  Phoresis, the drift of particles induced by scalar gradients in a flow, can
result in an effective compressibility, bringing together or repelling
particles from each other. Here, we ask whether this effect can affect the
transport of particles in a turbulent flow. To this end, we study how the
dispersion of a cloud of phoretic particles is modified when injected in the
flow, together with a blob of scalar, whose effect is to transiently bring
particles together, or push them away from the center of the blob. The
resulting phoretic effect can be quantified by a single dimensionless number.
Phenomenological considerations lead to simple predictions for the mean
separation between particles, which are consistent with results of direct
numerical simulations. Using the numerical results presented here, as well as
those from previous studies, we discuss quantitatively the experimental
consequences of this work and the possible impact of such phoretic mechanisms
in natural systems.
