Rouse model with fluctuating internal friction

Abstract

A coarse-grained bead-spring-dashpot chain model with the dashpots representing the presence of internal friction is solved exactly numerically for the case of chains with more than two beads. Using a decoupling procedure to remove the explicit coupling of a bead’s velocity with that of its nearest neighbors, the governing set of stochastic differential equations are solved with Brownian dynamics simulations to obtain material functions in oscillatory and steady simple shear flow. Simulation results for the real and imaginary components of the complex viscosity have been compared with the results of previously derived semi-analytical approximations, and the difference in the predictions is seen to diminish with an increase in the number of beads in the chain. The inclusion of internal friction results in a nonmonotonous variation of the viscosity with shear rate, with the occurrence of continuous shear-thickening following an initial shear-thinning regime. The onset of shear-thickening in the first normal stress coefficient is pushed to lower shear rates with an increase in the internal friction parameter.

Shear viscosity for finitely extensible chains with fluctuating internal friction and hydrodynamic interactions

“…In this paper, we prescribe an exact solution methodology for this model, and present preliminary rheological results. The present algorithm may also be applied to the free-draining IV model and is found to be an order of magnitude faster than the decoupling-methodology-based implementation developed recently 36 .…”

“…Preliminary investigations of the steady-shear rheology of bead-spring-dashpot models relied on a Gaussian approximation of IV [58][59][60] , predicting a shear-thinning of viscosity following a constant Newtonian plateau. Subsequent (exact) BD simulations 32,[34][35][36] established that internal friction causes shear-thinning at low-to-moderate shear rates, followed by a thickening of the viscosity at higher shear rates. Finite extensibility is known to exclusively induce shear-thinning 13 , while the inclusion of hydrodynamic interactions in coarse-grained models with greater than six beads has been shown to result in shearthinning followed by thickening 42,43,61 .…”

“…Manke and Williams 24 derived a semi-analytical approximation for the stress jump of free-draining beadspring-dashpots, using a recursive-algorithm for the decoupling of bead velocities, leveraging the fact that in the absence of HI only the velocities of nearest neighbors in the chain are coupled, and restricted their analysis to the linear viscoelastic regime. In a prior work 36 , we used the decoupling methodology developed by Manke and Williams 24 to derive and solve the exact set of stochastic differential equations governing the motion of freedraining bead-spring-dashpot chains that is valid both at equilibrium and in the presence of flow. By comparison against BD simulation results, it was established that the Manke and Williams 24 prediction for the stress jump improves with the number of beads in the chain.…”

“…The framework developed by Manke and Williams 24,37,38 is applicable, however, only for linear viscoelastic predictions, and numerical simulations are required, as explained in ref. 36, for the calculation of viscometric functions in the presence of a flow field.…”

“…SIV establishes the equivalence between the present methodology and the decoupling algorithm developed in ref. 36 for free-draining bead-spring-dashpot chains, and also compares the computational cost for the two approaches. Sec.…”