A particle transport study of vertical evaporation-driven colloidal deposition by the coffee-ring theory

In this paper, we present a theoretical discussion about colloidal particles transporting to a meniscus deposition region for the vertical evaporation-driven colloidal deposition by the coffee-ring theory. The vertically immersed substrate is gradually exposed with a low speed, and colloidal particles are deposited on the substrate as suspension surface descends. Due to a singular evaporation rate at the contact line, to keep a constant contact angle, a solvent flow toward the meniscus region is formed to replenish lost liquid. This solvent flow results in a particle flow to form a film on the substrate.