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Dip-coating of bidisperse particulate suspensions

Dip-coating consists in withdrawing a substrate from a bath to coat it with a thin liquid layer. This process is well-understood for homogeneous fluids, but heterogeneities such as particles dispersed in the liquid lead to more complex situations. Indeed, particles introduce a new length scale, their size, in addition to the thickness of the coating film. Recent studies have shown that at first order, the thickness of the coating film for monodisperse 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, suspensions involved in most practical applications are polydisperse, characterized by a wide range of particle sizes, introducing additional length scales. In this study, we investigate the dip coating of suspensions having a bimodal size distribution of particles. We show that the effective viscosity approach is still valid in the regime where the coating film is thicker than the diameter of the largest particles, although bidisperse suspensions are less viscous than monodisperse suspensions of the same solid fraction. We also characterize the intermediate regime that consists of a heterogeneous coating layer and where the composition of the film is different from the composition of the bath. A model to predict the probability of entraining the particles in the liquid film depending on their sizes is proposed and captures our measurements. In this regime, corresponding to a specific range of withdrawal velocities, capillarity filters the large particles out of the film.