Ring formation on an inclined surface

Abstract

A drop dried on a solid surface will typically leave a narrow band of solute deposited along the contact line. Here we examine variations of this deposit due to the inclination of the substrate using numerical simulations of a two-dimensional drop, equivalent to a strip-like drop. An asymptotic analysis of the contact line region predicts that the upslope deposit will grow faster at early times, but the growth of this deposit ends sooner because the upper contact line depins first. From our simulations we find that the deposit can be larger at either the upper or lower contact line depending on the initial drop volume and substrate inclination. For larger drops and steeper inclinations, the early lead in deposited mass at the upper contact line is wiped out by the earlier depinning of the upper contact line and subsequent continued growth at the lower contact line. Conversely, for smaller drops and shallower inclinations, the early lead of the upper contact line is insurmountable despite its earlier termination in growth. Our results show that it is difficult to reconstruct a posteriori the inclination of the substrate based solely on the shape of the deposit.

Evaporation of inclined water droplets

“…The evaporation rate of the inclined droplet shall be proportional to the contact radius as − dv / dt ∝ 2 πR 1 4 6 10 . This proportion is associated with the diffusion-limited evaporation by which the highest evaporative flux exists at the contact line 3 . The pinning-depinning transition is an important phenomenon that takes place at the contact line and that influences the contact radius, which is crucial to determine the evaporation lifetime 24 .…”

“…A droplet is an important element for inkjet printing, painting, and coating technologies that utilize a small volume of colloidal drops 1 2 3 4 5 6 7 8 . Evaporation of a droplet is an essential physical process in controlling final deposit patterns of colloids from suspensions, where colloids are uniformly dispersed into a liquid 2 9 .…”

“…Droplet deformation is determined by competition between surface tension and gravitational force: asphericity increases with drop size. Evaporation of a deformed droplet can be different for that of a spherical droplet, but not clearly understood yet because of geometry complexity of a deformed droplet 3 . A droplet that is slightly larger than l c and placed on an inclined surface can be asymmetric in shape and its static contact angle divides into front and rear contact angles by inclination.…”

“…For an inclined droplet, there must exist a larger ( θ f = front) contact angle and a smaller ( θ r = rear) contact angle, which are than its equilibrium contact angle ( θ eq ) that is radially identical for no inclination 16 17 18 . Droplet evaporation on inclined surfaces has been not well explored, except for a recent experimental study 3 , demonstrating that the coffee-ring patterns for an inclined surface can be produced differently from that for no inclination: the ring patterns that are deposited on an inclined surface are not uniform radially.…”

Evaporation of a sessile droplet on a slope

“…This simplification, however useful, is limiting, for in many practical situations, the droplets may rest on an incline. Among the small number of investigations that considered asymmetric sessile droplets, Espín and Kumar [27] and Du and Deegan [28] numerically examined the drying of (and the resulting flow field inside) two-dimensional colloidal droplets on inclined substrates. Also, Sáenz et al [29] With the drop geometries generated and the same assumptions as our analytical derivation, we numerically calculate the total rate of evaporation using a finite volume method.…”