Multiphase Lattice Boltzmann Models Based On Thermal Hydrodynamics Of Droplets And Their Application

Droplets and bubbles,dynamic problems of simultaneous flow with two phases and a clear interface,are typical physical forms in natural and industrial processes.In microscale,due to large surface/volume ratio,the droplets' surface tension force is far less than their body force and non-uniform pressure from environmental fluids,so that the droplets are stable and can be used as separate microcarriers.In recent years,the droplets have gradually become special microreactors which realize rapid mass and heat transfer on microfluidic chips and,as a result,the excessive consumption and the cross contamination of reagents are avoided.For manipulating microdroplets,many incentives have been developed and applied successfully.In these incentives,the thermal-induced capillary force is applicable for driving any fluids,including non-conducting fluids,and thus it gradually gets the attention of researchers.However,in practical implementations of thermally driving microdroplets,the phenomenon of evaporation,hysteresis and pinning with heating largely hampers the manipulation.In order to realize precise control of droplets,the thermal hydrodynamics of microdroplets needs further exploration.The lattice Boltzmann method,derived from the mesoscopic particle dynamics,is one of the numerical methods for describing fluid flows and physics in fluids.The lattice Boltzmann method has the advantages of microparticle dynamics and the picture of gas kinetics,and thus it has been widely applied in modeling complex phenomena and processes,including multiphase flows and their heat and mass transfer.Therefore,the lattice Boltzmann method is an alternative approach to explore the process of thermally driving microdroplets.This thesis mainly combined with the lattice Boltzmann method to study the thermal hydrodynamics of systems including interfacial microdroplets.The research includes establishing three-fluid thermal-hydrodynamic models,developing hybrid LB-FD(lattice Boltzmann-finite difference)schemes and simulating the thermal hydrodynamics of three fluids(including thermocapillary migration of interfacial droplets and droplets' Leidenfrost effect over a heated pool surface).The main works and relevant conclusions of this thesis are summaried briefly as follows:(1)Based on the two-and three-component Cahn-Hilliard equations,the interface dynamics models of multiphase flow were established,and the mathematical model for dynamic deformation of interfaces in a three-phase thermal convection was obtained.In addition,based on the concept of a continuum surface force,the expressions of surface tension for two-and three-phase flow were derived,which guarantee the numerical stability in modeling multiphase flow.(2)Inspired by the idea of solving the multiphase flow by the hybrid LB-FD scheme,the lattice Boltzmann method was introduced for the evolution of flow field,and the second-order finite difference method was adopted to other transport equations(including the Cahn-Hilliard equation(s)and the equation of temperature).Thanks to the explicitly time marching scheme,the codes are easy to parallelize and suitable for large-scale calculation.(3)In order to model the axisymmetric multiphase flow with a large density ratio,the distribution function related with radius was introduced,and the axisymmetric LBGK model(lattice Boltzmann-BGK model)and the corresponding multi-relaxation model(MRT-LB model)were established.Then,cases of Laplace law,droplet oscillation and droplet wettability were calculated.The results show that the present axisymmetric models can reach a density ratio of 1000 in static simulation and that of 500 in dynamic simulation.In addition,the numerical results also indicate that the present axisymmetric MRT-LB model has better numerical stability than the LBGK model.(4)To describe the thermalcapillary migration of interfacial droplets,a three-fluid thermal-hydrodynamic model was developed based on the three-component Phase Field method,and the model was solved by using the hybrid LB-FD scheme.After validating the model and codes,the thermocapillary migration of interfacial droplets was simulated.The results reveal the relation between the intensity of ambient thermocapillary flow and the direction of droplet motion,and demonstrate the effect of both droplets and interface deformations on droplet transfer.These results are useful for the systematic investigation on the thermocapillary migration of interfacial droplets.(5)To investigate the Leidenfrost effect of droplets on a heated liquid pool,a phase-change model including in a three-fluid system was developed based on the ternary Cahn-Hilliard model,and the axisymmetric mathematic model was solved by using the hybrid LB-FD scheme.After verifying the present model and codes,the liquid-substrate-based Leidenfrost system was simulated,and the results present the evolution of drop volume changes,the thickness of the vapor gap,and the distribution of temperature and velocity fields.In addition,we systematically analyzed the effects of some characteristic parameters on the Leidenfrost effect of droplets.These results provide a theoretical reference for optimizing the manipulation of droplets.