Microrheology with rotational Brownian motion

Passive rotational microrheology (RMR) for evaluating the dynamic modulus $G^*$ of a suspending fluid through the rotational Brownian motion of a spherical probe particle is validated using direct numerical simulations (DNS) of Brownian motion in a viscoelastic fluid. Two methods of RMR are compared: an inertialess RMR based on the Generalized Stokes--Einstein relation for rotational diffusion (RGSER) and the full RMR based on the generalized Langevin equation for rotation, which accounts for fluid and particle inertia. Our analysis, performed using DNS of the fluctuating Oldroyd-B fluid, reveals that inertialess RMR accurately estimates $G^*$ for $\omega\lambda \alt 1$, but deviates significantly at high frequencies. In contrast, the full RMR improves $G^*$ estimation accuracy up to the frequency $\omega \approx \tau_{s}^{-1}=\eta_{s}/\rho_{f}a^{2}$, where fluid inertia becomes relevant. However, in the ballistic regime ($t \ll \tau_{s}$), particle inertia dominates, making accurate $G^*$ evaluation challenging even with the full RMR. This study clarifies the applicability range of RMR. Additionally, rotational Brownian motion is turned out to be insensitive to periodic boundary conditions, which allows direct application to various mesoscale molecular simulations, including coarse-grained molecular dynamics, dissipative particle dynamics, and fluid dynamics simulations. In conclusion, rotational microrheology offers a promising approach for detailed rheological analysis in complex systems and conditions.