Systematic comparison of inverse Langevin function approximations in stochastic dumbbell dynamics

Area of Science:

• Polymer Physics
• Computational Fluid Dynamics
• Rheology

Background:

• Finite extensibility is crucial for polymer solution dynamics.
• Stochastic dumbbell models often use approximate inverse Langevin functions.
• Accurate representation of chain elasticity is key for predicting material behavior.

Purpose of the Study:

• To systematically evaluate the impact of inverse Langevin function approximations on stochastic dumbbell models.
• To compare the Finitely Extensible Nonlinear Elastic (FENE) model with Padé-based approximations.
• To assess how these approximations influence model predictions and numerical stability in various flow conditions.

Main Methods:

• Utilized the Brownian Configuration Field formulation for direct integration of stochastic equations.
• Compared three spring-force representations: FENE, Cohen's Padé, and Rickaby-Scott's Padé.
• Assessed model predictions in large-amplitude oscillatory shear, steady uniaxial extensional, and capillary thinning flows.

Main Results:

• Approximation differences become apparent at moderate chain extensions.
• FENE model predicts lower stretch and stress than Padé approximations in transitional regimes.
• Discrepancies increase with higher polymer chain extensibility.
• Approximation choice affects stochastic dynamics stiffness and numerical stability.

Conclusions:

• The selection of inverse Langevin approximation measurably impacts predictions in nonlinear viscoelastic flow simulations.
• Numerical robustness is directly influenced by the chosen approximation.
• Careful consideration of these approximations is necessary for accurate and stable simulations.