached.In summary, the lattice Boltzmann models for the interface capturing and axisymmetric multiphase flows are presented. And the immiscible displacement of multiphase fluid in microchannel patterned with a cavity, drop dynamics in the bifurcate microchannel and Rayleigh-Taylor instability problem in microchannel are studied numerically. The research results in present thesis not only improve the understanding of transport law and internal influence mechanism of multiphase fluid flows in complex microchannel, but also can provide some valuable attempts to promote the application of LBM in the engineering including multiphase flows.