The evaporation of sessile droplets on a flat surface involves a complex interplay between phase change, diffusion, advection and surface forces. In an attempt to significantly reduce the complexity of the problem and to make it manageable, we propose a simple model hinged on a surface free energy-based relaxation dynamics of the droplet shape, a diffusive evaporation model and a contact line pinning mechanism governed by a yield stress. Our model reproduces the known dynamics of droplet shape relaxation and of droplet evaporation, both in the absence and in the presence of contact line pinning. We show that shape relaxation during evaporation significantly affects the lifetime of a drop. We find that the dependence of the evaporation time on the initial contact angle is a function of the competition between the shape relaxation and evaporation, and is strongly affected by any contact line pinning.
The evaporation of a sessile droplet spontaneously induces an internal capillary liquid flow. The surface-tension driven minimisation of surface area and/or surface-tension differences at the liquid-gas interface caused by evaporation-induced temperature or chemical gradients set the liquid into motion. This flow drags along suspended material and is one of the keys to control the material deposition in the stain that is left behind by a drying droplet. Applications of this principle range from the control of stain formation in the printing and coating industry, to the analysis of DNA, to fore…
A finite element model was developed to compute the fluid flow inside a sessile evaporating droplet on hydrophilic substrate in ambient conditions. The evaporation is assumed as quasi-steady and the flow is considered as axisymmetric with a pinned contact line. The Navier-Stokes equations in cylindrical coordinates were solved inside the droplet. Galerkin weight residual approach and velocity pressure formulation was used to discretise the governing equations. Six node triangular mesh and quadratic shape functions were used to obtain higher accuracy solutions. Radial velocity profiles in axial…
We investigate evaporation of a sessile droplet on a non-wetted surface in the framework of diffusion-limited and quasi-steady evaporation. We extend previous models and numerically solve Laplace equation for the diffusion of liquid vapor in ambient. We propose a unified, simple and accurate expression of the evaporation mass flux valid for 90^o < theta < 180^o, where theta is the equilibrium contact angle. In addition, using the derived expression of the evaporation mass flux, we propose a simple and accurate expression of the evaporation mass rate for a non-wetted surface, which does not exh…
The investigation of evaporating liquid drop deposited onto a flat surface is of great importance for physical, engineering and medical applications. Novel analytical expressions are proposed to calculate the evaporation rate of sessile drop (mass loss per unit surface area per unit time) and total evaporation rate (mass loss per unit time). To obtain these results, the H.M. Macdonald's solution for a flat wedge was transformed by method of inversion in a sphere originally developed by J.C. Maxwell in the Treatise on Electricity and Magnetism with further derivation the solution for a lens bas…
Spreading of respiratory diseases, such as COVID-19, from contaminated surfaces is dependent on the drying time of the deposited droplets containing the virus. The evaporation rate depends on environmental conditions, such as ambient temperature and relative humidity and physical properties (e.g., droplet volume, contact angle and composition). The respiratory droplets contain salt (NaCl), protein (mucin), and surfactant (dipalmitoylphosphatidylcholine) in addition to water, which are expected to influence the evaporation in a big way. A diffusion-based theoretical model for estimating the dry…
Understanding flow patterns and coupled transport phenomena during evaporation of droplets loaded with colloidal particles is central to design technical applications such as organizing proteins/DNA on a solid surface. We review recent reports on evaporating sessile droplets of colloidal suspensions on a solid surface. Starting from the classical mechanism of formation of a ring-like deposit, we discuss the influence of several problem parameters. Notably, thermal or solutal Marangoni effect, particle size, particle concentration, particle shape, substrate wettability, pH of the suspension etc…
The evaporation of a binary sessile ethanol-water droplet on an inclined substrate is studied experimentally just below the critical sliding angles for different substrate temperatures. A customized goniometer equipped with a CMOS camera and an infrared (IR) camera is used. The droplet is observed to remain pinned in the advancing side during the evaporation process, while the receding side contracts. The asymmetry in the advancing and receding contact angles of the droplet on inclined substrate results in complex thermo-solutal Marangoni convection that is captured through IR images. The drop…
The article reports droplet evaporation kinetics on inclined substrates. Comprehensive experimental and theoretical analyses of the droplet evaporation behaviour for different substrate declination, wettability and temperatures have been presented. Sessile droplets with substrate declination exhibit distorted shape and evaporate at different rates compared to droplets on the same horizontal substrate and is characterized by more often changes in regimes of evaporation. The slip stick and jump stick modes are prominent during evaporation. For droplets on inclined substrates, the evaporative flu…
The stability of nonvolatile thin liquid films and of sessile droplets is strongly affected by finite size effects. We analyze their stability within the framework of density functional theory using the sharp kink approximation, i.e., on the basis of an effective interface Hamiltonian. We show that finite size effects suppress spinodal dewetting of films because it is driven by a long-wavelength instability. Therefore nonvolatile films are stable if the substrate area is too small. Similarly, nonvolatile droplets connected to a wetting film become unstable if the substrate area is too large. T…
Living microorganisms in confined systems typically experience an affinity to populate boundaries. The reason for such affinity to interfaces can be a combination of their directed motion and hydrodynamic interactions at distances larger than their own size. Here we will show that self-propelled Janus particles (polystyrene particles partially coated with platinum) immersed in droplets of water and hydrogen peroxide tend to accumulate in the vicinity of the liquid/gas interface. Interestingly, the interfacial accumulation occurs despite the presence of an evaporation-driven flow caused by a so…
Coalescence-induced alignment of anisotropic particles in drying sessile droplets
Forschungszentrum Jülich（于利希研究中心）；Helmholtz Institute Erlangen-Nürnberg for Renewable Energy (IET-2)（亥姆霍兹埃尔朗根-纽伦堡可再生能源研究所（IET-2））；Friedrich-Alexander-Universität Erlangen-Nürnberg（埃尔朗根-纽伦堡弗里德里希·亚历山大大学）
The present study experimentally and numerically investigates the evaporation and resultant patterns of dried deposits of aqueous colloidal sessile droplets, when the droplets are initially elevated to a high temperature before being placed on a substrate held at ambient temperature. The system is then released for natural evaporation without applying any external perturbation. Infrared thermography and optical profilometry were used as essential tools for interfacial temperature measurements and quantification of the coffee-ring dimensions, respectively. Initially, a significant temperature g…
Phase separated macromolecules play essential roles in many biological and synthetic systems. Physical characterization of these systems can be challenging because of limited sample volumes, particularly for phase-separated proteins. Here, we demonstrate that a classic method for measuring the surface tension of liquid droplets, based on the analysis of the shape of a sessile droplet, can be effectively scaled down for this application. The connection between droplet shape and surface tension relies on the density difference between the droplet and its surroundings. This can be determined with…
The present article experimentally and theoretically probes the evaporation kinetics of sessile saline droplets. Observations reveal that presence of solvated ions leads to modulated evaporation kinetics, which is further a function of surface wettability. On hydrophilic surfaces, increasing salt concentration leads to enhanced evaporation rates, whereas on superhydrophobic surfaces, it first enhances and reduces with concentration. Also, the nature and extents of the evaporation regimes constant contact angle or constant contact radius are dependent on the salt concentration. The reduced evap…
The evaporation of droplets occurs in a large variety of natural and technological processes such as medical diagnostics, agriculture, food industry, printing, and catalytic reactions. We study the different droplet morphologies adopted by an evaporating droplet on a surface with an elliptical patch with a different contact angle. We perform experiments to observe these morphologies and use numerical calculations to predict the effects of the patched surfaces. We observe that tuning the geometry of the patches offers control over the shape of the droplet. In the experiments, the drops of vario…
Water droplet freezing is a common phenomenon in our daily life. In both natural scenarios and industrial production, different surface inclinations bring distinctive deformation and freezing dynamics to frozen droplets. We explore the freezing of pendent and sessile droplets at different Bond number regimes. The effect of gravity on the droplet freezing process is analyzed by considering droplet morphology, freezing front dynamics, and freezing time. It is found that gravity can significantly influence droplet freezing processes via shaping the initial droplet, resulting in the flattening or …
Effects of substrate temperature, substrate wettability and particles concentration are experimentally investigated for evaporation of a sessile water droplet containing colloidal particles. Time-varying droplet shapes and temperature of the liquid-gas interface are measured using high-speed visualization and infrared thermography, respectively. The motion of the particles inside the evaporating droplet is qualitatively visualized by an optical microscope and profile of final particle deposit is measured by an optical profilometer. On a non-heated hydrophilic substrate, a ring-like deposit for…
Line tension from dual-geometry sessile droplet measurements: Combining contact-angle size-dependence data for axisymmetric and cylindrical droplets to determine the line tension
Coupled self-charging and self-propulsion of evaporating sessile droplets
Okinawa Institute of Science and Technology Graduate University（冲绳科学技术大学院大学）；Max Planck Institute for Polymer Research（马克斯·普朗克高分子研究所）；King Abdullah University of Science and Technology (KAUST)（阿卜杜拉国王科技大学）
The so-called coffee stain effect has been intensively studied over the past decades, but most of the studies are focused on sessile droplets. In this paper, we analyse the origin of the difference between the deposition of suspended particles in a sessile drop and in an axisymmetric drop deposited on a fibre. First, we model the shape of a drop on a fibre and its evaporative flux with some approximations to derive analytical calculations. Then, for pinned contact lines, we solve the hydrodynamics equations in the liquid phase under the lubrication approximation to determine the flow velocity …
We study the effects of vertical sinusoidal vibrations on a liquid droplet with a low surface tension (ethanol) deposited on a solid substrate. In a precise range of amplitudes and frequencies, the drop exhibits a dramatic worm-like shape instability with a strong symmetry breaking, comparable to the one observed by Pucci et al. (Phys. Rev. Lett., 106 (2011) 024503) on a vibrated floating lens. However, the geometry of our system is much simpler since it does not involve the oscillation and deformation of a liquid-liquid-air contact line. We show that the Faraday waves appearing on the surface…
Self-assembled filament layers in drying sessile droplets: from morphology to electrical conductivity
Helmholtz Institute Erlangen-Nürnberg for Renewable Energy (IET-2), Forschungszentrum Jülich（于利希研究中心埃尔朗根-纽伦堡亥姆霍兹可再生能源研究所）；Friedrich-Alexander-Universität Erlangen-Nürnberg（埃尔朗根-纽伦堡弗里德里希·阿列克桑德大学）
Stokes flows in a sessile hemispherical drop due to evaporation and surface tension gradient
Shubnikov Institute of Crystallography, Kurchatov Complex of Crystallography and Photonics of NRC‘Kurchatov Institute’（舒布尼科夫晶体学研究所，俄罗斯国家研究中心库尔恰托夫研究所晶体学与光子学库尔恰托夫综合体）
We numerically investigate both single and multiple droplet dissolution with droplets consisting of lighter liquid dissolving in a denser host liquid. The significance of buoyancy is quantified by the Rayleigh number Ra which is the buoyancy force over the viscous damping force. In this study, Ra spans almost four decades from 0.1 to 400. We focus on how the mass flux, characterized by the Sherwood number Sh, and the flow morphologies depend on Ra. For single droplet dissolution, we first show the transition of the Sh(Ra) scaling from a constant value to $Sh\sim Ra^{1/4}$, which confirms the e…
We study the free energy landscapes of a pair of submicron spherical particles floating at the surface of a sessile droplet. The particles are subjected to radial external forces resulting in a deformation of the droplet shape relative to the reference shape of a spherical cap. This deformation leads to tangential forces on the particles. For small deformations and for the contact angle $θ_0$ at the substrate being equal to $π/2$, the corresponding linearized Young-Laplace equation is solved analytically. The solution is constructed by employing the method of images from electrostatics, where …
A model is developed for describing the transport of charged colloidal particles in an evaporating sessile droplet on the electrified metal substrate in the presence of a solvent flow. The model takes into account the electric charge of colloidal particles and small ions produced by electrolytic dissociation of the active groups on the colloidal particles and solvent molecules. We employ a system of self-consistent Poisson and Nernst--Planck equations for electric potential and average concentrations of colloidal particles and ions with the appropriate boundary conditions. The fluid dynamics, …
We experimentally investigate the profile and morphology of the ring-like deposits obtained after evaporation of a sessile water droplet containing polystyrene colloidal particles on a hydrophilic glass substrate. In particular, the coupled effect of particle size and concentration are studied. The deposits were qualitatively visualized under an optical microscope and profile of the ring was measured by an optical profilometer. The profile of the ring resembles a partial torus-like shape for all cases of particles size and concentration. The cracks on the surface of the ring were found to occu…
We investigate deposit patterns and associated morphology formed after the evaporation of an aqueous droplet containing mono- and bi-dispersed colloidal particles. In particular, the combined effect of substrate heating and particle diameter is investigated. We employ high-speed visualization, optical microscopy and scanning electron microscopy to characterize the evaporating droplets, particle motion, and deposit morphology, respectively. In the context of mono-dispersed colloidal particles, an inner deposit and a typical ring form for smaller and larger particles, respectively, on a nonheate…
We study here the microscopic deformations of elastic lamellae constituting a superhydrophobic substrate under different wetting conditions of a sessile droplet using electrowetting. The deformation profiles of the lamellae are experimentally evaluated using confocal microscopy. These experimental results are then explained using a variational principle formalism within the framework of linear elasticity. We show that the local deformation profile of a lamella is mainly controlled by the net horizontal component of the capillary forces acting on its top due to the pinned droplet contact line. …
Evaporation of surfactant laden sessile droplets is omnipresent in nature and industrial applications such as inkjet printing. Soluble surfactants start to form micelles in an aqueous solution for surfactant concentrations exceeding the critical micelle concentration (CMC). Here, the evaporation of aqueous sodium dodecyl sulfate (SDS) sessile droplets on hydrophobic surfaces were experimentally investigated for SDS concentrations ranging from 0.025 to 1 CMC. In contrast to the constant contact angle of an evaporating sessile water droplet, we observed that, at the same surface the contact angl…
Evaporating droplets of polymer or colloid solution may produce a glassy crust at the liquid-vapour interface, which subsequently deforms as an elastic shell. For sessile droplets, the known radial outward flow of solvent is expected to generate crusts that are thicker near the pinned contact line than the apex. Here we investigate, by non-linear quasi-static simulation and scaling analysis, the deformation mode and stability properties of elastic caps with a non-uniform thickness profile. By suitably scaling the mean thickness and the contact angle between crust and substrate, we find data co…
The pinning of the contact line adversely influences the electrowetting performance of sessile liquid droplets. In this paper, we report the electrowetting hysteresis characteristics of 100 mM aq. KCl sessile liquid droplet placed on a hydrophobic PDMS surface. The effect of nanoparticles on the contact angle hysteresis under the imposed electric potential is further investigated. This study reveals that the contact angle hysteresis decreases beyond a certain threshold value of nanoparticles concentration. Therefore, nanoparticle suspension in the liquid droplet can be used to enhance or suppr…
The effects of line tension on the morphology of a sessile droplet placed on top of a convex spherical substrate are studied. The morphology of the droplet is determined from the global minimum of the Helmholtz free energy. The contact angle between the droplet and the spherical substrate is expressed by the generalized Young's formula. When the line tension is positive and large, the contact angle jumps discontinuously to $180^{\circ}$, the circular contact line shrinks towards the top of the substrate, and the droplet detaches from the substrate, forming a spherical droplet if the substrate …
We studied the dependence of solid deposit shape obtained by free drying of sessile drops on the particles concentration and Derjaguin-Landau-Verwey-Overbeek (DLVO) particle/substrate interaction. In contrast to previous contributions using pH as a control parameter of interactions, we investigated an unprecedentedly wide range of concentrations and particle/substrate DLVO forces by modifying the nature of the substrate and particles as well as their size and surface chemistry whereas long-distance repulsive interactions between particles were maintained for most of the drying time. Our main r…
We experimentally investigate the evaporation dynamics of sessile droplets of a fixed volume consisting of different compositions of ethanol-water binary mixture at different substrate temperatures (T_s). At T_s=25oC, we observe pinned-stage linear evaporation for pure droplets, but a binary droplet undergoes two distinct evaporation stages: an early pinned stage and a later receding stage. In the binary droplet, the more volatile ethanol, evaporates faster leading to a nonlinear trend in the evaporation process at the early stage. The phenomenon observed in the present study at T_s=25oC is si…
In this study, we present experimental and theoretical analyses of double emulsion drop evaporation. After the apparent completion of evaporation of the inner phase of a double emulsion drop, surprisingly, a resurfacing of a daughter droplet is observed. We further investigated to hypothesize this phenomenon which allowed us to obtain a prolonged fixed contact line evaporation for a single phase drop along with similar occurrence of resurfacing as of the double emulsion drops.
This short review is devoted to the simple process of drying a multi-component droplet consisting of a complex fluid containing a salt. These processes provide a fascinating subject for study. The explanation of the rich variety of patterns formed is not only an academic challenge, but a problem of practical importance, as applications are growing in medical diagnosis and improvement of coating/printing technology. The fundamental scientific problem is the study of the mechanism of micro- and nanoparticle self-organization in open systems. The specific fundamental problem to be solved, related…
Sessile droplets of aqueous poly(ethylene oxide) solution, with average molecular weight of 100 kDa, are monitored during evaporative drying at ambient conditions over a range of initial concentrations $c_0$. For all droplets with $c_0 \geq 3%$, central conical structures, which can be hollow and nearly 50% taller than the initial droplet, are formed during a growth stage. Although the formation of superficially similar structures has been explained for glass-forming polymers using a skin-buckling model which predicts the droplet to have constant surface area during the growth stage (L. Paucha…
Motile Bacteria Modify Salt Precipitation Patterns in Dried Sessile Droplet
Georgia Institute of Technology（佐治亚理工学院）；University of Nebraska - Lincoln（内布拉斯加大学林肯分校）；Illinois Institute of Technology（伊利诺伊理工学院）；Blue Valley North High School（蓝谷北高中）
On a sufficiently-soft substrate, a resting fluid droplet will cause significant deformation of the substrate. This deformation is driven by a combination of capillary forces at the contact line and the fluid pressure at the solid surface. These forces are balanced at the surface by the solid traction stress induced by the substrate deformation. Young's Law, which predicts the equilibrium contact angle of the droplet, also indicates an a priori radial force balance for rigid substrates, but not necessarily for soft substrates which deform under loading. It remains an open question whether the …
The influence of finite system size on the free energy of a spherical particle floating at the surface of a sessile droplet is studied both analytically and numerically. In the special case that the contact angle at the substrate equals $π/2$ a capillary analogue of the method of images is applied in order to calculate small deformations of the droplet shape if an external force is applied to the particle. The type of boundary conditions for the droplet shape at the substrate determines the sign of the capillary monopole associated with the image particle. Therefore, the free energy of the par…
We propose simple model of colloidal sessile drop desiccation. The model describes correctly both evolution of the phase boundary between sol and gel inside such a drop and the final shape of the dried film (deposit). The model is based on mass conservation and natural assumption that deposit (gel phase) prevents flows and evaporation.
