Abstract: An improved free energy approach Lattice Boltzmann model(LBM) is proposed by introducing a forcing term instead of the pressure tensor. This model can reach the proper thermodynamic equilibrium after enough simulation time. On the basis of this model, the phase separation in binary polymer mixtures is studied by applying a Flory-Huggins-type free energy. The numerical results show good agreement with the analytic coexistence curve. This model can also be used to study the coarsening of microdomains in binary polymer mixtures at the early and intermediate stages. The simulation results are in accordance with those found in experiments. To understand the coarsening of microdomains at the late stage, we study the relationship between the growth exponent of the characteristic domain size and the interaction parameter χ and chain length N. The rescaled simulation results show that the growth exponent dependence on χ and N is trivial, while the growth exponent dependence on the fluid viscosity is dominant.

Key words: Lattice boltzmann method, Phase separation, Coarsening