Monte Carlo simulation of steady extensional flows

Abstract

An efficient nonequilibrium Monte Carlo method using the Bond fluctuation model is used to simulate uniaxial and planar extension of dilute polymer solutions. The time scale is obtained from the stress relaxation of a fully stretched chain and can be related to the longest relaxation time of a real molecule, while the length scale is taken to be the statistical Kuhn segment length. The method leads to τ1∼N2.16 and D∼N−1.02 for a freely draining chain with an excluded volume constraint, where τ1, N, and D are the longest relaxation time, chain length, and diffusion coefficient, respectively. The finite extensibility of the bond causes extension thinning following the coil-stretch transition. The Monte Carlo predictions for the transient extension of isolated DNA molecules in a planar extensional flow agree reasonably well with published experimental measurements and Brownian dynamics simulations. “Molecular individualism” is observed in the unraveling of the polymer chain.

Rheology and Pinching Dynamics of Associative Polysaccharide Solutions

“…Though extensional thinning typically arises in structured fluids that exhibit shearthinning behavior, it is also observed for nondilute polymer solutions in experiments 158−161 and simulations. 65,161,162 In such cases, the extensional thinning can be described using constitutive models like the Wiest model 163 and the Primitive Chain Network model 164,165 that incorporate finite extensibility along with anisotropic hydrodynamic drag. 163−167 In addition to the measurement of extensional rheology response, the analysis of radius evolution data provides additional parameters (see Table 3 and Figure 7), including extensional power law index (n e ) and power law timescale (t PL ) obtained from the power law region, and filament lifespan (t f ) and η E ∞ from the TVEC response.…”

Characterization of hyaluronic acid and synovial fluid in stagnation point elongational flow

“…This suggests a saturation of the stress as macromolecules approach a steady‐state ensemble‐average extension ratio. Extensional thinning has been reported in a number of experimental and computational works although its origins are still a matter of debate . In the Monte‐Carlo simulations of Li and Denn, the extensional stress saturates at high macromolecular strains due to the reduction in conformational states available to highly extended chains.…”

Extensional opto-rheometry with biofluids and ultra-dilute polymer solutions

“…In fact, extensional thinning has been observed in many experiments with dilute and concentrated polymer solutions, 15,16,[94][95][96][97] as well as in simulations. 87,97,98 However, Brownian dynamics simulations for dilute solutions using bead-spring or bead-rod models in a continuum solvent (see discussion by Larson 87 ) as well as most multimode, differential constitutive models 99 show that extensional viscosity increases with extension rate, and then saturates to a steady state value as macromolecules achieve full extension. In fact the constitutive models -Bird-DeAguir, Giesekus and Acierno, Lamantia, Marrucci and Titomanlio (ALMT) -all give a constant steady state value for extensional viscosity, while the Upper Convected Maxwell (UCM) and White-Metzner (WM) models predict an extensional viscosity that grows without bound, as summarized by Quizani et al 97 and Bird et al 99 Experiments on melts and concentrated solutions also show extensional thinning beyond a critical strain or strain rate and constitutive models like the Wiest model 100 that incorporates finite extensibility along with anisotropic hydrodynamic drag can capture extensional thinning.…”

“…Gupta et al used the Wiest model to capture the extensional thinning behaviour and found that the limiting extensional viscosity scaled as h E fDe Àa GNS , where a ¼ 0.5. Interestingly, in non-equilibrium Monte Carlo simulations using a Bond Fluctuation model, Li and Denn 98 showed that both the coil-stretch transition and extensional thinning are manifested beyond De LD > 0.5 (based on a time scale needed for relaxation from a fully extended chain, which is closer to a Rouse relaxation time). In these simulations, the extensional stress saturates at high rates, as the possible microstates for a fully extended chain in lattice are limited, implying that the entropic stress is bounded, and therefore extensional thinning is caused by finite extensibility of the chain.…”