Onset of Marangoni convection for evaporating sessile droplets

We have generated stability parameters using a linear stability analysis to predict the onset criteria for Marangoni convection in evaporating sessile droplets for two types of substrates, insulating and conducting. The stability problem was formulated with boundary conditions that allow for a temperature discontinuity at the liquid-vapour interface and the inclusion of an expression for the evaporation flux that considers this temperature discontinuity. We introduce no fitting coefficients; therefore, the stability parameters we generate contain only physical variables. The results indicate that spherical sessile droplets evaporating on insulating substrates are predicted to have a similar onset criteria with sessile droplets evaporating on conducting substrates. The onset prediction for sessile droplets evaporating on insulating substrates is found to be considerably different than the case of liquids evaporating from conical funnels constructed of insulating materials owing to the modification of the boundary condition from the geometrical shift and the corresponding retention of modes in the solution. A parametric analysis demonstrates how the input variables impact the stability of evaporating sessile droplets.     

Lysozyme pattern formation in evaporating drops

Liquid droplets containing suspended particles deposited on a solid, flat surface generally form ringlike structures due to the redistribution of solute during evaporation (the "coffee ring effect"). The forms of the deposited patterns depend on interactions between solute(s), solvent, and substrate. In this study, deposition patterns from droplets of a simplified model biological fluid (DI water + lysozyme) are examined by scanning probe and optical microscopy. The overall lysozyme residue morphology is complex (with both a perimeter "rim" and undulating interior) but varies little with concentration. However, the final packing of lysozyme molecules is strongly dependent on initial concentration.     

Evaporation of sessile droplets of dilute aqueous solutions containing sodium n-alkylates from polymer surfaces: influences of alkyl length and concentration of solute

The evaporation of sessile droplets placed on polymer surfaces was studied by microscopic observation of the changes in shape of aqueous solution droplets in which the alkyl lengths and the initial concentrations of sodium n-alkylates were varied. Although the initial contact angles of the droplets were not significantly different, the evaporation process varied significantly with the alkyl length of the sodium n-alkylate employed. For the sodium dodecanoate (C 12), showing the highest surface activity, the concentration was found to have a significant effect on the evaporation process of the droplets. In the evaporation of water droplets, variations in the three distinct stages were caused by the different concentration of solutes distributed near or at the air/water interface. It is revealed that the concentration of droplet solute near the air/water interface requires not only solvent evaporation but also some affinity of the solute for the interface. The initial C 12 concentration-dependence of the evaporation of C 12 solution droplets is discussed with particular emphasis on the sudden spreading or sudden contraction of the contact area near the end of evaporation. It is suggested that the cluster formation by C 12 molecules at the air/liquid interface during the evaporation causes Marangoni instability in an evaporating droplet, and the clusters are expected to move dynamically, depending on the droplet concentration of C 12, from the droplet center to the contact line and vice versa, showing Marangoni flow along the air/water interface.     

Formation of fractal structures upon the evaporation of nanoparticle dispersion droplets

The regularities of the self-organization of silver nanoparticles on solid substrates upon the evaporation of droplets of their aqueous dispersions were studied. The evaporation rate of the dispersion medium varied within a wide range. Upon a slow evaporation of the dispersion medium, a dense ring-like precipitate is formed around the droplet perimeter, where almost all particles are accumulated. In the vicinity of a rim, an ordered nanoparticle arrangement was observed. As the evaporation rate of the dispersion medium increases, most of the silver nanoparticles remain in the inner zone, limited by a rather dense rim, and form 2D fractal structures. At some regimes of droplet evaporation, 3D fractal structures were assembled whose shape depended on the substrate nature.Translated from Kolloidnyi Zhurnal, Vol. 66, No. 6, 2004, pp. 862–864.Original Russian Text Copyright © 2004 by Vysotskii, Roldughin, Uryupina.     

On the effect of marangoni flow on evaporation rates of heated water drops

In this letter we show that the Marangoni flow contribution to the evaporation rate of small heated water droplets resting on hot substrates is negligible. We compare data of evaporating droplet experiments with numerical results and assess the effect of Marangoni flow and its contribution to the evaporation process. We demonstrate that heat conduction inside these water droplets is sufficient to give an accurate estimate of evaporation rates. Although convection in evaporating water droplets remains an open problem, our aim in this study is to demonstrate that these effects can be neglected in the investigation of evaporation rate evaluation. It is worth noting that the presented results apply to volatile heated drops which might differ from spontaneously evaporating cases.     

Evaporation of water droplets on polymer surfaces

The evaporation of water droplets on polymer surfaces was investigated by using a digital image analysis technique. There were three distinct stages in the water evaporation process: a constant contact area mode, a constant contact angle mode, and a mixed mode that is independent of both the initial quantity of water droplets and the hydrophobic properties of the polymer surfaces. The physical factors influencing the first and second transitions in the evaporation process were found to be the attainment of the receding angle on the polymer surfaces and the Marangoni instability in the evaporating water droplets, which result from the concentration gradient of contaminants. This study also provides qualitative information about the microfluid flows inside the evaporating water droplets and the morphology of drying stains on polymer surfaces. The contaminants were found to be concentrated at the perimeter of the stains, in agreement with the observed outward microfluid flow in the mixed mode of the evaporation process.     

Application of the quartz crystal microbalance to the evaporation of colloidal suspension droplets

An investigation into the evaporation of sessile droplets of latex and clay particle suspensions is presented in this work. The quartz crystal microbalance (QCM) has been used to study the interfacial phenomena during the drying process of these droplets. Characteristic changes of the crystal oscillating frequency and crystal resistance (damping of the oscillating energy) have been observed and related to the different stages of the evaporation process. Measurements have been made for latex particle sizes from 1.9 to 10 microm and for rough and polished crystals using drops from 0.3 to 1.5 microL. The behavior of the QCM is shown to depend strongly on the size of particles present and on the morphology of the crystal surface. One of the most striking features is a drastic damping of the oscillation energy and corresponding rise in frequency observed during the final stages of evaporation, particularly for the clay suspensions.     

Particle adsorption in evaporating droplets of polymer latex dispersions on hydrophilic and hydrophobic surfaces

Stain patterns formed by drying up of droplets of polymer latex dispersion on hydrophilic and hydrophobic surfaces were examined in light of the mechanism of particle adsorption in evaporating droplets. On hydrophilic surfaces, the volume of droplets decreased with time, keeping the initial outline of contact area, and circular stain patterns were formed after the dry-up of droplets. By the microscopic observation of particles in the droplets, it was found that a large portion of the particles were forced to adsorb on the outline of the contact area where a microscopic thin water layer was formed because of hydrophilicity of the surface. On hydrophobic surfaces, on the other hand, the contact area of droplets decreased as evaporation proceeded, while no particle was adsorbed on the surface at the early stages. The particles in the droplets started to aggregate when the concentration of particles reached a critical value, and the aggregates adsorbed on the surface forming tiny spots after the dry-up. Time evolutions of contact angle, contact area and volume of the droplets were analyzed in light of differences in the adsorption mechanisms between hydrophilic and hydrophobic surfaces. Received: 14 January 1998 Accepted: 1 May 1998     

Evaporative characteristics of sessile nanofluid droplet on micro‐structured heated surface

Micro‐structure patterned substrates attract our attention due to the special and programmable wettabilities. The interaction between the liquid and micro/nano structures gives rise to controllable spreading and thus evaporation. For exploration of the application versatility, the introduction of nanoparticles in liquid droplet results in interaction among particles, liquid and microstructures. In addition, temperature of the substrates strongly affects the spreading of the contact line and the evaporative property. The evaporation of sessile droplets of nanofluids on a micro‐grooved solid surface is investigated in terms of liquid and surface properties. The patterned nickel surface used in the experiments is designed and fabricated with circular and rectangular shaped pillars whose size ratios between interval and pillars is fixed at 5. The behavior is firstly compared between nanofluid and pure liquid on substrates at room temperature. For pure water droplet, the drying time is relatively longer due to the receding of contact line which slows down the liquid evaporation. Higher concentrations of nanoparticles tend to increase the total evaporation time. With varying concentrations of graphite at nano scale from 0.02% to 0.18% with an interval at 0.04% in water droplets and the heating temperature from 22 to 85°C, the wetting and evaporation of the sessile droplets are systematically studied with discussion on the impact parameters and the resulted liquid dynamics as well as the stain. The interaction among the phases together with the heating strongly affects the internal circulation inside the droplet, the evaporative rate and the pattern of particles deposition.     

Microwave-assisted self-organization of colloidal particles in confining aqueous droplets

Monodisperse aqueous emulsion droplets encapsulating colloidal particles were produced in the oil phase, and controlled microwave irradiation of the aqueous drop phase created spherical colloidal crystals by so-called evaporation-induced self-organization of the colloidal particles. Unlike usual colloidal crystals, colloidal crystals in spherical symmetry (or photonic balls) possessed photonic band gaps for the normal incident light independent of the position all over the spherical surface. While the consolidation of colloidal particles in emulsion droplets in an oven took several hours, the present microwave-assisted evaporation could reduce the time for complete evaporation to a few tens of minutes. Under the microwave irradiation, the aqueous phase in emulsions was superheated selectively and the evaporation rate of water could be controlled easily by adjusting the microwave intensity. The result showed that the packing quality of colloidal crystals obtained by the microwave-assisted self-organization was good enough to show photonic band gap characteristics. The reflectance of our photonic balls responded precisely to any change in physical properties including the size of colloidal particles, refractive index mismatch, and angle of the incident beam. In particular, for polymeric particles, the photonic band gap could be tuned by the intensity of microwave irradiation, and the reflection color was red-shifted with stronger microwave irradiation. Finally, for better photonic band gap properties, inverted photonic balls were prepared by using the spherical colloidal crystals as sacrificial templates.     

Evaporation-induced particle microseparations inside droplets floating on a chip

We describe phenomena of colloidal particle transport and separation inside single microdroplets of water floating on the surface of dense fluorinated oil. The experiments were performed on microfluidic chips, where single droplets were manipulated with alternating electric fields applied to arrays of electrodes below the oil. The particles suspended in the droplets were collected in their top region during the evaporation process. Experimental results and numerical simulations show that this microsepration occurs as a result of a series of processes driven by mass and heat transfer. An interfacial tension gradient develops on the surface of the droplet as a result of the nonuniform temperature distribution during the evaporation. This gradient generates an internal convective Marangoni flow. The colloidal particles transported by the flow are collected in the top of the droplets by the hydrodynamic flux, compensating for evaporation through the exposed top surface. The internal flow pattern and temperature distribution within evaporating droplets were simulated using finite element calculations. The results of the simulation were consistent with experiments using tracer particles. Such microseparation processes can be used for on-chip synthesis of advanced particles and innovative microbioassays.     

Fabrication of nanoscale latex arrays based on hydroxylated poly(butyl methacrylate-<Emphasis Type="Italic">b</Emphasis>-glycidyl methacrylate)

We succeeded in fabricating nanoscale arrays of polymers based on hydroxylated poly(butyl methacrylate-b-glycidyl methacrylate) which was prepared via a novel atom-transfer radical polymerization technique. Nanosized latex particles of the copolymer were obtained in the tetrahydrofuran/toluene solvent system. By evaporation of the latex solution on a substrate, the ordered self-organization monolayer was formed. Rather regular, two-dimensional arrays of nanopaticles with diameters down to approximately 12 nm were observed by means of transmission electron microscopy. The regular nature of the arrays can be controlled well by depositing the monolayer at a lower temperature.     

Single aerosol particle studies

This paper surveys the research carried out on single aerosol particles in the micron and submicron size range with emphasis on the work performed by the authors. The principles and design of the electrodynamic and electrostatic balances are reviewed, and experimental data for evaporating droplets in a stagnant gas at various total pressures and various temperature are compared with theoretical results for Knudsen aerosol evaporation and are used to determine Lennard-Jones interaction parameters, diffusivities and vapor pressures for relatively nonvolatile compounds. The use of the electrodynamic balance or “picoblance” developed to study aerosol particles of the order of a piogram is illustrated for diffusion-controlled droplet evaporation measurements, and new data and an analysis for binary dorplet evaporation are presented.     

Magnetic polystyrene nanocapsules with core-shell morphology obtained by emulsifier-free miniemulsion polymerization

Nanocapsules containing hexadecane and Fe₃O₄ magnetic nanoparticles as core materials and polystyrene as shell were produced in a new method through emulsifier-free miniemulsion polymerization using 2,2′-azobis(2-amidinopropane) dihydrochloride (V-50) as a water-soluble initiator. The effect of some parameters such as the amounts of Fe₃O₄ and initiator on morphology of resulting nanocapsules was studied. Transmission electron microscopy showed that the products had latex particles having a size range of about 300–1300 nanometer and both magnetic nanocapsules with core-shell morphology and solid particles. The phase transition temperature and phase transition heat of the produced capsules were determined by differential scanning calorimetric analyses. Thermal properties of the latex were compared with those of magneticparticles-free latex and with those of latex free of both magnetic particles and hexadecane. Thermogravimetric analysis was also used to confirm the encapsulation and to determine the amounts of hexadecane and Fe₃O₄ within the capsules.     

Self-organization of polymer particles on hydrophobic solid substrates in aqueous media. I. Self-organization of cationic polymer particles on alkylated glass plates

Monodisperse, cationic polymer particles bearing quaternary ammonium groups effectively self-organized on hydrophobic solid substrates such as alkylated glass plates and polymer films to form particle monolayers. With an increase of the particle surface charge density, the surface coverage decreased and the morphology of particle monolayers changed from aggregated type to dispersed type. The dispersed type of particle monolayers having a relatively regular particle distance was formed at higher temperature. The self-organization behaviors on alkylated glass plates were different from those on unmodified glass plates through electrostatic interaction. The formation of particle monolayers on alkylated glass plates occurred only over a certain latex concentration range in contrast with that on unmodified glass plate. The adhesive strength of particle monolayers was enhanced by annealing at temperatures above the glass transition temperature (T _g) of the particles. Lens-shaped particle monolayers were fabricated by annealing the dispersed type of particle monolayers.     

Highly magnetic latexes from submicrometer oil in water ferrofluid emulsions

The synthesis of functionalized submicrometer magnetic latex particles is described as obtained from a preformed magnetic emulsion composed of organic ferrofluid droplets dispersed in water. Composite (polystyrene/γ‐Fe₂O₃) particles were prepared according to a two‐step procedure including the swelling of ferrofluid droplets with styrene and a crosslinking agent (divinyl benzene) followed by seeded emulsion polymerization with either an oil‐soluble [2,2′‐azobis(2‐isobutyronitrile)] or water‐soluble (potassium persulfate) initiator. Depending on the polymerization conditions, various particle morphologies were obtained, ranging from asymmetric structures, for which the polymer phase was separated from the inorganic magnetic phase, to regular core–shell morphologies showing a homogeneous encapsulation of the magnetic pigment by a crosslinked polymeric shell. The magnetic latexes were extensively characterized to determine their colloidal and magnetic properties. The desired core–shell structure was efficiently achieved with a given styrene/divinyl benzene ratio, potassium persulfate as the initiator, and an amphiphilic functional copolymer as the ferrofluid droplet stabilizer. Under these conditions, ferrofluid droplets were successfully turned into superparamagnetic polystyrene latex particles, about 200 nm in size, containing a large amount of iron oxide (60 wt %) and bearing carboxylic surface charges. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 2642–2656, 2006     

Self-organised microdots formed by dewetting in a highly volatile liquid

Dewetting induced self-organisation was used to prepare an ordered microstructure from a highly volatile liquid. Dewetting of an evaporating iron oxide precursor solute on silicon substrate resulted in arrays of microdots with nearly hexagonal and tetragonal symmetries. Ordered structures form either by stick-slip motion or fingering instability at the receding contact line of evaporating droplets. Subsequent thermal treatment at 550 °C yields crystalline Fe(2)O(3) microdots with a diameter range of 1-4 μm. The size, density and shape of the microdots can be changed by using patterned substrates with different surface energies.     

Ultra-fine particles of TiN

Ultra-fine particles of TiN have been produced by evaporating titanium in an atmosphere of helium and nitrogen. After evaporation titanium is cooled by the helium gas and small particles are formed. These are extremely reactive and react with the nitrogen gas making nitride. The particles were either collected as a powder on a vertical tube cooled by liquid nitrogen, or as a surface coating on some areas of the tungsten crucible. The produced powder was observed to consist of single crystalline particles with sizes ranging from 5 to 20 nm. The only phase observed was the δ-phase (fcc, NaCl-structure), and the dominating particle morphology was cubic with (100)-surfaces. Due to the size of the particles it was not possible to determine the stoichiometry by accurate lattice parameter measurements. However, quantitative electron energy loss spectroscopy (EELS) was applied on single particles and indicated a quite low content of nitrogen (about 33 at%). Some areas of the tungsten evaporation source were covered with a 10 μm thick TiN coating with its typical yellowish colour. The grains had a size of 1–10 μm and a rectangular shape. The grains were heavily stressed and had an amount of nitrogen quite similar to that of the small particles.     

Nucleation and Growth of Amino Acid and Peptide Supramolecular Polymers through Liquid–Liquid Phase Separation

The transition of peptides and proteins from the solution phase into fibrillar structures is a general phenomenon encountered in functional and aberrant biology and is increasingly exploited in soft materials science. However, the fundamental molecular events underpinning the early stages of their assembly and subsequent growth have remained challenging to elucidate. Here, we show that liquid–liquid phase separation into solute‐rich and solute‐poor phases is a fundamental step leading to the nucleation of supramolecular nanofibrils from molecular building blocks, including peptides and even amphiphilic amino acids. The solute‐rich liquid droplets act as nucleation sites, allowing the formation of thermodynamically favorable nanofibrils following Ostwald's step rule. The transition from solution to liquid droplets is entropy driven while the transition from liquid droplets to nanofibrils is mediated by enthalpic interactions and characterized by structural reorganization. These findings shed light on how the nucleation barrier toward the formation of solid phases can be lowered through a kinetic mechanism which proceeds through a metastable liquid phase.     

Analysis of the effects of Marangoni stresses on the microflow in an evaporating sessile droplet

We study the effects of Marangoni stresses on the flow in an evaporating sessile droplet, by extending a lubrication analysis and a finite element solution of the flow field in a drying droplet, developed earlier. The temperature distribution within the droplet is obtained from a solution of Laplace's equation, where quasi-steadiness and neglect of convection terms in the heat equation can be justified for small, slowly evaporating droplets. The evaporation flux and temperature profiles along the droplet surface are approximated by simple analytical forms and used as boundary conditions to obtain an axisymmetric analytical flow field from the lubrication theory for relatively flat droplets. A finite element algorithm is also developed to solve simultaneously the vapor concentration, and the thermal and flow fields in the droplet, which shows that the lubrication solution with the Marangoni stress is accurate for contact angles as high as 40 degrees. From our analysis, we find that surfactant contamination, at a surface concentration as small as 300 molecules/microm(2), can almost entirely suppress the Marangoni flow in the evaporating droplet.