Dip coating of shear-thinning particulate suspensions†

Dip coating a planar substrate with a suspension of particles in a shear-thinning liquid will entrain particles in the liquid film, facilitating filtration and sorting of particles. Experiments were performed for both monodisperse and bidisperse particle suspensions of shear-thinning Xanthan Gum solutions. Particle entrainment occurs when the coating thickness at the stagnation point of the thin film flow is larger than the particle diameter. A model is developed to predict the entrainment criteria using lubrication theory applied to an Ostwald power-law fluid which yields a modified Landau–Levich–Derjaguin (LLD) law governing the coating film thickness that depends upon a properly defined capillary number Ca. The critical withdrawal velocity for particle entrainment depends upon the particle size and fluid rheology through a relationship between Ca and the bond number Bo, which agrees well with our model predictions and prior experimental results of A. Sauret et al. Phys. Rev. Fluids, 2019, 4, 054303 for the limiting case of Newtonian suspensions. Single particle entrainment and particle clustering is observed for monodisperse suspensions, which depends on Ca and the particle volume fraction ϕ. In bidisperse suspensions, particle sorting can occur whereby only the smaller particles are entrained in the film over an active filtration range of Ca and Bo, which also agrees well with our model predictions.