Dip-coating of bidisperse suspensions

Dip coating is an efficient method to entrain a thin layer of fluid when withdrawing a solid object from a liquid bath. Whereas the situation is well-understood for homogenous fluids, heterogeneities, such as particles dispersed in the liquid, lead to more complex situations. Indeed, in addition to the thickness of the coating film, the presence of monodisperse spherical particles introduces a new length scale: the particle diameter. Recent studies have shown that the thickness of the coating film for a monodisperse suspension of particles can be captured by an effective capillary number based on the viscosity of the suspension, providing that the film is thicker than the particle diameter. However, many practical applications involve polydisperse suspensions, characterized by a wide range of particle sizes, introducing additional length scales and complexities. In this study, we experimentally describe how the approach developed for monodisperse suspensions can be modified to account for bidisperse suspensions. The effective viscosity of bidisperse suspensions is smaller than that of monodisperse suspensions for the same particle volume fraction, but we show that the effective viscosity approach is still valid, providing that the thickness of the coating film is larger than the diameter of the largest particles. We also observe and rationalize an intermediate coating regime for a certain range of withdrawal velocities where large particles are filtered out of the liquid film owing to a capillary filtration mechanism.