Lattice Boltzmann Model Of Axisymmetric Three-phase Flow And Its Application To Rayleigh-Plateau Instability

In nature and engineering fields,three-phase flow systems involving three fluids are widely distributed,such as the transport of water pollutants,the transport process of oil,water and gas in enhanced oil recovery,and the generation technology of composite droplets in microfluidic devices.The interfacial dynamic behavior of three-phase fluid is very complicated due to the migration,deformation,rupture and merging of various fluid interfaces.With the rapid development of computer technology,we can use computers to deal with the numerical simulation of fluid flow.It can conveniently provide physical quantities that are not easy to measure in experimental research,such as the interface shape at a certain moment in the process of phase interface change,the velocity,pressure and density distribution of the fluid at the interface.Since the lattice Boltzmann(LB)method was developed in the late 1980 s,it has shown strong competitiveness in dealing with fluid flow problems,and has received great attention from scholars in numerical simulation of flow problems.The lattice Boltzmann method discretizes the fluid,and then derives the evolution process of the particles according to the distribution function of the particles,thereby characterizing the macroscopic dynamic characteristics of the fluid itself.Due to its microscopic nature and mesoscopic characteristics,the LB method has the advantages of simple programming,natural parallelism,and easy handling of microscopic interactions between fluids compared to traditional numerical methods,so it is more competitive in dealing with multiphase fluid flow problems.Based on the multicomponent phase field theory,this paper proposes a class of axisymmetric LB models for simulating three-phase fluid flow.This model uses two particle distribution functions to capture the phase interfaces between three different fluids,and another particle distribution function to solve fluid dynamics equations to obtain flow field information.In order to characterize the axisymmetric effect caused by coordinate transformation,the equilibrium distribution function and the external force term distribution function in the evolution equation have been ingeniously designed to theoretically ensure that the model in this paper can correctly restore the macro control equation of the three-phase fluid system,and the source terms generated by the axisymmetric effect do not contain any complex gradient terms,making it simpler and more efficient than the existing axisymmetric LB model.In order to verify the correctness and effectiveness of the LB model for axisymmetric threephase flows established in this paper,we simulated a series of benchmark examples of axisymmetric multiphase flows,including static double droplets,expansion of liquid lenses,and Rayleigh Plateau instability of two-phase fluids.Next,the interface evolution process of Rayleigh Plateau instability in three-phase fluids was studied using this model.The effects of wave number,surface tension ratio,liquid column radius ratio,density ratio,and viscosity on the interface dynamic behavior,interface fracture time,and the size of the resultant droplet during the thread fracture process of composite liquids were quantitatively analyzed.It can be found that when the wave number is large,the composite liquid thread ruptures and generates a composite main droplet and satellite droplet,while when the wave number is small,more satellite droplets can be generated,resulting in a trend of first increasing and then decreasing in the size of the composite main droplet and satellite droplet as the wave number increases.When increasing the ratio between surface tensions,increasing the ratio will accelerate the rate of liquid thread breakage.In the steady state,the size of the generated composite satellite droplet shows a gradually increasing trend,while the size of the generated composite main droplet shows a gradually decreasing trend.Increasing the liquid column radius ratio can promote the rupture of internal liquid threads,while delaying the rupture of intermediate liquid threads.The size of the composite main droplet increases with the increase of the liquid column radius ratio,while the size of the composite satellite droplet does not significantly change the liquid column radius ratio.When changing the density ratio among the three fluids in a three-phase fluid system,as the density ratio increases,it will slow down the rate of deformation of the liquid interface,and delay the time when the liquid thread breaks,but it has little impact on the size of the generated composite main droplet and composite satellite droplet.As the viscosity increases,the rupture time of the internal and intermediate liquid threads will be delayed,and the number of satellite droplets generated will also increase.For steady-state conditions,the radius of the composite main droplet will slightly increase.Due to the appearance of satellite droplets composed of a single fluid,the size of the composite satellite droplet will decrease according to the volume conservation law of three-phase fluid systems.