Coating flow of a liquid film with colloidal particles on a vertical fiber

A thin liquid film of colloidal suspension is considered which is spreading down on a vertical cylinder under the effect of gravity. A precursor film model is employed at the three-phase contact line to relieve the stress singularity. The curvature pressure leads to the formation of a capillary ridge at the contact-line. Bulk and surface colloids are assumed to be present in the liquid film. The interfacial pattern is governed by the film evolution equation, obtained by simplifying mass and momentum balance equations within the lubrication assumption, while rapid vertical diffusion is assumed for the advection–diffusion equation of the bulk concentration. Fluid viscosity and diffusivity are considered to be functions of the particle volume fraction. The effects of the bulk and surface colloids on the spreading film dynamics are systematically studied. The presence of bulk colloids leads to the thinning of the capillary ridge for smaller inlet bulk colloid concentrations. On the other hand, a larger inlet bulk concentration leads to the formation of a secondary advancing front behind the capillary ridge in the film profile. A reduced contact point velocity is observed with an increase in the upstream bulk concentration. Surface concentration is found to result in a hump-like structure behind the capillary ridge in the upstream direction due to solutal Marangoni stress. The Marangoni stress also hinders the surface-tension-driven spreading, resulting in a smaller contact line velocity. Reducing the Bond number results in unstable film profiles, which lead to a wave-like structure in the region with no bulk concentration gradients.