An exact solution of coarse-grained polymer models with fluctuating internal friction and hydrodynamic interactions has not been proposed so far due to a one-to-all coupling between the connector vector velocities that precludes the formulation of the governing stochastic differential equations. A methodology for the removal of this coupling is presented, and the governing stochastic differential equations, obtained by attaching a kinetic interpretation to the Fokker–Planck equation for the system, are integrated numerically using Brownian dynamics simulations. The proposed computational route eliminates the calculation of the divergence of the diffusion tensor, which appears in models with internal friction, and is about an order of magnitude faster than the recursion-based algorithm for the decoupling of connector-vector velocities previously developed [Kailasham et al., J. Rheol. 65, 903 (2021)] for the solution of freely draining models with internal friction. The effects of the interplay of various combinations of finite extensibility, internal friction, and hydrodynamic interactions on the steady-shear-viscosity are examined. While finite extensibility leads solely to shear-thinning, both internal friction and hydrodynamic interactions result in shear-thinning followed by shear-thickening. The shear-thickening induced by internal friction effects is more pronounced than that due to hydrodynamic interactions.
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