Scaling of transient hydrodynamic interactions in concentrated suspensions

Abstract

The mean-square displacement 〈Δ${\mathit{r}}^2$(τ)〉 of particles in concentrated suspensions is measured at times sufficiently short to observe the transient nature of hydrodynamic interactions. For all volume fractions φ, the velocity autocorrelation function decays as a power law R(τ)∼${\mathrm{\tau }}^{\mathrm{-}3/2}$. A remarkable scaling with φ is observed for the time-dependent self-diffusion coefficient ${\mathit{D}}_{\mathit{s}}$(τ)=〈Δ${\mathit{r}}^2$(τ)〉/6τ: If ${\mathit{D}}_{\mathit{s}}$(τ) is scaled by its asymptotic value and if time is scaled by a viscous time inversely proportional to the shear viscosity of the suspension, all the data fall onto a single master curve.