  Colloidal gels are formed by the aggregation of Brownian particles into
clusters that are, in turn, part of a space-spanning percolated network. In
practice, the microstructure of colloidal gels, which dictates their mechanical
properties, strongly depends on the particle concentration and on the nature of
their interactions. Yet another critical control parameter is the shear history
experienced by the sample, which controls the size and density of the cluster
population, via particle aggregation, cluster breakup, and restructuring. Here
we investigate the impact of shear history on acid-induced gels of boehmite, an
aluminum oxide. We show that following a primary gelation, these gels display a
dual response depending on the shear rate $\dot\gamma_{\rm p}$ used to
rejuvenate their microstructure. We identify a critical shear rate
$\dot\gamma_{\rm c}$, above which boehmite gels display a gel-like viscoelastic
spectrum upon flow cessation, similar to that obtained following the primary
gelation. However, upon flow cessation after shear rejuvenation below
$\dot\gamma_{\rm c}$, boehmite gels display a glassy-like viscoelastic spectrum
together with enhanced elastic properties. Moreover, the nonlinear rheological
properties of boehmite gels also differ on both sides of $\dot\gamma_{\rm c}$:
weak gels obtained after rejuvenation at $\dot\gamma_{\rm p}>\dot\gamma_{\rm
c}$ show a yield strain that is constant, independent of $\dot\gamma_{\rm p}$,
whereas strong gels obtained with $\dot\gamma_{\rm p}<\dot\gamma_{\rm c}$
display a yield strain that significantly increases with $\dot\gamma_{\rm p}$.
Our results can be interpreted in light of previous literature on shear-induced
cluster densification, while we rationalize the critical shear rate in terms of
a dimensionless quantity, the Mason number, comparing the strength of the shear
flow to the interparticle bond force.
