It is well known since the seminal work by Asakura and Oosawa (AO)  that large colloidal
particles supended in a dilute polymer solution suffer an effective short-ranged
attractive interaction arising from the depletion of solutes between the colloidal particles,
provided they are sufficiently close to each other. In the analytically soluble AO model,
the colloidal particles are modeled as hard objects of arbitrary shape and the depletion
agent as an ideal gas, whose interaction with the colloids is of the excluded volume type.
A peculiar prediction of the AO model is that the strength of attraction increases with the
size of the colloidal particles, at fixed solute volume fraction, implying that macroscopic
objects should feel extremely large attractive forces at short distances. Surface roughness
contrasts this paradoxical consequences by inhibiting the depletion mechanism.
During the last decade, the interest in this topic has been revived since the surface morphology
of the colloid can be used to tune the effective interaction. Rough colloids with
different shapes have been produced experimentally in order to investigate the change in
the interaction: From particles decorated with spheres or litographycally shaped to lock
and key colloids.
Theoretical studies of the effects of roughness on depletion have been recently performed
by Monte Carlo simulations  coupled with liquid state theories , in the case of colloidal
particles decorated with smaller spheres immersed in a ideal gas. However, analytical
expressions able to capture the main effects of surface roughness on the shape of
the depletion interaction are still missing.
We developed a simple model, in the framework of the AO theory, able to describe the
effects of surface rughness for a significant range of parameters. The resulting explicit
expressions are easily computed for a large interval of all the relevant parameters of the
problem. Comparison with the available numerical simulations  shows an encouraging
aggreement and allows to predict the onset of colloidal aggregation in dilute suspensions
of rough particles.
 S. Asakura and F. Oosawa, J. Polym. Sci. 33, 183 (1958)
 M. Kamp, M. Hermes, C. M. Van Kats, D. J. Kraft, W. K. Kegel, M. Dijkstra and A. Van
Blaaderen, Langmuir 32, 1233 (2016)
 D. Banerjee, J. Yang and K. S. Schweizer, Soft Matter 11, 9086 (2015)