Evaporation of a Sessile Colloidal Water–Glycerol Droplet: Marangoni Ring Formation

Abstract

The transport and aggregation of particles in suspensions is an important process in many physicochemical and industrial processes. In this work, we study the transport of particles in an evaporating binary droplet. Surprisingly, the accumulation of particles occurs not only at the contact line (due to the coffee-stain effect) or at the solid substrate (due to sedimentation) but also at a particular radial position near the liquid–air interface, forming a “ring”, which we term as the Marangoni ring . The formation of this ring is primarily attributed to the solutal Marangoni flow triggered by the evaporation dynamics of the water–glycerol droplet. Experiments and simulations show fair agreement in the volume evolution and the general structure of the solutal Marangoni flow, that is, the Marangoni vortex . Experiments show that the location of the Marangoni ring is strongly correlated with the Marangoni vortex. However, finite element numerical simulations fail to describe the particle distribution seen in the experiments. Interestingly, the particles not only accumulate to form the Marangoni ring but also assemble as colloidal crystals close to the liquid–air interface, yielding iridescence. The formation of the colloidal crystals in the experiments is strong evidence that non-hydrodynamic interactions, which are not represented in the simulations, also play a significant role in our system.

Evaporation-driven liquid flow in sessile droplets

“…103,105 When particles adsorb at the interface and the interfacial flow is directed towards the droplet apex, particles would instead accumulate around the apex, either forming a “Marangoni ring” or a cap, depending on the strength of the flow. This is typically observed with thermal Marangoni flows, 1,76,119,120 but the final fate of the particles agglomerated at the droplet apex depends on the particle affinity to the liquid interface, the interfacial/bulk flow and the receding interface. Nevertheless, when particle concentration is high enough and/or particles have a strong affinity for the interface, 121,122 particles form a dense network that immobilises the interface and leading to an homogeneous deposition of particles.…”

Geometrically-controlled evaporation-driven deposition of conductive carbon nanotube patterns on inclined surfaces

“…36 It was shown that insoluble surfactants do not produce Marangoni vortices, 37 but soluble surfactants can drive considerable recirculation. 38 Considering that Marangoni eddies can lead to unexpected distributions of solute particles 39 and have a tremendous impact on the deposition, 40 this contribution benefits from the results of the previous research done by our group. Inanlu et al 15 determined an optimum surfactant concentration in which CNTs are well dispersed in the aqueous phase and the surfactant-induced Marangoni flow has the lowest impact on the deposition, so the densest ring would be achievable.…”

Mathematical Modeling of the Evaporation of a Water Drop from a Heated Surface

“…These constants must be determined in special experiments. In the second group of models, the evaporation rate is calculated using the boundary condition at the evaporation boundary, which includes a mass transfer coefficient. ,, This coefficient must also be determined experimentally. In addition, in many cases the assumption is that the temperature field of the drop is uniform, but this assumption is valid only for very small drops (tens of micrometers).…”

“…55 Naturally, such problems are very difficult even for modern computer technology. Most likely, for this reason, the researchers working in the field of mathematical modeling of evaporation of liquid drops from heated surfaces simplify the problem and, as a rule, calculate the evaporation processes under the assumption that the temperature field of the drop is uniform (for example, refs 56 and 57) or describe the evaporation processes within the framework of the mass transfer law 39,54,58 (by analogy with the Newton−Richmann hypothesis 58 ) using a posteriori estimates. It should also be noted that the main problem that must be solved in the mathematical modeling of drop evaporation processes is the calculation of the evaporation rate.…”

“…Also noteworthy are a number of very interesting papers − in which the results of the experimental and theoretical studies of the Marangoni effect in liquid drops are presented, but it must be said that the studies are given under conditions where there is no intense heating of the droplet through the substrate. Under these conditions, natural convection is practically absent; as a result, the Marangoni effect manifests itself most strongly: vortex flows appear in a liquid drop with ascending flows at the water–steam interface and descending flows in the center of the drop.…”