A SPH-based particle model for computational microrheology

In this article we present a particle method based on smoothed particle hydrodynamics for microrheology simulations of polymeric fluids. The viscoelasticity of the solvent is modelled via a standard Oldroyd-B model and thermal fluctuations, inherently present at the microscopic scale, are incorporated into the particle framework by application of the GENERIC formalism, ensuring the strict fulfilment of the Fluctuation-Dissipation theorem at the discrete level. Rigid structures of arbitrary shape suspended in the viscoelastic solvent are modelled by freezing SPH particles within a given solid domain and letting them interact with the solvent particles. The rheological properties of the Oldroyd-B fluid, namely frequency-dependent storage and loss moduli, are extracted via macroscopic deterministic simulations under small amplitude oscillatory (SAOS) flow and, alternatively, through standard microrheological simulations of a probe particle suspended in the same Brownian viscoelastic medium, by assuming the validity of a generalized Stokes-Einstein relation (GSER). We check that good agreement with the analytical theory for the Oldroyd-B model is found in the deterministic SAOS flow over the entire regime of frequencies investigated. Concerning the microrheological measurements, good agreement is observed only up to a maximal frequencies corresponding to time scales considerably larger than the viscous time of the probe particle where the diffusive regime is fully established. At larger investigated frequencies, a crossover between diffusive and ballistic behaviour for the MSD of the probe is observed and validity of the GSER is questionable. The model presented here provides an optimal computational framework to complement experimental observations and to analyse quantitatively the basic assumptions involved in the theory of microrheology.