Lattice Boltzmann models for microscale fluid flows and heat transfer

The technology of Micro/Nano-Electro-Mechanical Systems and Micro-Total-Analysis Systems has developed rapidly over the last decade. The design and optimization of these miniaturized systems call for a robust mathematical model and efficient numerical algorithm for simulation of fluid flows and heat transfer at the micrometer scale. The lattice Boltzmann (LB) method is a kinetic-based approach for fluid flow computations. This method has been successfully applied to single-phase as well as multi-component and multi-phase flows. Owing to its kinetic nature and excellent numerical performance it can play an essential role as a simulation tool for understanding micro flows and heat transfer. To extend the application of the LB method to micro flows, some critical issues need to be addressed, noticeably the assumption of microscale gas as dilute, thermal effects arising from viscous dissipation, large pressure drop, surface-dominated effects (e.g. electrokinetic effect), boundary treatments for curved solid wall, etc. This thesis aims to investigate these fundamental issues and develop mesoscopic LB models for microscale fluid flows and heat transfer in a system with a characteristic length between 0.01-10 microns.; First, by introducing a different distribution function and starting from the Boltzmann equation as well as the Maxwellian, we obtain a double distribution function LB model for thermal flows with viscous dissipation. We then extend this double distribution function approach to curvilinear coordinates, and construct a finite-difference thermal LB model for simulation of the fluid flows and heat transfer with curved solid walls. Secondly, based on the Enskog equation and taking the finite size of particles into account, we propose an Enskog-equation based LB model for non-ideal fluid flows and demonstrate that our model can effectively suppress the compressibility error resulting from the large pressure drop through microchannels with a large length ratio. Thirdly, we propose an improved Boltzmann-equation based LB model for micro dilute gas flows. By simulating the micro-Poiseuille flow and the micro-cavity flow, we demonstrate that the numerical results simulated by the LB method are in good agreement with those by the DSMC method in the slip flow regime. Subsequently, we apply the finite-difference Enskog equation-based LB model to the study of micro dense gas flows. The numerical results show that the micro dense gas flow behavior depends not only on the Knudsen number but also on the ratio of the particle diameter to the mean particle spacing. Different length ratios make the dense gas in microchannels behave differently from the dilute gas, even at the same Knudsen number. Finally, this thesis focuses on the study of micro electric kinetic flows. We propose a finite-difference thermal LB model for simulation of electro-osmotic flow and heat transfer in micro/nanochannels. The numerical results show that Joule heating has a significant effect on electro-osmotic flows in both micro- and nanochannels while viscous dissipation becomes important for electro-osmotic flows in nanochannels only. In addition, to investigate the thermal electro-osmotic flows with an extremely thin electric double layer, we present an effective slip model. We then numerically solve this slip model using the double distribution LB algorithm and demonstrate that the slip model can not only accurately predict the electro-osmotic flow and heat transfer when channel size is about 400 times larger than the Debye length, but also substantially reduce the computational time as compared with the conventional complete model with inclusion of the electric double layer.