Rheology of wormlike micelles from non-equilibrium molecular dynamics

In this work, the rheology of complex fluids, i.e., surfactants of varying concentration in a Lennard-Jones fluid, is analyzed with non-equilibrium molecular dynamics simulations. The molecular model considers that the surfactant molecule is composed of a hydrophilic head, affine to solvent, and a hydrophobic tail made of four monomers. The solvent is modeled by a Lennard-Jones fluid, which shows mostly a Newtonian behavior, but at relatively high shear rates, a slight shear-thinning followed by a slight shear thickening are exhibited. The intermolecular potential produces an equilibrium configuration, in which the surfactant molecules self-assemble in a wormlike micelle. With the aim to analyze the system behavior with various stress fields, two flows are simulated under non-equilibrium conditions: (1) simple shear and (2) Poiseuille's flow. In simple shear, by keeping the velocity of the upper plate of the flow cell constant, a monotonic flow curve is predicted within a range of shear rates. At low shear rates, a concentration-dependent Newtonian region of viscosity η0 corresponds to an isotropic condition in which the wormlike micelle preserves its equilibrium conformation. At intermediate shear rates, the solution exhibits a slight shear thinning, generating bands placed normal to the gradient direction (gradient banding). At high shear rates the solution exhibits shear-thickening, with bands now generated normal to the vorticity direction. These predictions by molecular models explain, to our knowledge for the first time, experiments in shear-thickening wormlike micellar solutions, where shear-thickening appears simultaneously with bands generated perpendicular to the vorticity axis. In Poiseuille's flow, we also find agreement between predictions of the model with theoretical developments and experiments performed by other authors.