A Lattice Boltzmann model for polymeric liquids. (9th December 2004) - Onishi, Junya; Chen, Yu; Ohashi, Hirotada
A Lattice Boltzmann model for polymeric liquids is developed. In the proposed model, polymers are modelled as dumbbells suspended in a solvent. A distribution function is introduced to describe the configuration of the dumbbells, and is used to evaluate the viscoelastic stresses in flow fields. A discrete kinetic equation for the configurational distribution is derived, and is shown to recover the Oldroyd-B constitutive equation at the continuous level, when coupled with the standard Lattice Boltzmann equation for the flow of the solvent. Numerical simulations of both steady and unsteady flows are performed in order to investigate the validity of the current model. In the simulation of small-amplitude oscillatory shear flows, numerical results are quantitatively compared with the analytical solutions obtained with the Oldroyd-B equation, and good agreements are observed.