Simultaneous spreading and evaporation: recent developments

Spreading of aqueous surfactant solutions on oil substrates: Superspreaders vs non-superspreaders

HYPOTHESIS

The question of why aqueous solutions of some surfactants demonstrate a rapid spreading (superspreading) over hydrophobic solid substrates, while solutions of other similar surfactants do not, has no definitive explanation despite numerous previous studies. The suggested hypothesis for this study assumes that once the spreading coefficient of surfactant is positive, there is a concentration range for solutions of any surfactant which demonstrates rapid spreading. As it is impossible to calculate spreading coefficients for solid substrates, we compare the spreading performance of known superspreaders and non-superspreaders on liquid (oil) substrate.

EXPERIMENTS

The kinetics of spreading of aqueous solutions of a series of branched ionic surfactants and non-ionic trisiloxane surfactants on two liquid substrates was studied and compared with the spreading of a surfactant-free liquid, silicone oil. Both dynamic and equilibrium spreading coefficients were calculated using measured surface and interfacial tensions.

FINDINGS

There is no difference in spreading rate on liquid substrate between solutions of surfactants proven as superspreaders (while spreading on solid substrate) or non-superspreaders. A rapid spreading (superspreading) with the characteristic rate of spreading O(102-103) mm2/s occurs if the dynamic spreading coefficients exceeds the positive threshold value. If the dynamic spreading coefficient is negative or slightly positive, complete wetting still occurs, but the spreading is slow with the spreading rate is O(1) mm2/s. Spreading exponents for surfactant solutions in the rapid spreading regime are considerably larger than for the surfactant-free liquid. A number of spreading and dewetting patterns were observed depending on the surfactant type, its concentration and substrate.

Mathematical Modeling of the Evaporation of a Water Drop from a Heated Surface

This paper presents the results of mathematical modeling of the evaporation of a single water drop from the surface of a copper substrate using a new model, which does not require special experiments to close the system of equations and the corresponding boundary conditions with empirical constants. On the basis of the results of mathematical modeling, it was found that convective currents that occur in a small water drop (≤1 mm in diameter) do not significantly affect the characteristics or conditions of heat and mass transfer processes occurring in a liquid drop heated on a copper substrate. The results of numerical simulation showed that during the initial period of droplet heating, the latter undergoes a rapid transformation of the flow field. Five seconds after the beginning of the thermal action, a quasi-stationary regime of flows in the drop sets in. The model is tested on known experimental data. The theoretical analysis of temperatures at the characteristic points of a water drop and the surface on which the drop is located is carried out in ranges of thermal loads quite typical for practice, conditions for transferring heat and water vapor to the environment. According to the results of mathematical modeling, the possibility of using the developed model in the analysis of the state of cooling of surfaces heated to high temperatures, in cases typically used, is substantiated.

Droplet Spreading Characteristics on Ultra-Slippery Solid Hydrophilic Surfaces with Ultra-Low Contact Angle Hysteresis

Dynamic interactions of the droplet impact on a solid surface are essential to many emerging applications, such as electronics cooling, ink-jet printing, water harvesting/collection, anti-frosting/icing, and microfluidic and biomedical device applications. Despite extensive studies on the kinematic features of the droplet impact on a surface over the last two decades, the spreading characteristics of the droplet impact on a solid hydrophilic surface with ultra-low contact angle hysteresis are unclear. This paper clarifies the specific role of the contact angle and contact angle hysteresis at each stage of the droplet impact and spreading process. The spreading characteristics of the droplet impact on an ultra-slippery hydrophilic solid surface are systematically compared with those on plain hydrophilic, hydroxylated hydrophilic, and plain hydrophobic surfaces. The results reveal that the maximum spreading factor (βmax) of impacting droplets is mainly dependent on the contact angle and We. βmax increases with the increase in We and the decrease in the contact angle. Low contact angle hysteresis can decrease the time required to reach the maximum spreading diameter and the time interval during which the maximum spreading diameter is maintained when the contact angles are similar. Moreover, the effect of the surface inclination angle on the spreading and slipping dynamics of impacting droplets is investigated. With the increase in the inclination angle and We, the gliding distance of the impacting droplet becomes longer. Ultra-low contact angle hysteresis enables an impacting droplet to slip continuously on the ultra-slippery hydrophilic surface without being pinned to the surface. The findings of this work not only show the important role of the surface wettability in droplet spreading characteristics but also present a pathway to controlling the dynamic interactions of impacting droplets with ultra-slippery hydrophilic surfaces.

Pattern Formation upon Evaporation of Sessile Droplets of Polyelectrolyte/Surfactant Mixtures on Silicon Wafers

The formation of coffee-ring deposits upon evaporation of sessile droplets containing mixtures of poly(diallyldimethylammonium chloride) (PDADMAC) and two different anionic surfactants were studied. This process is driven by the Marangoni stresses resulting from the formation of surface-active polyelectrolyte-surfactant complexes in solution and the salt arising from the release of counterions. The morphologies of the deposits appear to be dependent on the surfactant concentration, independent of their chemical nature, and consist of a peripheral coffee ring composed of PDADMAC and PDADMAC-surfactant complexes, and a secondary region of dendrite-like structures of pure NaCl at the interior of the residue formed at the end of the evaporation. This is compatible with a hydrodynamic flow associated with the Marangoni stress from the apex of the drop to the three-phase contact line for those cases in which the concentration of the complexes dominates the surface tension, whereas it is reversed when most of the PDADMAC and the complexes have been deposited at the rim and the bulk contains mainly salt.

Wetting of Two-Component Drops: Marangoni Contraction Versus Autophobing

The wetting properties of multicomponent liquids are crucial to numerous industrial applications. The mechanisms that determine the contact angles for such liquids remain poorly understood, with many intricacies arising due to complex physical phenomena, for example, due to the presence of surfactants. Here, we consider two-component drops that consist of mixtures of vicinal alkanediols and water. These diols behave surfactant-like in water. However, the contact angles of such mixtures on solid substrates are surprisingly large. We experimentally reveal that the contact angle is determined by two separate mechanisms of completely different nature, namely, Marangoni contraction (hydrodynamic) and autophobing (molecular). The competition between these effects can even inhibit Marangoni contraction, highlighting the importance of molecular structures in physico-chemical hydrodynamics.

Evaporation of Sessile Droplets of Polyelectrolyte/Surfactant Mixtures on Silicon Wafers

The wetting and evaporation behavior of droplets of aqueous solutions of mixtures of poly(diallyldimethylammonium chloride) solution, PDADMAC, with two different anionic surfactants, sodium laureth sulfate, SLES, and sodium N-lauroyl N-methyl taurate, SLMT, were studied in terms of the changes of the contact angle θ and contact length L of sessile droplets of the mixtures on silicon wafers at a temperature of 25 °C and different relative humidities in the range of 30–90%. The advancing contact angle θa was found to depend on the surfactant concentration, independent of the relative humidity, with the mixtures containing SLES presenting improved wetting behaviors. Furthermore, a constant droplet contact angle was not observed during evaporation due to pinning of the droplet at the coffee-ring that was formed. The kinetics for the first evaporation stage of the mixture were independent of the relative humidity, with the evaporation behavior being well described in terms of the universal law for evaporation.

Evaporating droplets on inclined plant leaves and synthetic surfaces: Experiments and mathematical models

HYPOTHESIS

Evaporation of surfactant droplets on leaves is complicated due to the complex physical and chemical properties of the leaf surfaces. However, for certain leaf surfaces for which the evaporation process appears to follow the standard constant-contact-radius or constant-contact-angle modes, it should be possible to mimic the droplet evaporation with both a well-chosen synthetic surface and a relatively simple mathematical model.

EXPERIMENTS

Surfactant droplet evaporation experiments were performed on two commercial crop species, wheat and capsicum, along with two synthetic surfaces, up to a 90° incline. The time-dependence of the droplets' contact angles, height, volume and contact radius was measured throughout the evaporation experiments. Mathematical models were developed to simulate the experiments.

FINDINGS

With one clear exception, for all combinations of surfaces, surfactant concentrations and angles, the experiments appear to follow the standard evaporation modes and are well described by the mathematical models (modified Popov and Young-Laplace-Popov). The exception is wheat with a high surfactant concentration, for which droplet evaporation appears nonstandard and deviates from the diffusion limited models, perhaps due to additional mechanisms such as the adsorption of surfactant, stomatal density or an elongated shape in the direction of the grooves in the wheat surface.

The Impact of Nanofluids on Droplet/Spray Cooling of a Heated Surface: A Critical Review

Cooling by impinging droplets has been the subject of several studies for decades and still is, and, in the last few years, the potential heat transfer enhancement obtained thanks to nanofluids’ use has received increased interest. Indeed, the use of high thermal conductivity fluids, such as nanofluids’, is considered today as a possible way to strongly enhance this heat transfer process. This enhancement is related to several physical mechanisms. It is linked to the nanofluids’ rheology, their degree of stabilization, and how the presence of the nanoparticles impact the droplet/substrate dynamics. Although there are several articles on droplet impact dynamics and nanofluid heat transfer enhancement, there is a lack of review studies that couple these two topics. As such, this review aims to provide an analysis of the available literature dedicated to the dynamics between a single nanofluid droplet and a hot substrate, and the consequent enhancement or reduction of heat transfer. Finally, we also conduct a review of the available publications on nanofluids spray cooling. Although using nanofluids in spray cooling may seem a promising option, the few works present in the literature are not yet conclusive, and the mechanism of enhancement needs to be clarified.

Bioinspired Integrative Surface with Hierarchical Texture and Wettable Gradient-Driven Water Collection

At present, collecting water directly from the atmosphere has become an effective means to solve the growing shortage of fresh water. Inspired by the structures of trichomes (hairs) of Sarracenia to capture fog and transport water, a series of different high-low rib-like hierarchical texture surfaces were prepared based on the laser method. These surfaces have gradient superwetting and adhesion because of the differences in subsequent preparation methods. In addition, this work discusses the effect of the above performance differences on the efficiency of fog collection and the surface condensation characteristics during fog collection. The results show that the surface of the laser-prepared sample with the mixing unit combination has more efficient fog collection efficiency and droplet removal rate. After 30 min, the amount of drip measured in the atmospheric environment is 8.4 times that of the polished surface. This indicates that the multihierarchical textured surface and superhydrophobicity are essential for improving the droplet removal rate and coagulation efficiency.

Droplet Shape and Wetting Behavior under the Influence of Cyclically Changing Humidity

Relative humidity (RH) plays a crucial role in wetting and spreading phenomena by affecting the evaporation rate, evaporation modes, and spreading dynamics via precursor film formation, surface modification, and surface tension alteration. We examined the effect of the periodically varied relative humidity (RH) between low (20%) and high (85%) levels on the wetting of the droplet of nonhygroscopic (pure surfactants) and hygroscopic (ethylene glycol, glycerol) liquids on a hydrophobic surface. It was revealed that the changing RH induces two modes of transition between the wetting states of the droplet: with hysteresis and without hysteresis. Droplets of both nonhygroscopic and hygroscopic liquids exhibit shape hysteresis during the first cycle: (i) droplets of surfactants irreversibly spread saving an initial volume; and (ii) ethylene glycol and glycerol droplets irreversibly absorb the moisture, increasing the volume and the base diameter. Further, cyclically changing the RH results in the droplet breathing effect, i.e., the nonhysteresis transition of the droplet shape between two wetting states corresponding to the minimum and maximum RH levels. In the case of the glycerol droplet for three cycles of the RH variation, the volume hysteresis (the droplet volume increases in each cycle) was observed. This is determined by the moisture absorption due to high hygroscopicity of glycerol. We also revealed that for all liquids studied, the droplet spreading at each increase in RH started at reaching the RH threshold level.

Droplet desorption modes at high heat flux

Nonisothermal droplet desorption of aqueous salt solution H2O/LiBr during nucleate boiling was studied experimentally. A droplet was placed on a horizontal heated wall. The initial concentration of salt C0= 25 %. The wall temperature Tw= 120 °C and ambient air pressure is 1 bar. Thermal images of the temperature field on the droplet surface show an extremely non-uniform temperature field. At nucleate boiling in LiBr salt solution it is incorrect to predict the desorption behavior in stationary approximation. It was previously believed that the rate of evaporation does not vary with time. For the first time it is shown that the desorption rate is divided into several characteristic time intervals. These intervals is characterized by a significant change in the desorption rate.

Mathematical Modeling of Diffusion of a Hydrophilic Ionic Fertilizer in Plant Cuticles: Surfactant and Hygroscopic Effects

The agricultural industry requires improved efficacy of sprays being applied to crops and weeds to reduce their environmental impact and increase financial returns. One way to improve efficacy is by enhancing foliar penetration. The plant leaf cuticle is the most significant barrier to agrochemical diffusion within the leaf. The importance of a mechanistic mathematical model has been noted previously in the literature, as each penetration experiment is dictated by its specific parameters, namely plant species, environmental conditions such as relative humidity and spray formulation including adjuvant addition. A mechanistic mathematical model has been previously developed by the authors, focusing on plant cuticle diffusion of calcium chloride through tomato fruit cuticles including pore swelling, ion binding and evaporation, along with the ability to vary the active ingredient concentration and type, relative humidity and plant species. Here we further develop this model to include adjuvant effects as well as the hygroscopic nature of deliquescent ionic solutions with evaporation on the cuticle surface. These modifications to a penetration and evaporation model provide a novel addition to the literature and allow the model to be applied to many types of evaporating ionic hygroscopic solutions on many types of substrates, not just plant cuticles. We validate our theoretical model results against appropriate experimental data, discuss key sensitivities and relate theoretical predictions to physical mechanisms. The important governing mechanisms influencing surfactant enhanced penetration of ionic active through plant cuticles were found to be aqueous pore radius, pore density, cuticle thickness and initial contact angle of the applied droplet; ion binding, relative humidity and evaporation including hygroscopic water absorption parameters for point of deliquescence. The sensitivity analysis indicated surfactants increase penetration by changing the point of deliquescence of a solution, which alters the water absorption and the initial contact angle, which alters the number of pores under the droplet. The results of the validation and sensitivity analysis imply that this model accounts for many of the mechanisms governing penetration in plant cuticles.

Evaporation dynamics of a sessile droplet on glass surfaces with fluoropolymer coatings: focusing on the final stage of thin droplet evaporation

The evaporation dynamics of a water droplet with an initial volume of 2 μl from glass surfaces with fluoropolymer coatings are investigated using the shadow technique and an optical microscope. The droplet profile for a contact angle of less than 5° is constructed using an image-analyzing interference technique, and evaporation dynamics are investigated at the final stage. We coated the glass slides with a thin film of a fluoropolymer by the hot-wire chemical vapor deposition method at different deposition modes depending on the deposition pressure and the temperature of the activating wire. The resulting surfaces have different structures affecting the wetting properties. Droplet evaporation from a constant contact radius mode in the early stage of evaporation was found followed by the mode where both contact angle and contact radius simultaneously vary in time (final stage) regardless of wettability of the coated surfaces. We found that depinning occurs at small contact angles of 2.2-4.7° for all samples, which are smaller than the measured receding contact angles. This is explained by imbibition of the liquid into the developed surface of the "soft" coating that leads to formation of thin droplets completely wetting the surface. The final stage, which is little discussed in the literature, is also recorded. We have singled out a substage where the contact line velocity is abruptly increasing for all coated and uncoated surfaces. The critical droplet height corresponding to the transition to this substage is about 2 μm with R/h = 107. The duration of this substage is the same for all coated and uncoated surfaces. Droplets observed at this substage for all the tested surfaces are axisymmetric. The specific evaporation rate clearly demonstrates an abrupt increase at the final substage of the droplet evaporation. The classical R² law is justified for the complete wetting situation where the droplet is disappearing in an axisymmetric manner.

Sessile nanofluid droplet can act like a crane

Interactive droplet systems form the backbone for emerging avenues in droplet based technologies like cell sorting, inkjet printing and digital microfluidics, to name a few. These and their associated fields have gained significant importance in the recent times. Here, we report one such phenomenon wherein a naturally evaporating nanocolloidal sessile droplet interacts with a porous silica gel bead to mimic a macro scale mechanical crane assembly. Precisely, we show a sequence of events displayed by the particle laden aqueous droplet (nanoparticles of silica at different loading rates placed on a hydrophobic substrate) when brought in contact with a meso-porous silica gel bead. First, preferential self-assembly along droplet-bead interface is followed by formation of an adhesive bond. The phenomenon continues until the evaporating droplet naturally lifts the bead. The kinematics of the lift mechanism can be represented by a simple four bar linkage. This work provides insights into interactions between droplets and freely placed porous objects across multiple spatio-temporal scales. Present study should not just motivate researchers to design interactive droplet based systems but also use the same to perform engineering tasks like the crane action.

Recent advances in droplet wetting and evaporation

Wetting and evaporation of a simple sessile droplet is a very complex problem involving strongly coupled physics.

Confinement-induced alterations in the evaporation dynamics of sessile droplets

Evaporation of sessile droplets has been a topic of extensive research. However, the effect of confinement on the underlying dynamics has not been well explored. Here, we report the evaporation dynamics of a sessile droplet in a confined fluidic environment. Our findings reveal that an increase in the channel length delays the completion of the evaporation process and leads to unique spatio-temporal evaporation flux and internal flow. The evaporation modes (constant contact angle and constant contact radius) during the droplet lifetime however exhibit global similarity when normalized by appropriate length and timescales. These results are explained in light of an increase in vapor concentration inside the channel due to greater accumulation of water vapor on account of increased channel length. We have formulated a theoretical framework which introduces two key parameters namely an enhanced concentration of the vapor field in the vicinity of the confined droplet and a corresponding accumulation lengthscale over which the accumulated vapor relaxes to the ambient concentration. Using these two parameters and modified diffusion based evaporation we are able to show that confined droplets exhibit a universal behavior in terms of the temporal evolution of each evaporation mode irrespective of the channel length. These results may turn out to be of profound importance in a wide variety of applications, ranging from surface patterning to microfluidic technology.

Kinetic effects regularize the mass-flux singularity at the contact line of a thin evaporating drop

We consider the transport of vapour caused by the evaporation of a thin, axisymmetric, partially wetting drop into an inert gas. We take kinetic effects into account through a linear constitutive law that states that the mass flux through the drop surface is proportional to the difference between the vapour concentration in equilibrium and that at the interface. Provided that the vapour concentration is finite, our model leads to a finite mass flux in contrast to the contact-line singularity in the mass flux that is observed in more standard models that neglect kinetic effects. We perform a local analysis near the contact line to investigate the way in which kinetic effects regularize the mass-flux singularity at the contact line. An explicit expression is derived for the mass flux through the free surface of the drop. A matched-asymptotic analysis is used to further investigate the regularization of the mass-flux singularity in the physically relevant regime in which the kinetic timescale is much smaller than the diffusive one. We find that the effect of kinetics is limited to an inner region near the contact line, in which kinetic effects enter at leading order and regularize the mass-flux singularity. The inner problem is solved explicitly using the Wiener-Hopf method and a uniformly valid composite expansion is derived for the mass flux in this asymptotic limit.

Predictive Model for the Meniscus-Guided Coating of High-Quality Organic Single-Crystalline Thin Films

A model that describes solvent evaporation dynamics in meniscus-guided coating techniques is developed. In combination with a single fitting parameter, it is shown that this formula can accurately predict a processing window for various coating conditions. Organic thin-film transistors (OTFTs), fabricated by a zone-casting setup, indeed show the best performance at the predicted coating speeds with mobilities reaching 7 cm² V^-1 s^-1 .

Interfacial phenomena at a surface of individual and complex fumed nanooxides

Investigations of interfacial and temperature behaviors of nonpolar and polar adsorbates interacting with individual and complex fumed metal or metalloid oxides (FMO), initial and subjected to various treatments or chemical functionalization and compared to such porous adsorbents as silica gels, precipitated silica, mesoporous ordered silicas, filled polymeric composites, were analyzed. Complex nanooxides include core-shell nanoparticles, CSNP (50-200nm in size) with titania or alumina cores and silica or alumina shells in contrast to simple and smaller nanoparticles of individual FMO. CSNP could be destroyed under high-pressure cryogelation (HPCG) or mechanochemical activation (MCA). These treatments affect the structure of aggregates of nanoparticles and agglomerates of aggregates, resulting in their becoming more compacted. The analysis shows that complex FMO could be more sensitive to external actions than simple nanooxides such as fumed silica. Any treatment of 'soft' FMO affects the interfacial and temperature behaviors of polar and nonpolar adsorbates. Rearrangement of secondary particles and surface functionalization affects the freezing-melting point depression of adsorbates. For some adsorbates, open hysteresis loops became readily apparent in adsorption-desorption isotherms. Clustering of adsorbates bound in textural pores in aggregates of nanoparticles (i.e., voids between nanoparticles in secondary structures) causes reduced changes in enthalpy during phase transitions (freezing, fusion, evaporation). Freezing point depression and melting point elevation cause significant hysteresis freezing-melting effects for adsorbates bound to FMO in the textural pores. Relaxation phenomena for both low- and high-molecular weight adsorbates or filled polymeric composites are affected by the morphology of primary particles, structural organization of secondary particles of differently treated or functionalized FMO, content of adsorbates, co-adsorption order, and temperature.

Towards universal buckling dynamics in nanocolloidal sessile droplets: the effect of hydrophilic to superhydrophobic substrates and evaporation modes

The evaporation of a nanocolloidal sessile droplet exhibits preferential particle assembly, nanoporous shell formation and buckling to form cavities with unique morphological features. Here, we have established many universal trends that explain the buckling dynamics under one umbrella irrespective of hydrophobicity, evaporation mode and particle loading. We provide a regime map explaining the droplet morphology and buckling characteristics for droplet evaporation on various substrates. Specifically, we find that the final droplet volume and the radius of curvature at the buckling onset are universal functions of particle concentration. Furthermore, we establish that post-buckling cavity growth is evaporation driven regardless of the substrate.

Stick-Jump (SJ) Evaporation of Strongly Pinned Nanoliter Volume Sessile Water Droplets on Quick Drying, Micropatterned Surfaces

We present an experimental study of stick-jump (SJ) evaporation of strongly pinned nanoliter volume sessile water droplets drying on micropatterned surfaces. The evaporation is studied on surfaces composed of photolithographically micropatterned negative photoresist (SU-8). The micropatterning of the SU-8 enables circular, smooth, trough-like features to be formed which causes a very strong pinning of the three phase (liquid-vapor-solid) contact line of an evaporating droplet. This is ideal for studying SJ evaporation as it contains sequential constant contact radius (CCR) evaporation phases during droplet evaporation. The evaporation was studied in nonconfined conditions, and forced convection was not used. Micropatterned concentric circles were defined having an initial radius of 1000 μm decreasing by a spacing ranging from 500 to 50 μm. The droplet evaporates, successively pinning and depinning from circle to circle. For each pinning radius, the droplet contact angle and volume are observed to decrease quasi-linearly with time. The experimental average evaporation rates were found to decrease with decreasing pining radii. In contrast, the experimental average evaporation flux is found to increase with decreasing droplet radii. The data also demonstrate the influence of the initial contact angle on evaporation rate and flux. The data indicate that the total evaporation time of a droplet depends on the specific micropattern spacing and that the total evaporation time on micropatterned surfaces is always less than on flat, homogeneous surfaces. Although the surface patterning is observed to have little effect on the average droplet flux-indicating that the underlying evaporation physics is not significantly changed by the patterning-the total evaporation time is considerably modified by patterning, up to a factor or almost 2 compared to evaporation on a flat, homogeneous surface. The closely spaced concentric circle pinning maintains a large droplet radius and small contact angle from jump to jump; the result is a large evaporation rate leading to faster evaporation.

Control of stain geometry by drop evaporation of surfactant containing dispersions

Control of stain geometry by drop evaporation of surfactant containing dispersions is an important topic of interest because it plays a crucial role in many applications such as forming templates on solid surfaces, in ink-jet printing, spraying of pesticides, micro/nano material fabrication, thin film coatings, biochemical assays, deposition of DNA/RNA micro-arrays, and manufacture of novel optical and electronic materials. This paper presents a review of the published articles on the diffusive drop evaporation of pure liquids (water), the surfactant stains obtained from evaporating drops that do not contain dispersed particles and deposits obtained from drops containing polymer colloids and carbon based particles such as carbon nanotubes, graphite and fullerenes. Experimental results of specific systems and modeling attempts are discussed. This review also has some special subtopics such as suppression of coffee-rings by surfactant addition and "stick-slip" behavior of evaporating nanosuspension drops. In general, the drop evaporation process of a surfactant/particle/substrate system is very complex since dissolved surfactants adsorb on both the insoluble organic/inorganic micro/nanoparticles in the drop, on the air/solution interface and on the substrate surface in different extends. Meanwhile, surfactant adsorbed particles interact with the substrate giving a specific contact angle, and free surfactants create a solutal Marangoni flow in the drop which controls the location of the particle deposition together with the rate of evaporation. In some cases, the presence of a surfactant monolayer at the air/solution interface alters the rate of evaporation. At present, the magnitude of each effect cannot be predicted adequately in advance and consequently they should be carefully studied for any system in order to control the shape and size of the final deposit.

Effect of particle geometry on triple line motion of nano-fluid drops and deposit nano-structuring

We illustrate the importance of particle geometry on droplet contact line pinning, 'coffee-stain' formation and nano-structuring within the resulting rings. We present the fundamentals of pure liquid droplet evaporation and then discuss the effect of particles on the evaporation process. The resulting coffee-stain patterns and particle structuring within them are presented and discussed. In the second part, we turn our attention to the effect of particle geometry on the evaporation process. A wide range of particle shapes, categorised according to aspect ratio, from the simple shape of a sphere to the highly irregular shapes of platelets and tubes is discussed. Particle geometry effect on evaporation behaviour was quantified in terms of change in contact angle and contact radius for the stick-slip cases. Consequently the hysteretic energy barrier pinning the droplets was estimated, showing an increasing trend with particle aspect ratio. The three-phase contact line (TL) motion kinetics are complemented with analysis of the nano-structuring behaviour of each shape, leading to the identification of the two main parameters affecting nanoparticle self-assembly behaviour at the wedge. Flow velocity and wedge constraints were found to have antagonist effects on particle deposition, although these varied with particle shape. This description should help in understanding the drying behaviour of more complex fluids. Furthermore, knowing the fundamentals of this simple and inexpensive surface patterning technique should permit its tailoring to the needs of many potential applications.

Hysteresis of Contact Angle of Sessile Droplets on Smooth Homogeneous Solid Substrates via Disjoining/Conjoining Pressure

A theory of contact angle hysteresis of liquid droplets on smooth, homogeneous solid substrates is developed in terms of the shape of the disjoining/conjoining pressure isotherm and quasi-equilibrium phenomena. It is shown that all contact angles, θ, in the range θr < θ < θa, which are different from the unique equilibrium contact angle θ ≠ θe, correspond to the state of slow "microscopic" advancing or receding motion of the liquid if θe < θ < θa or θr < θ < θe, respectively. This "microscopic" motion almost abruptly becomes fast "macroscopic" advancing or receding motion after the contact angle reaches the critical values θa or θr, correspondingly. The values of the static receding, θr, and static advancing, θa, contact angles in cylindrical capillaries were calculated earlier, based on the shape of disjoining/conjoining pressure isotherm. It is shown now that (i) both advancing and receding contact angles of a droplet on a on smooth, homogeneous solid substrate can be calculated based on shape of disjoining/conjoining pressure isotherm, and (ii) both advancing and receding contact angles depend on the drop volume and are not unique characteristics of the liquid-solid system. The latter is different from advancing/receding contact angles in thin capillaries. It is shown also that the receding contact angle is much closer to the equilibrium contact angle than the advancing contact angle. The latter conclusion is unexpected and is in a contradiction with the commonly accepted view that the advancing contact angle can be taken as the first approximation for the equilibrium contact angle. The dependency of hysteresis contact angles on the drop volume has a direct experimental confirmation.

Evaporation of droplets on strongly hydrophobic substrates

The manner in which the extreme modes of droplet evaporation (namely, the constant contact radius and the constant contact angle modes) become indistinguishable on strongly hydrophobic substrates is described. Simple asymptotic expressions are obtained which provide good approximations to the evolutions of the contact radius, the contact angle, and the volume of droplets evaporating in the extreme modes for a wide range of hydrophobic substrates. As a consequence, on strongly hydrophobic substrates it is appropriate to use the so-called "2/3 power law" to extrapolate the lifetimes of droplets evaporating in the constant contact radius mode as well as in the constant contact angle mode.