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Description
Viscoelastic behavior in biological fluid arises from the stretching of polymeric structures. Capturing finite extensibility is essential for predicting phenomena like strain hardening and elastic instabilities. This work develops a multiscale framework linking the statistical mechanics of freely jointed chains, expressed through the inverse Langevin function (ILF), to stochastic microscale simulations and continuum constitutive models.
Using the Brownian Configuration Field approach [1], we compare stochastic dumbbell dynamics across three ILF approximations: the classical FENE model and the more accurate Pade-based approximations of Cohen and Rickaby–Scott (RS). While models coincide in weak and fully stretched limits, significant differences emerge in the moderate extension regime critical to biofluids. FENE consistently underestimates chain stretch and stress. Linear stability analysis shows that the ILF choice influences eigenvalue growth, impacting numerical stiffness.
To enable large-scale simulations, we derive corresponding macroscopic closures—FENE-P, FENE-CR, and new Cohen/RS-based variants—which preserve Pade-based accuracy while maintaining computational efficiency. Validation against stochastic data demonstrates enhanced prediction of strain hardening, oscillatory responses, and thinning dynamics.
[1] M. A. Hulsen, A. P. G. Van Heel, and B. H. A. A. Van Den Brule. Simulation of viscoelastic flow using Brownian configuration fields. Journal of Non-Newtonian Fluid Mechanics, 70(1):79–101, 1997.
