Evaporation of Sessile Droplets Laden with Particles and Insoluble Surfactants

Abstract

We consider the flow dynamics of a thin evaporating droplet in the presence of an insoluble surfactant and non-interacting particles in the bulk. Based on lubrication theory, we derive a set of evolution equations for the film height, the interfacial surfactant and bulk particle concentrations, taking into account the dependence of the liquid viscosity on the local particle concentration. An important ingredient of our model is that it takes into account the fact that the surfactant adsorbed at the interface hinders evaporation. We perform a parametric study to investigate how the presence of surfactants affects the evaporation process as well as the flow dynamics with and without the presence of particles in the bulk. Our numerical calculations show that the droplet life-time is affected significantly by the balance between the ability of surfactant to * To whom correspondence should be addressed † Department of Chemical Engineering, University of Patras, Patras 26500, Greece ‡ Department of Chemical Engineering, Indian Institute of Technology Hyderabad, Sangareddy 502 285, Telangana, India ¶ Department of Chemical Engineering, Imperial College London, London SW7 2AZ, UK 1 enhance spreading suppressing the effect of thermal Marangoni stresses-induced motion and to hinder the evaporation flux through the reduction of effective interfacial are of evaporation, which tend to accelerate and decelerate the evaporation process, respectively. For particle-laden droplets and in the case of dilute solutions, the droplet life-time is found to be weakly-dependent on the initial particle concentration. We also show that the particle deposition patterns are influenced strongly by the direct effect of surfactant on the evaporative flux; in certain cases, the "coffee stain" effect is enhanced significantly. A discussion of the delicate interplay between the effects of capillary pressure, solutal and thermal Marangoni stresses, which drive the liquid flow inside the evaporating droplet giving rise to the observed results is provided herein.

A minimal model for solvent evaporation and absorption in thin films

“…Such films are rarely encountered in practice and, therefore, the predictions from a one-dimensional model could deviate slightly from experimental data due to geometric effects associated with the change in surface area. Extending the model to multiple spatial dimensions is certainly possible [63], although this can come with a marked increase in complexity as one begins to account for contact line motion and other hydrodynamic effects [69]. However, the excellent agreement between our theoretical and experimental results, the latter of which involve films with pinned contact lines and a height-to-width ratio of roughly 1:100, suggests that our one-dimensional model can capture the key features with sufficient accuracy to function as a useful predictive tool of solvent evaporation and absorption in thin films.…”

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“…It is known that the morphology and properties of the final micro-and or nano-structured dry products assembled via evaporation-driven processes can equally be modified by several mechanisms. These may include: chemical transformations [27], charge tuning [3], number concentration of the particles inside the initial droplet [5,28], choice of the solvent and nanoparticle sizes [7,29] as well as the addition of surfactant to the initial droplet composition [1,30]. The latter is known to have an effect on the interfacial tension and thereby on the shape of the droplet [31,32].…”

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“…At the air-water interface, the boundary stress is speci-ed. 33 The force balance in the normal direction is…”