In this letter, we describe the capillary sorting of particles by size based
on dip coating. A substrate withdrawn from a liquid bath entrains a coating
whose thickness depends on the withdrawal speed and the liquid properties. If
the coating material contains particles, they will only be entrained when the
viscous force pulling them with the substrate overcomes the opposing capillary
force at the deformable meniscus. This force threshold occurs at different
liquid thicknesses for particles of different sizes. Here, we show that this
difference can be used to separate small particles from a mixed suspension
through capillary filtration. In a bidisperse suspension, we observe three
distinct filtration regimes. At low capillary numbers, Ca, no particles are
entrained in the liquid coating. At high Ca, all particle sizes are entrained.
For a range of capillary numbers between these two extremes, only the smallest
particles are entrained while the larger ones remain in the reservoir. We
explain how this technique can be applied to polydisperse suspension. We also
provide an estimate of the range of capillary number to separate particles of
given sizes. The combination of this technique with the scalability and
robustness of dip coating makes it a promising candidate for high-throughput
separation or purification of industrial and biomedical suspensions.
