Gravitational Effect in Evaporating Binary Microdroplets

Abstract

The flow in an evaporating glycerol-water binary sub-millimeter droplet with Bond number Bo 1 is studied both experimentally and numerically. First, we measure the flow fields near the substrate by micro-PIV for both sessile and pendant droplets during the evaporation process, which surprisingly show opposite radial flow directions -inward and outward, respectively. This observation clearly reveals that in spite of the small droplet size, gravitational effects play a crucial role in controlling the flow fields in the evaporating droplets. We theoretically analyze that this gravitydriven effect is triggered by the lower volatility of glycerol which leads to a preferential evaporation of water then the local concentration difference of the two components leads to a density gradient that drives the convective flow. We show that the Archimedes number Ar is the nondimensional control parameter for the occurrence of the gravitational effects. We confirm our hypothesis by experimentally comparing two evaporating microdroplet systems, namely a glycerol-water droplet and a 1,2-propanediol-water droplet. We obtain different Ar, larger or smaller than a unit by varying a series of droplet heights, which corresponds to cases with or without gravitational effects, respectively. Finally, we simulate the process numerically, finding good agreement with the experimental results and again confirming our interpretation.The evaporation of a microdroplet on a flat substrate has attracted a lot of attention because of its beautiful and phenomenologically rich fluid dynamics [1][2][3][4][5][6][7][8][9][10][11][12][13][14] and its relevance in various technological applications, such as medical diagnostics [15] and the fabrication of electronic devices [16]. For many of these applications, an understanding of the internal flow structure is crucial. One example is the so-called "coffee stain problem" [2], i.e. an evaporating colloidal drop in which an outward capillary flow along the substrate carries the dispersed material from the interior towards the pinned contact line. This seminal study opened up a new line of research for surface coatings and patterning technologies, which is crucial for various applications in inkjet printing [17], 3D printing technology [18] and molecular biology [19].However, in nearly all of these applications, the droplet liquid is not pure, but a binary or even ternary liquid. As is well known, then Marangoni flow, which is driven by surface tension gradients, is coming into play [6, 20-23], strongly affecting the evaporative behavior. The variation of the surface tension originates from two mechanisms or the combination of both, namely a temperature gradient [20,21] or a solute concentration gradient [13,[22][23][24][25][26], due to the spatially varying local evaporation rates at the droplet surface. The conventional understanding is that the flows within submillimeter droplets can only be attributed to capillary and Marangoni convections, while natural convection is considered to be negligible as the sur...

Buoyancy-driven dispersion in confined drying of liquid binary mixtures

“…This equation displays a dispersion coefficient D eff to account for buoyancy-driven flows, see Eq. (5). Solute mass transport remains dominated by diffusion as long as: with real units, where α = 362880.…”

Physicochemical hydrodynamics of droplets out of equilibrium

“…The reason lies in a combination of the (in general) different volatility of the components and the singularity of the evaporation (or dissolution) rate at the rim of the droplet [8,110,112,121] (provided the contact angle is smaller than 90 o ), leading to a concentration gradient at the interface of the droplet. The resulting surface tension gradient drives a Marangoni flow inside the droplet [17,38,40,[122][123][124][125][126][127][128][129][130][131][132], see figure 4a. This effect is very similar to what leads to the so-called tears of wine [133] inside a partially filled wine-glass: In this case, selective evaporation of ethanol at the edge of the meniscus leads to larger surface tension, which thus pulls part of the remaining wine upwards along the alcohol-wetting glass, finally leading to an instability of the film and droplets sinking down the glass wall.…”

“…To that end, with Eulerian-Lagrangian methods originally developed for fluid-structure interaction [36,37], the mesh can be treated as pseudo-elastic body, so that the bulk nodes follow the motion of the interfacial nodes, which is connected via Lagrange multipliers to the kinematic boundary condition of the interface [35]. This technique has proven to be extremely versatile for binary and ternary droplets [17,[38][39][40], but the challenge remains to efficiently parallelize such codes.…”

Convection-dominated dissolution for single and multiple immersed sessile droplets

“…For a multi-component drop dissolving in a host liquid, there is formation of Marangoni flow caused by the variation of surface tension over the droplet surface, which in addition can influence the behaviour of emulsification (Tan et al 2019). Similarly, the Marangoni flow also plays a crucial role in multi-component sessile Convection-dominated dissolution for immersed sessile drops 892 A21-3 droplet evaporation (Scriven & Sternling 1960;Tan et al 2016;Diddens et al 2017;Kim et al 2017;Edwards et al 2018;Li et al 2018bLi et al , 2019.…”