Spontaneous pattern formation by dip coating of colloidal suspensions on homogeneous surfaces

We study the slow withdrawal of a partially wet vertical plate at velocity U from a suspension of well-wet particles. Periodic horizontal striped assemblies form spontaneously at the three-phase contact line on energetically uniform surfaces. Stripe width and spacing depend on the withdrawal velocity U relative to a transition velocity U-t. Thick stripes separated by large spaces form for U < U-t. For U > U-t, thin stripes separated by small spaces form. The stripe spacing is reduced by an order of magnitude and varies weakly with U until a maximum velocity is reached at which the stripes fail to form. A partially wet surface can entrain a meniscus. For U < U-t, the meniscus forms a finite contact angle wedge with a pinned contact line. As the plate moves upward, it stretches the meniscus until it becomes too heavy to be retained by the wet, porous network provided by the particles at the contact line. The contact line then jumps backward to find a new equilibrium location, and the process begins anew. For U > U-t, we infer that a film of thickness h is entrained above the meniscus. When h is smaller than the particle diameter D, particles aggregate where the entrained film thickens to match up to the wetting meniscus. When an entrained particle becomes exposed to air by evaporation, it becomes the new pinning site from which the next film is entrained. The film thickness h increases with U; at some velocity, h becomes comparable to D. Particles flow into the film and deposit there in a disordered manner. A diagram summarizing particle deposition is developed as a function of D, U, and h.