Convective rolls and hydrothermal waves in evaporating sessile drops

Recent experiments on the evaporation of sessile droplets have revealed the spontaneous formation of various patterns including the presence of hydrothermal waves. These waves had previously been observed, in the absence of evaporation, in thin liquid layers subjected to an imposed, uniform temperature gradient. This is in contrast to the evaporating droplet case wherein these gradients arise naturally due to evaporation and are spatially and temporally varying. In the present paper, we present a theory of evaporating sessile droplets deposited on a heated surface and propose a candidate mechanism for the observed pattern formation using a linear stability analysis in the quasi-steady-state approximation. A qualitative agreement with experimental trends is observed.     

Dendrimer pattern formation in evaporating drops

The redistribution of organic solutes during drop evaporation is a nanoscale self-assembly process with relevance to technologies ranging from inkjet printing of organic displays to synthesis of biosmart interfaces for sensing and screening. We have used solutions of dendrimer molecules with incrementally varying terminal site chemistry to explore whether the condensed dendrimer patterns resulting from microdroplet evaporation sensitively depend on, and are characteristic of, the surface chemistry of the solute molecules. This hypothesis has been experimentally confirmed by comparing the behavior of microdroplets of G4, G4-25%C12, and G4-50%C12 dendrimers dissolved in pentanol and deposited on mica substrates. For the dilute concentration studied here, the presence of periodically 'scalloped' dendrimer rings is ubiquitous. The instability wavelength of the scalloped rings is found to be proportional to the width of the ring, similar to observations of the rim instability in dewetting holes. The effect of dendrimer surface chemistry is obvious in the detailed structure of the self-assembled rings. G4 rings are diffuse and disordered with no evidence for layered growth. G4-25%C12 exhibits highly ordered ring structures and the onset of monomolecular terracing. G4-50%C12 exhibits highly periodic scallops and very distinct monomolecular height terraced growth of the rings with flat terraces and sharply defined steps. On the basis of these results, it is likely that the morphology of condensed molecule-based ring patterns formed by evaporation of microdroplets on surfaces can be used as a 'fingerprint' to identify, for example, solute molecule surface chemistry and concentration and function as a sensor for a variety of biochemical events.     

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.     

Liquid ring formation from contacting, nonmiscible sessile drops

When two pure and nonmiscible liquid drops at rest on a rigid substrate come into close contact with a quasi-zero spreading velocity, one of them may be sucked around the second into a liquid ring, leading in some cases to the complete engulfment of the latter. We here show that the conditions for this amazing and unusual capillary effect to develop are defined by two sets of criteria: the "reciprocal" spreading of one drop with respect to the other and a "geometrical-wetting" criterion related to the opening of the groovelike channels along the base of the attracting drop. Despite the exceeding simplicity and roughness of liquid drops as compared to living cells, the phenomenon strangely recalls, at least in its mechanistic aspect, the fundamental biological process of phagocytosis. Besides these fundamental aspects, this effect may also have interesting implications for microstructuring techniques.     

The dynamics of evaporating sessile droplets

Experiments on sessile drops evaporating in a normal atmosphere without an applied thermal gradient are reported and compared with an available theoretical model. The liquids used are alkanes; water; and, more recently, polydimethylsiloxane oligomers. The substrates are silicon wafers, completely wetted by the liquid. Experiments with hanging drops allow us first to discard any influence of convection in the gas phase on the drop dynamics. The model assumes the process to be controlled by the stationary diffusion of the evaporating molecules in the gas phase. For alkanes and water, and in a limited range of drop sizes where gravity can be ignored, the model accounts very well for the dynamics of the drop radius, and rather well for the contact angle. This is no longer the case with the polydimethylsiloxane oligomers, where the very small contact angles require a more elaborated analysis of the drop edge. The text was submitted by the authors in English.     

On the lifetime of evaporating sessile droplets

The evaporation of sessile droplets with a constant base radius (pinning mode) and a constant contact angle (depinning mode) has been experimentally observed. Here we analyzed the effect of substrate hydrophobicity on the lifetimes of evaporating droplets for the two modes. Theoretical predictions were obtained and compared with available experimental results. The theoretical analysis and experimental results show that linear methods of extrapolating limited experimental data for a transient droplet contact angle and base radius overpredict the droplet lifetime. Likewise, the linear extrapolation of limited experimental data for transient droplet volume underpredicts the droplet lifetime. Correct methods of extrapolating limited experimental data for transient droplet parameters are described, discussed, and validated. The new methods removed inconsistencies in the previous theory and experimental analysis. Master equations and master curves for the droplet lifetime for the two evaporation modes are obtained and experimentally confirmed.     

Rescaling the dynamics of evaporating drops

The dynamics of evaporation of wetting droplets is investigated experimentally in an extended range of drop sizes to provide trends relevant for a theoretical analysis. A model is proposed, which generalizes Tanner's law in the presence of evaporation. A qualitative agreement is obtained, which represents a first step toward the solution of a very old, complex problem.     

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.     

As-placed contact angles for sessile drops

As-placed contact angle is the contact angle a drop adapts as a result of its placement on a surface. As expected, the as-placed contact angle, thetaAP, of a sessile drop on a horizontal surface decreases with the drop size due to the increase in hydrostatic pressure. We present a theoretical prediction for thetaAP which shows that it is a unique function of the advancing contact angle, thetaA, drop size, and material properties (surface tensions and densities). We test our prediction with published and new data. The theory agrees with the experiments. From the relation of the as-placed contact angle to drop size the thermodynamic equilibrium contact angle is also calculated.     

Self-assembly of spherical particles on an evaporating sessile droplet

Particles adsorbed on the surface of a droplet form three-dimensional packings when the droplet evaporates. We study the final packings when the liquid droplet is attached to a solid substrate. In contrast to a droplet evaporating away from a substrate, here the final packings are highly dependent on both the number of particles and the contact angle between the droplet and the surface. Simple geometrical constraints quantitatively determine the parameter regions that particular packings can form.     

Surface-induced patterns from evaporating droplets of aqueous carbon nanotube dispersions

Evaporation of aqueous droplets of carbon nanotubes (CNTs) coated with a physisorbed layer of humic acid (HA) on a partially hydrophilic substrate induces the formation of a film of CNTs. Here, we investigate the role that the global geometry of the substrate surfaces has on the structure of the CNT film. On a flat mica or silica surface, the evaporation of a convex droplet of the CNT dispersion induces the well-known "coffee ring", while evaporation of a concave droplet (capillary meniscus) of the CNT dispersion in a wedge of two planar mica sheets or between two crossed-cylinder sheets induces a large area (>mm(2)) of textured or patterned films characterized by different short- and long-range orientational and positional ordering of the CNTs. The resulting patterns appear to be determined by two competing or cooperative sedimentation mechanisms: (1) capillary forces between CNTs giving micrometer-sized filaments parallel to the boundary line of the evaporating droplet and (2) fingering instability at the boundary line of the evaporating droplet and subsequent pinning of CNTs on the surface giving micrometer-sized filaments of CNTs perpendicular to this boundary line. The interplay between substrate surface geometry and sedimentation mechanisms gives an extra control parameter for manipulating patterns of self-assembling nanoparticles at substrate surfaces.     

Analysis of the microfluid flow in an evaporating sessile droplet

The axisymmetric time-dependent flow field in an evaporating sessile droplet whose contact line is pinned is studied numerically and using an analytical lubrication theory with a zero-shear-stress boundary condition on the free surface of the droplet at low capillary and Reynolds numbers. A finite element algorithm is developed to solve simultaneously the vapor concentration and flow field in the droplet under conditions of slow evaporation. The finite element solution confirms the accuracy of the lubrication solution, especially when terms of higher order in the droplet flatness ratio (the ratio of droplet height to radius, h/R) are included in the lubrication theory to account more accurately for the singular flow near the contact line.     

Carbon nanotube formation and growth via particle-particle interaction

Carbon nanotubes are observed to form under a wide range of temperatures, pressures, reactive agents, and catalyst metals. In this paper we attempt to rationalize this body of observations reported in the literature in terms of fundamental processes driving nanotube formation. Many of the observed effects can be attributed to the interaction of three key processes: surface catalysis and deposition of carbon, diffusive transport of carbon, and precipitation effects. A new nanotube formation mechanism is proposed that describes the nanotube structures observed experimentally in a premixed flame and can account for certain shortcomings of the prevailing mechanism that has been repeatedly applied to explain nanotube formation in nonflame environments. The interacting particle model (IPM) attributes the initiation of nanotube growth to the physical interaction between catalyst particles. Coalescence of two (or more) catalyst particles leads to partial blocking of the particle surface, causing a disparity in carbon deposition over the particle surface. The resulting concentration gradient generates a net diffusive flux toward the interparticle contact point. Dimers that separate in this condition can support continuous nanotube growth between the particles. The model can also be extended to multiple particles to account for more complex morphologies. The IPM is consistent with many of the structures observed in the flame-produced material. The validity of the model is evaluated through analysis of diffusion dynamics and a force analysis of particle binding and separation. The IPM is also discussed in relation to identifying the requirements and best conditions to support nanotube growth in the premixed flame. The formation of nanotubes between particles as described by the IPM indicates that a single mechanism cannot completely describe nanotube synthesis; more likely, multiple pathways exist with varying rates that depend on specific process conditions.     

Surfactant-induced Marangoni eddies alter the coffee-rings of evaporating colloidal drops

The influence of the small ionic surfactant sodium dodecyl sulfate (SDS) on the evaporation of drying colloidal droplets is quantitatively investigated. The addition of SDS leads to a significantly more uniform deposition of colloidal particles after evaporation (i.e., the so-called "coffee-ring effect" is dramatically altered). We understand this phenomenon in the context of circulating radial Marangoni flows induced by the variation of SDS concentration along the air-water interface. Video microscopy permits the direct visualization of the colloidal particles involved in these flows, revealing a surprisingly stable "Marangoni eddy" that prevents particle deposition at the drop perimeter.     

Interfacial turbulence in minute drops evaporating on a flat plate

Surface tension/temperature driven interfacial turbulence in evaporating minute drops was studied photographyically using the laser shadowgraphy. Liquids of relatively low boiling point were employed: ethyl ether, acetone, methanol, carbon tetrachloride, benzene and heptane. A drop surface on a glass plate at room temperature was photographed straight down with motion picture. During drop lifetime, the interface exhibited a dominant pattern of radial stripes over a very brief duration followed by polygonal cells and ended in ripples. These interfacial forms are related to three stages of drop evaporation. The mechanism of interfacial turbulence is proposed.     

Lipid nanotube formation from streptavidin-membrane binding

A novel transformation of giant lipid vesicles to produce nanotubular structures was observed upon the binding of streptavidin to biotinylated membranes. Unlike membrane budding and tubulation processes caused by proteins involved with endocytosis and vesicle fusion, streptavidin is known to crystallize at near the isoelectric point (pI 5 to 6) into planar sheets against biotinylated films. We have found, however, that at neutral pH membranes of low bending rigidity (<10kT), such as 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC), spontaneously produce tubular structures with widths ranging from micrometers to below the diffraction limit (<250 nm) and lengths spanning up to hundreds of micrometers. The nanotubes were typically held taut between surface-bound vesicles suggesting high membrane tension, yet the lipid nanotubes exhibited a fluidic nature that enabled the transport of entrained vesicles. Confocal microscopy confirmed the uniform coating of streptavidin over the vesicles and nanotubes. Giant vesicles composed of lipid membranes of higher bending energy exhibited only aggregation in the presence of streptavidin. Routes toward the development of these highly curved membrane structures are discussed in terms of general protein-membrane interactions.     

An analytical solution for determination of small contact angles from sessile drops of arbitrary size

An analytical solution to the capillary equation of Young and Laplace is derived that allows determination of the static contact angle based on the volume of a sessile drop and the wetted area of the substrate. This solution does not require numerical integration to determine the drop profile and accounts for surface deformation due to gravitational effects. Calculation of the static contact angle by this method is remarkably simple and accurate when the contact angle is less than 30 degrees. A natural scaling arises in the solution, which provides indication of when a drop is small enough so as to neglect gravitational influences on the surface shape which, for small contact angles, is generally less than 1 microl. The technique described has the simplicity of the spherical cap approximation but remains accurate for any size of sessile drop.     

Carbon nanotube motors driven by carbon nanotube

We propose a new type of carbon nanotube (CNT) motor composed of a single-wall CNT (SWCNT) and a double-wall CNT (DWCNT), that are in mechanical contact. The rotational motion of our CNT motor is controllable by the translational motion of the SWCNT along the axis of the DWCNT. From molecular dynamics simulations, we show how our CNT motor can be driven in a controlled manner.     

Evaporation of pure liquid sessile and spherical suspended drops: a review

A sessile drop is an isolated drop which has been deposited on a solid substrate where the wetted area is limited by a contact line and characterized by contact angle, contact radius and drop height. Diffusion-controlled evaporation of a sessile drop in an ambient gas is an important topic of interest because it plays a crucial role in many scientific applications such as controlling the deposition of particles on solid surfaces, in ink-jet printing, spraying of pesticides, micro/nano material fabrication, thin film coatings, biochemical assays, drop wise cooling, deposition of DNA/RNA micro-arrays, and manufacture of novel optical and electronic materials in the last decades. This paper presents a review of the published articles for a period of approximately 120 years related to the evaporation of both sessile drops and nearly spherical droplets suspended from thin fibers. After presenting a brief history of the subject, we discuss the basic theory comprising evaporation of micrometer and millimeter sized spherical drops, self cooling on the drop surface and evaporation rate of sessile drops on solids. The effects of drop cooling, resultant lateral evaporative flux and Marangoni flows on evaporation rate are also discussed. This review also has some special topics such as drop evaporation on superhydrophobic surfaces, determination of the receding contact angle from drop evaporation, substrate thermal conductivity effect on drop evaporation and the rate evaporation of water in liquid marbles.