Multiscale modeling of the electroviscoelasticity of charged polymers in combined flow and electric fields

The behavior of polymers in combined flow and electric fields underlies many manufacturing processes but remains poorly understood. We model charged polymers across scales, extending the Rouse model for a bead-spring chain to include a charge density distributed along the polymer chain and derive the viscoelastic stress under homogeneous shear and electric fields. The viscosity increase depends on field-flow orientation, scaling quadratically with select components of the electric field strength, modulated by the effective charge sequence relaxation time and dielectric constant. Inspired by this, a new continuum model—the upper-convected electro-Maxwell (UCEM) model—is proposed. It resembles an upper-convected Maxwell model with polarization stresses expressed through an electric field dyadic subject to upper-convected time derivatives. The UCEM model captures the electrorheological coupling for unentangled, salt-free melts at low shear rates and remains predictive into the moderately nonlinear regime (Wi ≈ 2 − 4) provided its parameters are treated as state-dependent material functions. We analyze the constitutive response for various flows under applied electric fields, discussing model limitations and demonstrating compliance with the second law of thermodynamics. Coarse-grained molecular dynamics (MD) simulations of Kremer–Grest chains confirm distinct relaxation timescales for chain dynamics versus charge redistribution, consistent with UCEM predictions. Critically, the upper-convected time derivative of the electric field dyadic is required in the stress evolution to account for stretching and rotation of charge pairs in flow. This reproduces the viscosity scaling observed in both the Rouse and MD results, whereas standard continuum formulations without these terms fail to capture this scaling.