Lattice Fokker Planck for dilute polymer dynamics

Area of Science:

• Computational polymer physics
• Rheology
• Fluid dynamics

Background:

• Polymer dynamics are often described by Fokker-Planck equations for momentum relaxation.
• Simulating inertial polymer dynamics, especially at high Weissenberg numbers, presents computational challenges.
• Existing methods may struggle to accurately capture both momentum and configurational dynamics.

Purpose of the Study:

• To investigate the replacement of Fokker-Planck dynamics with BGK-type relaxation for polymer momentum.
• To develop a lattice-Boltzmann (LB) based direct discretization approach for phase-space description of inertial polymer dynamics.
• To benchmark the proposed LB formulation by calculating rheological properties.

Main Methods:

• Formulation of a BGK-type relaxation dynamics to model polymer momentum.
• Development of a direct discretization approach using the lattice-Boltzmann method for phase-space description.
• Benchmarking through simulations of steady and time-dependent shear and extensional flows.

Main Results:

• The BGK-type relaxation dynamics effectively replaces Fokker-Planck dynamics without altering slow configurational dynamics.
• The lattice-Boltzmann based approach provides accurate predictions of bulk rheological properties.
• Comparison of different discrete velocity models within the LB framework for diffusive dynamics is presented.

Conclusions:

• BGK-type relaxation offers a viable alternative to Fokker-Planck equations for polymer momentum dynamics in LB simulations.
• The developed LB method is suitable for simulating inertial polymer dynamics across various flow conditions.
• The study provides insights into selecting appropriate discrete velocity models for diffusive dynamics in LB.