  We study analytically the joint dispersion of Gaussian patches of salt and
colloids in linear flows, and how salt gradients accelerate or delay colloid
spreading by diffusiophoretic effects. Because these flows have constant
gradients in space, the problem can be solved almost entirely for any set of
parameters, leading to predictions of how the mixing time and the Batchelor
scale are modified by diffusiophoresis. We observe that the evolution of global
concentrations, defined as the inverse of the patches areas, are very similar
to those obtained experimentally in chaotic advection. They are quantitatively
explained by examining the area dilatation factor, in which diffusive and
diffusiophoretic effects are shown to be additive and appear as the divergence
of a diffusive contribution or of a drift velocity. An analysis based on
compressibility is developed in the salt-attracting case, for which colloids
are first compressed before dispersion, to predict the maximal colloid
concentration as a function of the parameters. This maximum is found not to
depend on the flow stretching rate nor on its topology (strain or shear flow),
but only on the characteristics of salt and colloids (diffusion coefficients
and diffusiophoretic constant) and the initial size of the patches.
