Modeling And Numerical Simulation Of Polymer Crystallization By Phase Field Lattice-dynamics Method

In the general phase field method,high resolution is always required for the calculation of interface accuracy,while in numerical simulation,high resolution requires very small time step(especially in diffusion using explicit scheme).The common solution is to use implicit time step format,which will bring complex matrix problem solving for each time step.In this paper,the lattice Boltzmann method is coupled in the phase field method to simulate the grain growth morphology of the polymer during crystallization,which avoids the shortcomings of the traditional phase field method.The main work done in this paper is as follows:Firstly,on the basis of the improved phase field model of polymer crystallization,the lattice Boltzmann equation with multi-relaxation scheme is used to replace the temperature diffusion equation in the phase field method,and a new phase field lattice-dynamics coupling model is established by coupling the phase field method and lattice Boltzmann method.The new coupling model proposes an adaptive time step,which is no longer required to be too small in numerical simulation,and avoids the divergence caused by too small time step.The phase field lattice-dynamics coupling model of dynamic crystallization is obtained by coupling flow in lattice Boltzmann equation considering the morphology of crystallization in flow conditions.The parameters in the coupled model are obtained by calculating the given physical parameters of the material,and can present a variety of grain morphologies under static and dynamic conditions.Secondly,the finite difference method is used to discretize the coupled model.The coupling model is dimensionless.For the time and space discretization,the forward difference scheme and the central difference scheme are used respectively,and the nine-point discrete scheme is used to solve the Laplace operator.The phase field lattice-dynamic coupling model was implemented to simulate the crystallization process of polymer by Fortranprogramming language.Thirdly,in order to prove the feasibility of the new coupling model in simulating polymer crystallization,the model parameters were changed under static and dynamic crystallization,and compared with the experimental results.In the static crystallization process,the effects of supercooling,anisotropic strength and latent heat on the morphology of polymer crystallization were studied quantitatively.In the dynamic crystallization process,the effects of flow velocity,interface thickness and driving force parameters on the morphology of polymer crystallization were studied quantitatively.The results show that supercooling determines the morphology of polymer crystals;secondary branching increases with the increase of anisotropic strength;arbor escent dendritic growth occurs with the increase of latent heat;dendritic growth in the direction of downstream and countercurrent is affected by flow rate;and the growth rate of polymer in the dynamic crystallization process is accelerated with the increase of interface thickness and driving force parameters.