Phase-field-based Lattice Boltzmann Model For Simulating Non-Newtonian Droplet Impact And Coalescence

The impact and coalescence of liquid droplets on solid surface are universal in industrial applications,such as ink printing on paper,pesticide spraying on vegetable leaf,surface spray and spray cooling.The impact and coalescence processes are greatly affected by factors such as impact velocity,droplet physical properties and surface wettability.In particular,the processes for droplet impact and coalescence could differ greatly due to the constitutive difference between non-newtonian fluid and Newtonian fluid.In the last ten years,non-Newtonian fluid has been widely applied in industrial production and is playing a crucial part in controlling droplets deposition nowadays.For example,to obtain high quality products in producing printed circuit boards,chips and sensors,it is important to control finely droplet behavior and suppress droplets splashing and rebounding.In practice,non-Newtonian fluid is often applied in controlling the droplet deposition.Therefore,it is of great significance to explore the impact and coalescence of non-Newtonian droplet.However,there is a lot of work remianed to be done in experimental and numerical research.For example,the effect of surface wettability,impact velocity and surface tension on the droplet impact and coalescence is not adequately studied yet.Hence,it is necessary to further explore the physical process of droplet impact and coalescence for non-Newtonian fluids.The lattice Boltzmann(LB)method,derived from the mesoscopic particle dynamics,is one of the numerical methods for describing fluid flow.LB method has been widely applied to describe two phase flows and non-Newtonian fluid flows for its mesoscopic characteristics.Compared to other methods,the LB method is easy to program and parallel.Therefore,the LB method is an alternative approach to explore the process of droplet impact and coalescence.A coupled model of LB method and phase-field method for non-Newtonian power-law fluid and Newtonian fluid was developed.An incompressible multi-relaxation LB model was adopted to describe accurately incompressible fluid flow.The convective Cahn-Hilliardin equation was solved with finite difference method to compute dynamic interface deformation.In this paper,the impact and coalescence of non-Newtonian fluid droplet on solid surface were investigated numerically.The main works and relevant conclusions of this thesis are summaried briefly as follows:(1)Firstly,the LB method was briefly introduced.The lattice Boltzmann-BGK model(LBGK model)was recovered back to macroscopic equations.Incompressible multi-relaxation LB model was established.(2)The LB model for simulating non-Newtonian fluid was developed,and based on phase field equation,we developed a two-phase flow LB model of Newtonian fluid and non-Newtonian fluid.The cavity flow of non-Newtonian fluid and the Laplace law were computed.(3)The wettability boundary condition was applied at no-slip boundary and the LB model for different types of surface wettability was developed.The equilibrium process and dynamic process of droplet on solid surface were simulated.(4)For droplet impact,the results showed that the droplet is easier to deposit as power-law exponent n becomes smaller,and it is more likely to splash as power-law exponent n gets higher.The stable spreading length of droplet on wall is only affected by the wettability of wall.In addition,with the increase of Weber number,the pseudoplastic droplet achieves stability faster,while dilatant droplet is more prone to splash.When the equilibrium contact angle is large enough where the solid surface is highly hydrophobic,the dilatant droplet will rebound completely during retraction.(5)For droplet coalescence,it was found that the speed of dilatant fluid in the coalescence process is the fastest,followed by Newtonian fluid,and the speed of pseudoplastic fluid is the slowest.When the equilibrium contact angle equals to 90 °,for power-law droplet,the liquid bridge radius is proportional to the the square root of time at early stage of coalescence,which is consistent with Newtonian fluid.