Drying of Droplets of Colloidal Suspensions on Rough Substrates

Abstract

In many technological applications, excess solvent must be removed from liquid droplets to deposit solutes onto substrates. Often, the substrates on which the droplets rest may possess some roughness, either intended or unintended. Motivated by these observations, we present a lubrication-theory-based model to study the drying of droplets of colloidal suspensions on a substrate containing a topographical defect. The model consists of a system of one-dimensional partial differential equations accounting for the shape of the droplet and depth-averaged concentration of colloidal particles. A precursor film and disjoining pressure are used to describe the contact-line region, and evaporation is included using the well-known one-sided model. Finite-difference solutions reveal that when colloidal particles are absent, the droplet contact line can pin to a defect for a significant portion of the drying time due to a balance between capillary-pressure gradients and disjoining-pressure gradients. The time-evolution of the droplet radius and contact angle exhibits the constant-radius and constant-contact-angle stages that have been observed in prior experiments. When colloidal particles are present and the defect is absent, the model predicts that particles will be deposited near the center of the droplet in a cone-like pattern. However, when a defect is present, pinning of the contact-line accelerates droplet solidification, leading to particle deposition near the droplet edge in a coffee-ring pattern. These predictions are consistent with prior experimental observations, and illustrate the critical role contact-line pinning plays in controlling the dynamics of drying droplets.

Deposition of Colloidal Particles during the Evaporation of Sessile Drops: Dilute Colloidal Dispersions

“…is ring pattern was also observed by other groups for the deposition of polystyrene latex colloids on glass substrates [6,7]. While some studies focus on the influence of microfluidic flow on the deposition [8,9], the deposition patterns can also vary from a ring to a uniform layer according to the substrate roughness [10], particle morphology [11], the evaporation speed [12] and mode [13], and the composition of the solvent [14]. Sommer compared the deposition pattern in an evaporating sessile drop between polystyrene latex particles and the hydroxyapatite particles [15].…”

“…Once the "solid" elements are determined, the C P values on the nodes inside the solid element will be equal to the critical value, noted as C P,max � 130.86. e common nodes between the solid element and the neighboring fluid elements are fixed and are applied under no-flux boundary condition of particles as in equation (10) in the Method section.…”

Heterogeneous drying and nonmonotonic contact angle dynamics in concentrated film-forming latex drops

“…Equations (17) and (18) describe the evolution of the drying drop for early and intermediate times during the evaporation process. These equations successfully capture the early-time contactangle decay and the intermediate-time nonmonotonic contact-angle response for drying drops of concentrated latex suspensions.…”

“…In recent years, sessile drop-drying experiments [5,15] have been used to study emergent deposition behaviors such as the coffee-ring effect [15] and the role of surface tension and Marangoni flow in determining deposition patterns [16]. Evaporation of droplets laden with colloidal particles has been studied numerically in the limit of rapid evaporation [17] and drying droplets of colloidal suspensions on rough surfaces were recently studied using simulations [18]. However, most prior studies have focused on dispersions in the dilute or ultradilute concentration regime, which are known to exhibit qualitatively different drying dynamics compared to more concentrated suspensions [8,19].…”

Controlled evaporative self‐assembly of polymer nanoribbons using oscillating capillary bridges

“…During ESA, as the solvent evaporates, the contact angle of the pinned meniscus continues to decrease from an initial value, and at a certain critical angle, capillary forces overcome pinning forces causing the meniscus to depin and shift to a new position. 21,23,25,26,35,36 For a controlled/programmed meniscus depinning, a process must control when the meniscus reaches the critical contact angle. With the stop-and-go method, the critical angle is reached as the translating substrate stretches the pinned meniscus.…”