Transport and deposition patterns in drying sessile droplets

Abstract

The literature on drying sessile droplets and deposition of suspended material is reviewed including the simple explanation of the "coffee ring" deposit given by Deegan et al.1 Analytical and numerical solutions for the flow are given, including the effect of Marangoni stresses, pinning or movement of the contact line, and viscous, thermal, gravitational, and other effects. The solution space is explored using dimensionless groups governing mass, momentum, and heat transfer effects in the droplet, external gas, and substrate. The most common types of deposition patterns are summarized, including those produced by pinned contact lines, sticking-and-slipping contact lines, and Marangoni effects. The influence of contact-line deposits is also reviewed, and the effects of colloidal, polymeric, and other depositing materials. Advanced applications from ink-jet printing to disease diagnosis are discussed as well. The review helps readers take stock of what has been learned and what remains incompletely explained.

Evaporation of water: evaporation rate and collective effects

“…2 (b) for the superhydrophobic substrate, we observed the radius to decrease continuously, with no indications of contact line pinning. Since the speed of retraction is slow, as measured for example by the capillary number (Larson 2014), the dynamic contact angle is close to its constant equilibrium value, and the mode of evaporation is one of constant contact angle (Stauber et al 2015). As is well known (Cazabat & Guéna 2010;Stauber et al 2015), combining the evaporation rate (2.5) with the formula for the volume of a small (i.e.…”

“…The slow evaporation of small drops is limited by diffusion (Larson 2014). The total rate of evaporation per unit mass J equals the area of the drop, multiplied by the local flux density.…”

“…These varied problems involve both evaporation from a single drop and from collections of drops. The physical processes which control the evaporation of a drop on a solid substrate have been the subject of a number of recent reviews (Cazabat & Guéna 2010;Erbil 2012;Larson 2014). Here we focus on two important aspects of this problem, which so far have received little attention: the influence drops inside a collection of drops have on one another, and the evaporation from very large drops.…”

On the lifetimes of evaporating droplets with related initial and receding contact angles

“…As a result, the evaporation of a fluid droplet on a solid substrate has been the subject of extensive theoretical and experimental investigations by a wide range of research groups from many different countries in recent years (see, for example, the recent review articles by Cazabat and Guéna, 1 Erbil, 2 Larson, 3 and Lohse and Zhang 4 ). One aspect of droplet evaporation that has, until recently, received relatively little attention is that of the lifetime of a droplet (i.e., the time it takes for a droplet to evaporate entirely) and, in particular, how it depends on the manner in which it evaporates.…”

Heat and mass transfer boundary conditions at the surface of a heated sessile droplet

“…To clarify such issues it is important that sessile droplet evaporation, including the internal flow, is further investigated. Evaporating sessile droplets (from now on called droplets) have been studied frequently experimentally and numerically [1,2]. Evaporation induced flow, natural convection and Marangoni convection are main mechanisms that have been coupled to the flow inside evaporating droplets [3,4].…”