  We study the joint mixing of colloids and salt released together in a
stagnation point or in a globally chaotic flow. In the presence of salt
inhomogeneities, the mixing time is strongly modified depending on the sign of
the diffusiophoretic coefficient $D_\mathrm{dp}$. Mixing is delayed when
$D_\mathrm{dp}>0$ (salt-attracting configuration), or faster when
$D_\mathrm{dp}<0$ (salt-repelling configuration). In both configurations, as
for molecular diffusion alone, large scales are barely affected in the dilating
direction while the Batchelor scale for the colloids, $\ell_{c,\mathrm{diff}}$,
is strongly modified by diffusiophoresis. We propose here to measure a global
effect of diffusiophoresis in the mixing process through an effective P\'eclet
number built on this modified Batchelor scale. Whilst this small scale is
obtained analytically for the stagnation point, in the case of chaotic
advection, we derive it using the equation of gradients of concentration,
following Raynal \& Gence (\textit{Intl J. Heat Mass Transfer}, vol. 40 (14),
1997, pp. 3267--3273). Comparing to numerical simulations, we show that the
mixing time can be predicted by using the same function as in absence of salt,
but as a function of the effective P\'eclet numbers computed for each
configuration. The approach is shown to be valid when the ratio
$D_\mathrm{dp}^2/D_s D_c \gg 1$, where $D_c$ and $D_s$ are the diffusivities of
the colloids and salt.
