Fractal aggregates and gels in shear flow

We consider the steady-state rheology of aggregating colloidal suspensions, where cluster size is limited by the imposed shear. Brittle versus work-hardening behavior of the clusters is distinguished. For brittle clusters at large shear rates we predict a scaling law for their size and corresponding viscosity increment, Δη∼γ̇ ${}_{}{}^{\mathrm{-}\left(3\mathrm{}\mathrm{-}\mathit{D}\right)/3\mathrm{}}{}_{}{}^{}$, where D is their fractal dimension. At low shear rates the system will gel due to cluster interpenetration and we discuss a crossover from brittle to work-hardening behavior at large length scales, and the corresponding yield stress. Above this yield stress we find a power-law creep regime with viscosity η∼${\mathrm{\sigma }}^{\mathrm{-}2/3}$. The predictions are compared with experimental results.