Phase-field-based Lattice Boltzmann Model For Immiscible Multiphase Flows And Its Applications

Multiphase flow problems are ubiquitous in nature and engineering,such as enhanced oil recovery,geological CO2 storage,offshore oil spill,emulsion and foam formation,as well as rain drops,and so on,which are the key scientific problems in many fields such as biology,energy,environment,and micro fluidic chips.Multiphase flow problems involve flow between different phases,mass transfer,complex interface motion,and fluid-solid interactions,and it is a multi-field coupling problem involving flow field and phase field,hence it is very complex.Due to limitations of theoretical and experimental methods,numerical simulation plays an important role in the study of multiphase flows.In recent years,based on the development of mesoscopic non-equilibrium statistical thermodynamics,the lattice Boltzmann(LB)method has developed into an effective method for studying multiphase fluid flow due to its intrinsic parallelism,simple calculation and ease to handle of complex boundaries.At present,there are many multiphase flow LB models.Among them,the phase-field-based LB model has attracted more and more attention from scholars around the world because of its simple structure and clear physical background.Up to now,in the aspects of studies on phase-field-based LB model for multiphase flows,there are still some basic issues that have not been resolved.Firstly,the LB model for solving the Navier-Stokes(N-S)equation is not perfect,and there are still some defects that can be further optimized.Second,there are few researches on N-phase flows(N?4),and it is urgent to design an effective LB model to solve such problems;Third,for certain specific multiphase flow problems,such as droplets passing through a confining orifice,and movement of droplets and bubbles in N-phase flows(N?4),there is still a lack of research on their dynamic behavior.In response to the above problems,this paper mainly carried out the following work:(1)A generalized LB model with a source term in the continuity equation is proposed to solve both incompressible and nearly incompressible Navier-Stokes(N-S)equations,and we theoretically prove that some existing incompressible single-phase flow LB models are special cases of this generalized model.A modified pressure scheme is introduced to calculate the pressure,and then to ensure the accuracy of the model.Through Chapman-Enskog analysis,the governing equations can be recovered correctly from the present LB model.Besides,in the frame work of our generalized LB model,a new phase-field-based LB model is developed for incompressible and quasi-incompressible two-phase flows.The numerical results indicate that the current model is accurate and effective in studying two-phase problems.(2)We develop an efficient LB model for simulating immiscible incompressible Nphase flows(N?2)based on the Cahn-Hilliard phase field theory.In order to facilitate the design of LB model and reduce the calculation of the gradient term,the governing equations of the N-phase system are reformulated,and they satisfy the conservation of mass,momentum and the second law of thermodynamics.In the present model,(N-1)LB equations are employed to capture the interface,and another LB equation is used to solve the N-S equations,where a new distribution function for the total force is delicately designed to reduce the calculation of the gradient term.In addition,the governing equations can be recovered correctly from the present LB model through Chapman-Enskog analysis.Numerical simulation results show that the current LB model is accurate and efficient to simulate incompressible N-phase flows.(3)Based on the generalized LB model,the motion of gravity-driven deformable droplets passing through a confining orifice in two-dimensional(2D)space is numerically studied by the phase-field-based multiple-relaxation-time(MRT)LB model.In this work,we mainly consider the effects of the Bond number(Bo),orifice-to-droplet diameter ratio(r=d/D),plate thickness(Ht),wettability(or contact angle)and the diameter ratio of two droplets(rd=D1/D2)on the dynamic behavior of droplet through the orifice.The results show that these issues have great influences on the typical flow patterns(i.e.,release and capture).For the phenomenon that a single droplet with a fixed contact angle and plate thickness,we establish the relation r=0.572/3Bo-1/3 to separate droplet release from capture.Besides,with the decrease of contact angle,the droplet is more easily captured;with the increase of plate thickness,the droplet is easier to pass through the orifice;two droplets with larger diameters are easier to pass through the orifice.(4)Dynamics of droplet collision for four and five fluid phases are investigated by using the immiscible N phase flow(N?2)model proposed in this paper.The differences in the dynamic behavior of droplets under different surface tension and gravity are explored and the reasons for these differences are analyzed.The study shows that the larger surface tension(?13)will result in a larger drop velocity,which in turn will make the movement of the droplets and interfaces more complicated.In summary,we not only propose a generalized LB model for N-S equations with a source term in the continuity equation,then combine it with phase field theory to solve the problem of incompressible or quasi-incompressible two-phase flow problems,but also develop an efficient phase-field-based LB model for simulating immiscible incompressible N-phase flow(N?2).In addition,based on the above work,we also study the dynamics of droplet passing through a confining orifice and dynamics of droplet collision for four and five fluid phases.These works have played a certain role in promoting the application of the LB method in the engineering field involving multiphase flow.