Residual stresses and shear-induced overaging in boehmite gels

Abstract

Colloidal gels respond as soft solids at rest, whereas they flow as liquids under external shear. Starting from a fluidized state under an applied shear rate ${\stackrel{\ifmmode \dot{}\else \.{}\fi{}}{\ensuremath{\gamma}}}_{p}$, abrupt flow cessation triggers a liquid-to-solid transition during which the stress relaxes towards a so-called residual stress ${\ensuremath{\sigma}}_{\mathrm{res}}$ that tallies a macroscopic signature of previous shear history. Here, we report on the liquid-to-solid transition in gels of boehmite, an aluminum oxide, that shows a remarkable nonmonotonic stress relaxation towards a residual stress ${\ensuremath{\sigma}}_{\mathrm{res}}({\stackrel{\ifmmode \dot{}\else \.{}\fi{}}{\ensuremath{\gamma}}}_{p})$ characterized by a dual behavior relative to a critical value ${\stackrel{\ifmmode \dot{}\else \.{}\fi{}}{\ensuremath{\gamma}}}_{c}$ of the shear rate ${\stackrel{\ifmmode \dot{}\else \.{}\fi{}}{\ensuremath{\gamma}}}_{p}$. Following shear at ${\stackrel{\ifmmode \dot{}\else \.{}\fi{}}{\ensuremath{\gamma}}}_{p}>{\stackrel{\ifmmode \dot{}\else \.{}\fi{}}{\ensuremath{\gamma}}}_{c}$, the gel obtained upon flow cessation is insensitive to shear history, and the residual stress is negligible. However, for ${\stackrel{\ifmmode \dot{}\else \.{}\fi{}}{\ensuremath{\gamma}}}_{p}<{\stackrel{\ifmmode \dot{}\else \.{}\fi{}}{\ensuremath{\gamma}}}_{c}$, the gel encodes some memory of the shear history, and ${\ensuremath{\sigma}}_{\mathrm{res}}$ increases for decreasing shear rate, directly contributing to reinforcing the gel viscoelastic properties. Moreover, we show that both ${\ensuremath{\sigma}}_{\mathrm{res}}$ and the gel viscoelastic properties increase logarithmically with the strain accumulated during the shear period preceding flow cessation. Such a shear-induced ``overaging'' phenomenon bears great potential for tuning the rheological properties of colloidal gels.