Dip coating of bidisperse particulate suspensions

Abstract

Dip coating consists of 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 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.

Particulate suspension coating of capillary tubes

“…( 3) allows predicting the evolution of h/R for a homogeneous liquid. 12 In addition, the dip coating experiments have established that using Ca φ leads to a quantitative prediction of h. 26,27,34 Since our measurements of h are very accurate with the present method, we can estimate the local viscosity η eff (φ) that would lead to a coating film of measured thickness h when the rear of the plug is traveling at the velocity ur. 34 More specifically, for each experimental data point of h, we use Eqs.…”

“…with η f the viscosity of the interstitial fluid, φ the volume fraction of the suspension, and φm = 0.59 the maximal packing fraction for the particles and fluid used. 22,34 In the thick film regime, the thickness of the suspension film coating the inner wall of the capillary tube should be given by: 26,27 h R = 1.34 Ca…”

“…q z e I a S q Z s l Q Q Y 7 q + l 9 g g I 9 p y K t i 0 1 E s N S w g d k y H r O q q I Z C b I 5 g d P 8 Z l T B j i K t S t l 8 V z 9 P Z E R a c x E h q 5 T E j s y y 9 5 M / M / r p j a q B R l X S W q Z o o t F U S q w j f H s e z z g m l E r J o 4 Q q r m 7 regimes depending on the particle diameter d and the coating thickness. 26,27,34 At small capillary number Ca, corresponding to very thin films (h d), no particles are entrained, and only a liquid film coats the plate. At intermediate capillary numbers leading to h d, a heterogeneous coating made of clusters of particles arranged as a monolayer is observed on the substrate.…”

“…A similar behavior has also been reported for the dip coating of cylindrical substrates when accounting for the change in the LLD law due to the curvature of the substrate. 35 The role of the particle diameter, compared to the film thickness, has allowed the development of new capillary filtration 36 and sorting methods 34,37 leveraging the dip coating platform.…”

The onset of heterogeneity in the pinch-off of suspension drops

“…Since the interactions occur because of external stress, these length scales themselves depend on this applied stress. Future studies will apply these concepts to other systems involving suspensions, such as the formation of thin films ( 23 , 24 , 25 ) and the fragmentation of suspension ligaments and sheets ( 26 ). In addition, beyond polydisperse suspensions, the dislocation of other kinds of complex suspensions (for example, made of nonspherical particles, such as fibers, or even active particles) should be considered.…”