Non-Newtonian dynamics modelled with non-linear transport coefficients at the mesoscale by using dissipative particle dynamics

We derive the algorithms for the dynamics of the standard dissipative particle dynamics model (DPD) for a velocity-dependent friction coefficient. By introducing simple estimators of the local rate of strain we propose an interparticle friction coefficient that decreases for high deformation rates, eventually leading to the macroscopic shear-thinning behaviour. We have derived the appropriate fluctuation-dissipation theorems that include the correction of the spurious behaviour due to the coupling of the non-linear friction and the fluctuations. The consistency of the model has been numerically investigated, including the Maxwell-Boltzmann distribution for the particle velocities as well as the comparison with the standard linear model for various stresses. The shear-thinning behaviour is clearly reported. Finally, along with the important methodological aspects related to the derivation of the algorithms for non-linear interparticle friction, we introduce a novel two-step algorithm that permits us the integration of the dynamic equations of the DPD model without the explicit derivation of the corrective terms due to the spurious behaviour.