A phenomenological approach to the deposition pattern of evaporating droplets with contact line pinning

When an evaporating droplet of colloidal suspension dries on a solid surface with the contact line pinned, the solute particles are driven by the solvent flow toward the edge and form a ring-like deposition pattern. In this work, we take into account the contact angle hysteresis and incorporate it into the effective model of Man and Doi (2016 Phys. Rev. Lett. 116 066101) which is based on Onsager's variational principle. We show that single-ring pattern is formed when the contact line pinning and/or friction are sufficiently strong. We demonstrate that there exists an appropriate range for contact line pinning and friction in which two rings can be formed in the deposition pattern, one at the initially pinned contact line and the other a bit closer to the center of droplet.