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The evaporation of sessile droplets has wide applications in various industrial fields. Therefore, it is important to accurately predict the temporal evolution behavior of sessile droplets during e...

Experiments on measuring the rate of evaporation of liquid sessile droplets into air show that the rate of evaporation increases in the presence of forced convection flows. However, data on the effect of convection on evaporation are often contradictory and should be clarified. The paper presents a numerical analysis of evaporation from the surface of a water droplet subjected to forced convection in the gas phase. The drop is located on a smooth horizontal isothermal substrate; the mode with constant contact angle is considered. The shape of the drop has axial symmetry, the same for the velocities and pressure. Forced convection compatible with the symmetry conditions are represented by flows directed downward along the axis of the system and diverging along the sides near the drop and the substrate. The mathematical model is constructed for evaporation controlled by diffusion in the gas phase and takes into account surface tension, gravity, and viscosity in both media, buoyancy and Marangoni convection. The results indicate the existence of the mutual influence of liquid and gaseous media. Thus, a drop vibrates under the influence of movements in the atmosphere, which generates a density wave in the gas: the drop «sounds». The magnitude of the velocity in a liquid is 50 times less than the characteristic velocity in air. It is found that the evaporation rate does not change in the presence of forced convection flows, which contradicts most of the experimental works. The reason for the discrepancies is supposed to be the appearance of nonequilibrium conditions at the boundary of the condensed phase: under these conditions, the evaporation regime ceases to be diffusional.

Evaporation of sessile droplets on the surface of plant leaves is a process that frequently occurs during plant growth as well as postharvest processes. Evaporation-driven internal flows within sessile droplets can transport microorganisms near the leaf surface, facilitating their adhesion to surface microstructures such as trichomes, and infiltration into available openings such as stomata and grooves. A mechanistic model for this retention and infiltration pathway was developed. Solution domain is a sessile droplet located on a leaf surface, as well as its surrounding gas. The model includes fluid flow within the droplet and gas phases, gas-water interface tracking, heat transfer, transport of vapor in gas, and transport of sugar and bacteria within water. The model results are validated based on available literature data and experimental images. The results showed that a hydrophilic surface would promote bacterial retention and infiltration. Evaporation-driven flows increase concentration of bacteria around or inside microstructures at the leaf surface, facilitating their adhesion and infiltration. Larger microstructures having wider spacing between them increased the retention. A higher evaporation rate led to higher infiltration. Chemotaxis toward nutrients at the leaf surface and random motility were shown to decrease the retention and infiltration during evaporation.

Convection in a sessile droplet of water in a laminar air flow was studied. The experiments were conducted in the air velocity range $$U_{1}=2$$ –5 m/s. The experimental data are compared with approximate numerical solutions and an approximate analytic solution made for small numbers Re for both the liquid and gas phase. It has been shown experimentally and theoretically that the maximum velocity in the droplet is proportional to the air velocity to the power of 1.5 and the droplet radius to the power of 0.5. An explanation of the fact that the experimental data are up to 50 times as small as the theoretical calculations has been suggested for the first time. The obtained dependencies may be useful for modeling the behavior of droplets in a spray.

The contact angle and static equilibrium of the triple contact line of a sessile droplet are investigated. New wetting equations are derived by minimising the total potential energy of the droplet....

Surface temperature is a critical factor affecting the droplet evaporation; however, it is a continuous matter under discussion. We design controllable experiments for sessile ethanol droplet evaporation to investigate the surface temperature distribution evolution. It is found that the evaporation process of a droplet with a constant contact radius can involve five phases: non-wave phase, onset of thermal waves, decrease of thermal waves, transition phase, and final non-wave phase. Under fixed evaporation conditions and a fixed substrate temperature, the phase sequence is solely dependent on the instantaneous contact angle, but independent of the droplet initial volume. Three typical radial temperature distributions are observed at the evaporating droplet surface: a monotonic decrease from the edge to the apex; a nonmonotonic distribution with the highest temperature observed between the edge and the apex; or a monotonic increase from the edge to the apex. The three temperature distributions and the two transitions between them are responsible for the five phases in the evaporation process. However, the early phases may not exist in the sessile droplet with a relatively small initial contact angle. Both the evaporation pressure and the substrate temperature can affect the occurrence of the five phases in the evaporation process. It is noteworthy that the splitting and merging of thermal waves occur simultaneously during evaporation. During the decrease of the thermal waves phase, the number of waves decreases linearly with the contact angle tangent. The decreasing slope is influenced by the evaporation pressure and the substrate temperature. Agency for Science, Technology and Research (A*STAR) The authors would like to thank Agency of Science, Technology and Research (A*STAR), Individual Research Grant (IRG), grant number A1783c0006 for the financial support

The evaporation of a drop deposited on a heated substrate is a complex process, which combines several phenomena such as the Marangoni effect, mass and thermal transfers, etc. We developed, in this paper, a mathematical model and a numerical simulation code used to carry out an in-depth study about the evaporation of a drop deposited on a heated substrate surrounded by air. This numerical study was supported by experimental work. The numerical findings obtained showed the existence of a condensation phenomenon for certain configurations. At the beginning of the experiment, the evaporation started at the triple point. However, a local region of the interface remained relatively cold. In this region, the concentration gradient (Cv, Csat) directed from the liquid-gas interface to the air resulted in condensation of water steam. Although this phenomenon is temporary and visible only at the start of evaporation process, its study makes it possible to better understand and optimize the evaporation kinetics.

I nyere tid har manipulering av nanopartikler på nanoskala blitt et tema av stor interesse blant det vitenskapelige miljøet. Fordelene ved å bruke SAW representerer et stort fremskritt innen felt som biomedisin eller biosensorer. Utviklingen av disse teknikkene er faktisk relatert til fremskrittene som er oppnådd innen mikrofluidikkvitenskapen. Av denne grunn blir kunnskapen om fysikken som råder i håndteringen av små partikler noe vesentlig. Dette prosjektet ønsker å komme videre i forståelsen av fysikk bak og diskutere effektene produsert av kreftene involvert i samspillet med nanopartikler på nanoskala. For det formål sammenligner eksperimentene som er utført de oppnådde resultatene med de som ble gjort av andre grupper av forskere og later til å kaste lys over hullene som er identifisert i den relaterte litteraturen. I denne forbindelse forsøkes det å finne svar på hvordan en endring i for eksempel overflatespenning, kontaktvinkelen til dråpen med underlaget, viskositeten og væskens tetthet påvirker partiklenes bevegelse. Bruken av SAW innebærer utvikling av en spesifikk enhet som kan kanalisere bølgen til den aktuelle overflaten, denne enheten kalles interdigital transducer IDT. En SAW er den akustiske bølgen som produseres av IDT når en elektrisk strøm påføres elektrodene. Takket være den piezoelektriske effekten av substratet der IDT er plassert, blir det elektriske signalet til en akustisk bølge som samhandler med overflaten til dråpen og forårsaker at det dannes et akustisk felt i den. Med den hensikt å bevise de forutsagte hendelsene som finner sted inne i vanndråpen når den er underlagt SAW, produseres forskjellige typer IDT-er som kan operere ved forskjellige frekvenser. Andre parametere som inngangseffekt, frekvens eller partikkeldiameter vurderes også for å evaluere de involverte kreftene ved håndtering av nanopartikler inne i den fastsittende vanndråpen. Kombinasjonen av disse forskjellige parameterne påvirker direkte bevegelsen av partiklene inne i dråpen og reiser følgende spørsmål. For eksempel genererer samspillet mellom SAW og dråpen når den forplanter seg langs substratet tre kjente forskjellige typer krefter inne i dråpen. Den akustiske strømningskraften ASF oppsto fra forplantningen av den akustiske bølgen, den akustiske strålingskraften ARF og sentrifugalkraften Fc oppsto som en konsekvens av lekkasjen av den forplantede SAW over underlaget. Slik sett blir disse kreftene oppfattet av partiklene som oppstår en bevegelse rundt dråpen de er nedsenket i og danner forskjellige bevegelsesmønstre som studeres i dette prosjektet. På den annen side, slik det er beskrevet i litteraturen, er disse kreftene nært knyttet til partikkeldiameteren, frekvensen og inngangseffekten som påføres IDT. I denne venen ble forskjellige partikkelstørrelser 7 µm og 1 µm av polystyrennanopartikler nedsenket i et 2 µL dråpevannvolum testet og fire forskjellige IDT-er med varierende nominelle frekvenser 20,40,80 og 160 MHz ble produsert. In recent times, the manipulation of nanoparticles at nanoscale has become a topic of great interest among the scientific community. The advantages of using SAW represent a great advance in fields such as biomedicine or biosensors. The develop of these techniques is actually related with the advances achieved in the microfluidics science. For this reason, the knowledge of the physics that prevails in the handling of tiny size particles becomes something essential. This project wants to advance in the understanding of physics behind and discuss the effects produced by the forces involved in the interaction with nanoparticles at nanoscale. For that purpose, the experiments carried out compare the obtained results with those which were made by other groups of researchers and pretends to shed light on the gaps identified in the related literature. In this regard, an attempt is made to find an answer to how a change in, for example, surface tension, the contact angle of the drop with the substrate, the viscosity and the density of the fluid affects the movement of the particles. The use of SAW implies the development of a specific device that can channel the wave to the surface in question, this device is called interdigital transducer IDT. A SAW is the acoustic wave produced by the IDT when an electric current is applied to its electrodes. Thanks to the piezoelectric effect of the substrate where the IDT is located, the electrical signal becomes into an acoustic wave that interacts with the surface of the droplet causing an acoustic field to be created within it. With the intention of proving the predicted events that take place inside the water droplet when it is subdue to the SAW, diverse types of IDTs able to operate at different frequencies are produced. Other parameters like the input power, frequency or the particles diameter are considered also to evaluate the involved forces when handling nanoparticles inside the sessile water droplet. The combination of these different parameters directly affects the movement of the particles inside the droplet and raises the following questions. For instance, the interaction of the SAW with the droplet when it propagates along the substrate generates three known distinct types of forces inside the droplet. The acoustic streaming force ASF emerged from the propagation of the acoustic wave, the acoustic radiation force ARF and the centrifugal force Fc arisen as a consequence of the leakage of the propagated SAW over the substrate. In this sense, these forces are perceived by the particles arising a movement around the droplet in which they are immersed and forming different patterns of movement which are studied in this project. On the other hand, as it has been described in the literature, these forces are closely related with the particle diameter, the frequency and the input power applied to the IDT. In this vein, different particles sizes 7 µm and 1 µm of polystyrene nanoparticles immersed in a 2 µL droplet water volume were tested and four different IDTs with varying nominal frequencies 20,40,80 and 160 MHz are produced.

In humid environments, the formation of sessile droplets containing pollutants, such as sodium chloride, on certain materials can lead to atmospheric corrosion phenomena. The prediction and understanding of these corrosion phenomena are closely linked to the dynamics of the droplet, and in particular to its evaporation. Ambient parameters such as relative humidity, temperature, substrate material as well as the composition of the droplet, e.g. its pollutant concentration, modify the evaporation dynamics and influence the characteristic time of corrosion. Salt deposits left after evaporation show complex hydrodynamics and indicate potential corrosion sites. Anticipating corrosion zones is crucial in many industrial applications to limit material degradation. This study seeks to better understand the evaporation dynamics of sessile droplets,through parametric studies, with numerical simulations and experimental tests. Pure water droplets are first considered, in order to simplify the studied system and to analyze the different modes. Droplets of saline solution are studied in a second time. During evaporation, salt concentrates inhomogeneously inside the droplet causing surface tension gradients. These stresses along the interface, called Marangoni stresses, give rise to internal flows. Depending on the initial concentration of pollutant, the relative humidity, and the size of the droplet, the morphology of the resulting salt deposits is analyzed., Polluants, comme le chlorure de sodium, sur certains matériaux peut conduire à des phénomènes de corrosion atmosphérique. La prédiction et la compréhension de ces phénomènes de corrosion sont étroitement liées à la dynamique de la goutte, et notamment à l’évaporation de celle-ci. Les paramètres ambiants comme l’humidité relative, la température, le matériau du substrat ainsi que la composition de la goutte, par exemple sa concentration en polluant, modifient la dynamique d’évaporation et influencent le temps caractéristique de la corrosion. Les dépôts laissés après évaporation témoignent d’une hydrodynamique complexe et indiquent les potentiels sites de corrosion. Anticiper les zones de corrosion se révèle crucial dans de nombreuses applications industrielles pour limiter la dégradation des matériaux. Cette étude cherche à mieux comprendre la dynamique d’évaporation des gouttes sessiles, à travers des études paramétriques, avec des simulations numériques et des essais expérimentaux. Des gouttes d’eau pure sont considérées dans un premier temps, afin de simplifier le système étudié et d’analyser les différents modes. Des gouttes de solution saline sont étudiées dans un second temps. Lors de l’évaporation le sel se concentre de façon non homogène à l’intérieur de la goutte entraînant des gradients de tension de surface. Ces contraintes le long de l’interface, dites de Marangoni, donnent naissance à des écoulements internes. En fonction de la concentration initiale en polluant, de l’humidité relative, et de la taille de la goutte la morphologie des dépôts salins qui en résulte est analysée.

The droplet phase transition process on the cold surface of a T300 carbon fiber substrate was studied by observing the droplet freezing process. Through the construction of visualized experimental device, the change in the droplet phase transition time under different experimental conditions, the progression of the solid–liquid interface during the phase transition process, the droplet deformation rate, and the ratio of growth of the interface height after the phase interface appears were experimentally obtained. The influence of different surface temperatures and different droplet volumes on the phase transition process was investigated. The experimental results show that the phase interface shows an irregular profile during the phase transition of the sessile droplet on the cold surface of the carbon fiber substrate; it presents a wave shape early and a smooth concave shape later. The influence of droplet volume on the phase transition time is not a proportional relationship. The height of the solid–liquid phase interface during the droplet phase transition process first grows rapidly, then slowly, and then fast once again. In other words, the growth rate of the phase interface is relatively fast when the phase transition has just occurred and then when the bulged tip is formed. At different cold surface temperatures, the droplet deformation rate with a volume of 10 µL on the carbon fiber substrate is basically the same, which is about 32.4%, within an uncertainty of about 1%, and it is higher than the contrast substrate. However, the influence of gravity factor is important in determining the droplet deformation rate for different droplet volumes.

Digital microfluidics based on sessile droplets has emerged as a promising technology for various applications including biochemical assays, clinical diagnostics, and drug screening. Digital microfluidic platforms provide an isolated microenvironment to prevent cross-contamination and require reduced sample volume. Despite these advantages, the droplet-based technology has the inherent limitation of the quiescent flow conditions at low Reynolds number, which causes mixing samples confined within the droplets to be challenging. Recently, solutal Marangoni flows induced by volatile liquids have been utilized for sessile droplet mixing to address the above-mentioned limitation. The volatile liquid vaporized near a sessile droplet induces a surface tension gradient throughout the droplet interface, leading to vortical flows inside a droplet. This Marangoni flow-based droplet mixing method does not require an external energy source and is easy to operate. However, this passive method requires a comparably long time of a few tens of seconds for complete mixing since it depends on the natural evaporation of the volatile liquid. Here, we propose an improved ultrasound-induced heating method based on a nature-inspired ultrasound-absorbing layer and apply it to enhance solutal Marangoni effect. The heater consists of an interdigital transducer deposited on a piezoelectric substrate and a silver nanowire-polydimethylsiloxane composite as an ultrasound-absorbing layer. When the transducer is electrically actuated, surface acoustic waves are produced and immediately absorbed in the composite layer by viscoelastic wave attenuation. The conversion from acoustic to thermal energy occurs, leading to rapid heating. The heating-mediated enhanced vaporization of a volatile liquid accelerates the solutal Marangoni flows and thus enables mixing high-viscosity droplets, which is unachievable by the passive solutal Marangoni effect. We theoretically and experimentally investigated the enhanced Marangoni flow and confirmed that rapid droplet mixing can be achieved within a few seconds. The proposed heater-embedded sessile droplet mixing platform can be fabricated in small size and easily integrated with other digital microfluidic platforms. Therefore, we expect that the proposed sample mixing method can be utilized for various applications in digital microfluidics and contribute to the advancements in the medical and biochemical fields.

In this work, the interaction between a sessile droplet’s contact angle and a quartz crystal microbalance (QCM) is elucidated. We differentiate the QCM’s frequency response to changes in the droplet contact area from variations in the dynamic contact angle. This is done by developing a computational model that couples the electrical and mechanical analysis of the quartz substrate with the visco-acoustic behavior of the sessile droplet. From our analysis, we conclude that changes in the contact angle have an effect on the frequency response of the QCM when the droplet height is on the order of the viscous decay length or smaller. On the other hand, changes in the interfacial contact area of the sessile droplets have a significant impact on the frequency response of the QCM regardless of the droplet size.

Physical mechanisms of explosive boiling of an ethanol-in-decane emulsion droplet are investigated by numerical simulation. Vapor bubble growth due to explosive boiling leads to secondary breakup of the droplet. The ethanol mass ratio is chosen in the regime of puffing (vapor ejection and partial breakup), which is generally likely to occur for a fuel spray in a combustor. Using both free and sessile droplet configurations and varying the initial number of boiling bubbles and the depth of the bubble formation in the dispersed sub-droplets, the droplet breakup and vapor mixing processes are discussed. For both free and sessile configurations, the basic dynamics of puffing is the same. When the bubble depth is deeper in the sub-droplet, the bubble growth is eventually larger. When the number of bubbles is more, puffing occurs several times, or the bubbles coalesce leading to larger bubble size, larger breakup and enhanced vapor mixing. In the sessile droplet configuration, the vapor ejection dynamics is essentially similar, but particularly when puffing is strong, the droplet bounces from the wall, first pushed toward the wall by the ejected vapor and then pulled from the wall due to the repelling and recoiling motion. Under such a condition, the initially attached droplet finally detaches from the wall and returns into the ambient gas. This phenomenon may transiently influence the mixture formation in a combustor when a fuel spray collides with the combustor wall. The present study serves as a first step toward a goal of quantitatively evaluating the puffing/microexplosion effect on a real fuel turbulent spray in internal combustion engines as to how large it can contribute to improving combustion performance, and insights have been obtained for future modeling which is expected to fill the gap between the droplet-scale and spray-scale knowledge.

Marangoni instabilities in a sessile droplet evaporating at constant contact angle mode on a heated substrate were investigated through a series of experiments. The quasi-steady state flower-like patterns of Benard-Marangoni instabilities were observed, which uniformly distributed along the azimuthal direction of droplet. With the receding of triple line, the cell number of the Benard-Marangoni convection decreases one by one following a square function of the evaporating time while the flower-like pattern maintains the quasi-steady state continuously. Different from the classical polygonal cells in flat liquid layer, the shape of cells in droplet is circular-arc. The critical Marangoni numbers for the incipience as well as those for the disappearance of the Benard-Marangoni patterns were determined experimentally. Besides numerical simulations were conducted and the detailed characteristics of the Benard-Marangoni instability patterns inside the droplet are explained thoroughly.

In this paper, the Gibbs dividing surface method is used to derive a formula to determine curvature-dependent surface tension in a system with two phases. The well-known Tolman formula is a special case of this formula. The problem of a sessile droplet is considered. The Bashforth–Adams equation analogue (in view of curvature-dependent surface tension) is obtained, and the numerical solution of the equation is carried out. It is shown that if the droplet size is not very large relative to the thickness of the surface layer (micro- or nanodroplets), the dependence of the surface tension on the curvature is very important. In addition, the case is considered where the diameters of cylindrical nanodroplets are shorter than the Tolman length.

Hypothesis The rate of stain growth of a sessile droplet deposited on paper has been previously studied (Kissa, 1981; Danino and Marmur, 1994; Kawase et al., 1986; Borhan and Rungta, 1993) but is not fully understood. In particular, the mechanism by which the abrupt decrease in growth rate occurs is unknown. This process is expected to follow a model where the disappearance of the droplet is represented by a change to the boundary condition at the droplet-paper interface when the volume of the fluid inside the paper is equal to the volume of the simulated droplet. Experiments The stain size of sessile droplets on paper was monitored against time. A series of fluids varying in surface tension and viscosity was studied. The kinetics of stain growth was modelled and compared with experiments and existing models of stain growth. Findings The measured stain area formed by a sessile droplet deposited on paper follows a two regime mechanism (Danino and Marmur, 1994). In the initial regime, the dynamics are governed by the filling of pores. However, in the later stage, the process is influenced by the emptying/redistribution of fluid. Simulations show that experimental results are well described by a model that identifies the change in boundary conditions after the droplet is no longer present above the paper, coupled with the change to a redistribution dominated mechanism.

Sessile droplet freezing on textured micropillar surfaces was observed visually and thermographically. Hydrophobic surfaces with three different topographies were selected, the contact angles of water on which were 141°, 102°, and 138°. Droplet surface temperature distribution measurements from lateral view enabled quantitative evaluation of the freezing stages. According to the experiment, it was found that the surface hydrophobicity decreases with the increasing pillar distance. Only a slight increase in hydrophobicity was found with the decreasing pillar diameter. The liquid water droplet experienced five successive stages to become fully frozen. It was also confirmed that the droplet’s opaque appearance is caused by the sudden ice shell formation at the ice incipience. Besides, the solidification frontier (SF) movement inside the droplet was analyzed. The freezing rate was higher at the SF edge. Moreover, the textured surfaces with higher hydrophobicity were prone to further postpone the droplet’s freezing onset. However, surface topography showed minor impact on the droplet surface recalescence stage duration. Additionally, the droplet internal solidification stage lasted longer on samples with higher hydrophobicity.

Confinement effects may trigger certain non-trivial characteristics of droplet evaporation, which may incur far-reaching implications in practical scenarios. In effect, the vapor mediated interactions in a confined droplet may alter its intrinsic evaporation characteristics altogether, primarily as a consequence of significant increase in droplet lifetime due to enriched accumulation of the vapor field in the vicinity. Here, we derive a universal scaling law for the evaporation lifetime of a geometrically confined sessile droplet, appropriate to a wide gamut of droplet-substrate combinations. With asymptotic convergence to the classical picture in case of an unconfined droplet, the validity of our scaling law for droplet lifetime is comprehensively tested and benchmarked against a wide range of experimental data sets. These findings may turn out to be of profound importance in several emerging applications including micro-scale combustion and droplet based microfluidic technology.

International audience; 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.

The effect of the thermal properties of the system on the lifetime of an evaporating sessile droplet of water is analysed using a fully coupled model which involves determining the temperature of the droplet, the substrate and the atmosphere. The evolutions, and hence the lifetimes, of droplets of water evaporating in both of the extreme modes are calculated. In particular, it is shown how the lifetimes of droplets of water can be strongly influenced by thermal effects. Droplets with larger initial contact angles or on less conductive substrates generally have longer lifetimes than those with smaller initial contact angles or on more conductive substrates, and the physical mechanism by which the thermal properties of the system influence the evaporation can be understood in terms of the thermal anchoring between the droplet and the lower surface of the substrate.

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.

We experimentally investigate the dissolution of microscale sessile alcohol droplets in water under the influence of impermeable vertical confinement. The introduction of confinement suppresses the mass transport from the droplet to bulk medium in comparison with the nonconfined counterpart. Along with a buoyant plume, flow visualization reveals that the dissolution of a confined droplet is hindered by a mechanism called levitated toroidal vortex. The morphological changes in the flow due to the vortex-induced impediment alters the dissolution rate, resulting in enhancement of droplet lifetime. Further, we have proposed a modification in the key nondimensional parameters [Rayleigh number ${\mathrm{Ra}}^{\ensuremath{'}}$ (signifying buoyancy) and Sherwood number ${\mathrm{Sh}}^{\ensuremath{'}}$ (signifying mass flux)] and droplet lifetime ${{\ensuremath{\tau}}_{c}}^{\ensuremath{'}}$, based on the hypothesis of linearly stratified droplet surroundings (with revised concentration difference $\mathrm{\ensuremath{\Delta}}{C}^{\ensuremath{'}}$), taking into account the geometry of the confinements. We show that experimental results on droplet dissolution under vertical confinement corroborate scaling relations ${\mathrm{Sh}}^{\ensuremath{'}}\ensuremath{\sim}\mathrm{Ra}{{}^{\ensuremath{'}}}^{1/4}$ and ${{\ensuremath{\tau}}_{c}}^{\ensuremath{'}}\ensuremath{\sim}\mathrm{\ensuremath{\Delta}}C{{}^{\ensuremath{'}}}^{\ensuremath{-}5/4}$. We also draw attention to the fact that the revised scaling law incorporating the geometry of confinements proposed in the present work can be extended to other known configurations such as droplet dissolution inside a range of channel dimensions, as encountered in a gamut of applications such as microfluidic technology and biomedical engineering.

The study of sessile droplet evaporation has attracted widespread interest due to the plethora of industrial and every day applications ranging from inkjet printing, to DNA micro-array chips, to spray cooling.

The fall of a small droplet from a height H = 20 mm onto the surface of a sessile drop leads to a change in its shape: the drop is periodically stretched and then compressed. At H = 500 mm, after the fall of a small droplet, the formation of splashes and fingers is observed. Subsequently, the sessile droplet is compressed with the formation of closely spaced smaller droplets. The PIV method was used to obtain experimental data on the change in velocity in the horizontal section a sessile drop after the fall of a small droplet. The fall of one droplet onto the surface of another drop from a height of H = 20 mm leads to the formation of vortices in the drop and the flow velocity in the drop increases many times from 0.035-0.5 mm/s to 4.1-4.8 mm/s. After 5 s the drop, the flow velocity in the sitting drop approaches the velocity before the fall, and a toroidal vortex is formed in the drop.

Experimental studies for the evaporation of a sessile and hanging droplet of aqueous salt solution were carried out. When spray cooling a hot wall, it is required to simulate both the heat transfer of falling droplets and the heat transfer of sessile droplets on the wall. It is shown that the ratio of the maximum velocity to the average convection velocity is approximately 2.5-3 both for a hanging and a sessile droplet of salt solution.

Experiments on the evaporation of a hanging drop of water in a stream of air were carried out. The velocity for a hanging drop is about 30-40% higher than for a sessile droplet of water. It is shown that the ratio of the maximum convection velocity to the average convection velocity is approximately equal to three, for both a hanging and a sessile droplet of water.

In this communication a novel implementation was outlined to simulate surface tension and adhesion by weakly compressible Smoothed Particle Hydrodynamics (SPH). Physical effects in a liquid phase of surface tension and adhesion toward a solid surface were generated by including proper particle-particle interactions within the SPH scheme. The analytical relationship describing intensities of such forces as a function of mutual distance, was derived from the literature and was given a dimensionally consistent form. Four computational approaches were compared, including as ingredients: Monaghan or Riemann solvers, for the viscous/dissipative term of momentum conservation equation; two diverse strategies to compute the overall adhesion force acting onto each liquid particle, one exploiting as sampling points “ghost” particles (already present for boundary conditions), another one based on numerical quadrature within the support of the approximating Kernel. For very preliminary simulations a single phase scenario was considered, describing in a simplified fashion a sessile droplet experiment for wettability assessment. A semicircular liquid droplet was discretized by particles, and subjected to surface tension and adhesion forces exerted by a solid, flat substrate, coincident with a boundary of the problem domain. On the basis of results so far available, Monaghan solver exhibited superior robustness; on the other hand, Riemann solver was preferable as for the smoothness of pressure field. However, severe numerical problems were met: locally, within the droplet, spurious and unphysical negative pressure were predicted by both solvers, endowed by unexpected instability of particle flow and by a global lack of robustness at varying the analysis parameters.

When a water drop is deposited on a hole drilled in a superhydrophobic plate in contact with a bath of water from underneath, the liquid in the drop will transport into the bath and a jet is then produced. It is found that the evolution of the drop diameter $D(t)$ with time $t$ obeys scaling relations $D(t)\ensuremath{\sim}{t}^{2/7}$ and $D(t)\ensuremath{\sim}{t}^{1/2}$ for small drops and large puddles, respectively, arising from the competition between the surface tension and inertia.

A sessile droplet of a complex fluid exhibits several stages of drying leading to the formation of a final pattern on the substrate. We report such pattern formation in dehydrating droplets of protein (BSA) and salts (MgCl2 and KCl) at various concentrations of the two components (protein and salts) as part of a parametric study for the understanding of complex patterns of dehydrating biofluid droplets (blood and urine), which will eventually be used for diagnosis of bladder cancer. The exact analysis of the biofluid patterns will require a rigorous parametric study; however, the current work provides an initial understanding of the effect of the basic components present in a biofluid droplet. Arrangement of the protein and the salts, due to evaporation, leads to the formation of some very distinctive final structures at the end of the droplet lifetime. Furthermore, these structures can be manipulated by varying the initial ratio of the two components in the solution. MgCl2 forms chains of crystals beyond a threshold initial concentration of protein (>3 wt %). However, the formation of such a crystal is also limited by the maximum concentration of the salt initially present in the droplet (≤1 wt %). On the other hand, KCl forms dendritic and rectangular crystals in the presence of BSA. The formation of these crystals also depends on the relative concentration of salt and protein in the droplet. We also investigated the dried-out patterns in dehydrating droplets of mixed salts (MgCl2 + KCl) and protein. The patterns can be tuned from a continuous dendritic structure to a snow-flake type structure just by altering the initial ratio of the two salts in the mixture, keeping all other parameters constant.

The evaporation of antigen-laden sessile droplets on antibody-immobilized PDMS substrates could be used in place of microwells for detection purposes owing to the lesser requirements of analytes and a reduced reaction time. To develop such techniques, the effects of different parameters on the reaction efficiency and on the resulting deposition patterns of antigens on the surface after evaporation need to be well understood. While the resultant deposition patterns from the evaporation of droplets of biological fluids on surfaces are being studied for various biomedical applications, systems where the analyte of interest in the droplet binds to the surface have not been investigated until now. While the effect of temperature on the internal convection within sessile droplets has been studied, the effect of the analyte (antigen in this work) concentration and the analyte-surface (antigen-antibody in this work) binding on the internal convection has not been studied until now. Therefore, to gain insight, the evaporation dynamics of sessile droplets with different concentrations of antigens along with polystyrene microspheres (used as tracers) in phosphate-buffered saline (PBS) on antibody-immobilized PDMS substrates were experimentally studied using microparticle image velocimetry (PIV). It was found that Marangoni flow due to concentration gradients and surface reactions was responsible for the observed velocity field. The antibody-antigen reaction (as compared to the control case of no surface reaction) and higher concentrations of prostate specific antigen (PSA) resulted in increased strength of Marangoni convection. To obtain further insight into the different deposition patterns obtained, the contributions of different particle-particle and particle-substrate forces were determined, and it was observed that the Marangoni forces along with surface tension and DLVO forces create a uniform deposition of the particles present within the droplet. This learning could be used to design biosensors.

Cell-laden hydrogels can be engineered using evaporating droplets of collagen., When a sessile droplet containing a solute in a volatile solvent evaporates, flow in the droplet can transport and assemble solute particles into complex patterns. Transport in evaporating sessile droplets has largely been examined in solvents that undergo complete evaporation. Here, we demonstrate that flow in evaporating aqueous sessile droplets containing type I collagen—a self-assembling polymer—can be harnessed to engineer hydrated networks of aligned collagen fibers. We find that Marangoni flows direct collagen fiber assembly over millimeter-scale areas in a manner that depends on the rate of self-assembly, the relative humidity of the surrounding environment, and the geometry of the droplet. Skeletal muscle cells that are incorporated into and cultured within these evaporating droplets collectively orient and subsequently differentiate into myotubes in response to aligned networks of collagen. Our findings demonstrate a simple, tunable, and high-throughput approach to engineer aligned fibrillar hydrogels and cell-laden biomimetic materials.

Sessile droplet evaporation is widely encountered in nature, and it has numerous applications in industrial and scientific communities; therefore, the accurate prediction of droplet evaporation has great significance in practical applications. In this paper, for the first time, a comprehensive theoretical model is built up for diffusion-controlled heat and mass transfer for sessile droplet evaporation on a curved substrate in toroidal coordinates. The evaporative mass transfer is coupled with the heat transfer across the gas-liquid droplet interface, as well as the heat transfer across the solid-liquid interface of the curved substrate. The effects of interfacial cooling and thermal conductivity of the droplet and substrate as well as their initial shapes on the droplet evaporation are provided in details. It is found that the evaporative flux usually increases sharply near the droplet edge due to the short distance for heat conduction from the substrate to the droplet; however, it can be reversed from sharp increasing to decreasing at a low thermal conductivity ratio

When a sessile droplet of a complex mixture evaporates, its nonvolatile components may deposit into various patterns. One such phenomena, the coffee ring effect, has been a topic of interest for several decades. Here, we identify what we believe to be a fascinating phenomenon of droplet pattern deposition for another well-known beverage-what we have termed a "whiskey web". Nanoscale agglomerates were generated in diluted American whiskeys (20-25% alcohol by volume), which later stratified as microwebs on the liquid-air interface during evaporation. The web's strandlike features result from monolayer collapse, and the resulting pattern is a function of the intrinsic molecular constituents of the whiskey. Data suggest that, for our conditions (diluted 1.0 μL drops evaporated on cleaned glass substrates), whiskey webs were unique to diluted American whiskey; however, similar structures were generated with other whiskeys under different conditions. Further, each product forms their own distinct pattern, demonstrating that this phenomenon could be used for sample analysis and counterfeit identification.

The recent development of a superhydrophobic surface enhances the droplet shedding under a shear flow. The present study gives insights into the effects of shear flow on a pinned droplet over a superhydrophobic surface. To experimentally simulate the change in the size of a sessile droplet on an aerodynamic surface, the volume of the pinned droplet is expanded by water supplied through a pore. Under a continuous airflow that provides a shear flow over the superhydrophobic surface, the size of a pinned water droplet shed from the surface is experimentally characterized. The air velocity ranges from 8 to 61 m/s, and the size of pinned droplets shed at a given air velocity is measured using an instantaneous snapshot captured with a high-speed camera. It is found that the size of the shedding pinned droplet decreases as air velocity increases. At higher air velocities, shedding pinned droplets are fully immersed in the boundary layer. The present findings give a correlation between critical air velocity and the size of pinned droplets shed from the pore over the superhydrophobic surface.

The spreading of a sessile droplet on a solid substrate is enhanced if a non-uniform electric field is applied at the contact-line region. This so-called dielectrowetting effect holds great potential in controlling the spreading of droplets by varying the strength of the electric field. In this paper, we experimentally and theoretically study the effect of the dielectrowetting on the dynamics of droplets impacting on a solid surface having electrodes to impose the non-uniform electric field to the liquid. We experimentally study the anisotropic behaviours in both the spreading and retracting stages: the droplets spread more but retract with significantly smaller rates in the direction parallel to the electrodes. We provide a theoretical explanation for the spreading enhancement caused by dielectrowetting by decoupling it from inertia-induced spreading. We also theoretically account for the reduction in retraction rate using force balance at the contact line. The theoretical analysis in both the spreading and retracting stages is verified experimentally. Agency for Science, Technology and Research (A*STAR) Nanyang Technological University This study is supported by Nanyang Technological University and the Agency for Science, Technology and Research (A*STAR), Singapore, under its Pharos Funding Scheme (Grant No. 1523700102). We also acknowledge support from JSPS KAKENHI (Grant No. 17H01246). We thank Dr Phu Tran from Air Traffic Management Research Institute (ATMRI, NTU) for the fruitful discussions relating to applying the gradient descent algorithm in our paper.

The Particle Finite Element Method (PFEM) is used to develop a model to study two-phase flow in fuel cell gas channels. First, the PFEM is used to develop the model of free and sessile droplets. The droplet model is then coupled to an Eulerian, fixed-grid, model for the airflow. The resulting coupled PFEM-Eulerian algorithm is used to study droplet oscillations in an air flowand droplet growth in a lowtemperature fuel cell gas channel. Numerical results show good agreement with predicted frequencies of oscillation, contact angle, and deformation of injected droplets in gas channels. The PFEM-based approach provides a novel strategy to study droplet dynamics in fuel cells.

Driven by nanoparticle plasmonic heating, sessile droplet evaporation presents challenges on the coupling mechanisms between time-spatial heat source distribution and flow/temperature fields in a droplet. Here, symmetric/asymmetric solar-driven droplet evaporation is investigated. An infrared camera captures droplet surface temperatures in the micrometer scale after correction. An optical three-dimensional profiler quantifies nanoparticle deposition in the nanoscale. We show that droplet surface temperatures do display a nonmonotonic variation trend. Based on measurements, we are able to decouple the droplet into a contact line region (CLR) and a bulk volume region (BVR). The CLR volume is two to three magnitudes smaller than the droplet volume. The temperature gradient is significant in CLR, but flat temperature exists in BVR. Radial flow in BVR transports nanoparticles from the droplet body to the contact line, while Marangoni flow in CLR stabilizes nanoparticles there. Light energy is also decoupled based on its wavelength band. It is found that CLR dominates the visible energy absorption, but BVR has a weak contribution. Top light heating causes symmetry temperatures and a coffee-ring profile along the circumference. However, side heating yields higher temperatures and more nanoparticles deposition on the sunny side than on the night side. The above findings are valid when the initial droplet volume and incident irradiation flux are changed on the hydrophilic wall. The hydrophilic wall and hydrophobic wall maintain the evaporation modes of constant contact diameter and "stick-slip", respectively. The present paper enhances the understanding of light-induced droplet evaporation from the multiscale point of view.

This article reports experimental results of the presence of a mixed regime where rebound or coalescence occurs when a liquid droplet with low impact velocity impinges on a static sessile droplet, deposited on a flat aluminum surface. In particular, the present study suggests possible reasons why this mixed occurs with nearly the same probabilities with the use of the sequential images captured by two high-speed cameras from the 767 experimental cases. It is also demonstrated that the mixed regime is substantially affected by static droplet volumes, Weber numbers, and offset distances between impinging and static droplets. In the mixed regime, rebound may occur because a relatively large air-film maintains to prevent film drainage for coalescence. The lubrication theory is utilized to estimate film thickness between two droplets and is compared to the critical film thickness. The upper limit of the Weber numbers in the mixed regime decreases with an increase in the offset distance, owing to a rotational droplet motion causing air-film elongation. The contact time during rebound slightly increases with the static sessile droplet volume. It is observed that the measured contact times increases with a decrease in impact velocity, showing cushioning effect by air-film. On the other hand, a coalescence is observed to intermittently in the mixed regime because the air-film layer existing at the interface has an irregular shape by oscillation of an impinging droplet.

In this study, for the first time, the natural (diffusion-limited) evaporation of a sessile drop under an electric field was experimentally examined. A sessile drop natural evaporation is affected by the geometry of the drop, e.g. baseline, contact angle, and surface area, which all can be changed in the presence of an electric field. As such, first, the effect of electric field on sessile water droplet geometry was studied, together with how it differs for surfaces with various contact angle and contact angle hysteresis (for both hydrophilic and hydrophobic surfaces). Then, the dynamics (evaporation time and mode) of natural evaporation of sessile droplet under an electric field was studied by measuring the evaporation rate, surface area, contact angle, and baseline of the droplet. It is found that compare to when there is no electric field, the evaporation time of a sessile droplet increases when there is an electric field. This was statistically shown to be significant for drops placed on surfaces with contact angle hysteresis lower than 32°. For droplets that evaporate in constant baseline mode initially and then by evaporation in constant contact angle mode, the presence of the electric field resulted in a decrease in the duration of constant baseline mode when the surface had a low contact angle hysteresis.

Here, we investigate deposit patterns and associated morphology formed after the evaporation of an aqueous droplet containing mono- and bidispersed 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 monodispersed colloidal particles, an inner deposit and a typical ring form for smaller and larger particles, respectively, on a nonheated surface. The formation of the inner deposit is attributed to early depinning of the contact line, explained by a mechanistic model based on the balance of several forces acting on a particle near the contact line. At larger substrate temperature, a thin ring with inner deposit forms, explained by the self-pinning of the contact line and advection of the particles from the contact line to the center of the droplet due to the Marangoni flow. In the context of bidispersed colloidal particles, self-sorting of the colloidal particles within the ring occurs at larger substrate temperature. The smaller particles deposit at the outermost edge compared to the larger particles, and this preferential deposition in a stagnation region near the contact line is due to the spatially varying height of the liquid-gas interface above the substrate. The sorting occurs at a smaller ratio of the diameters of the smaller and larger particles. At larger substrate temperature and larger ratio, the particles do not get sorted and mix into each other. Our measurements show that there exists a critical substrate temperature as well as a diameter ratio to achieve the sorting. We propose regime maps on substrate temperature-particle diameter and substrate temperature-diameter ratio plane for mono- and bidispersed solutions, respectively.

The evaporation of a sessile droplet is here investigated numerically with a design of experiment approach. Boundary conditions are chosen based on forced convection in humid air, i.e., mimicking the conditions inside a dishwasher. Computational fluid dynamic simulations of an axisymmetrical droplet placed on a heated plate show that relative humidity, initial contact angle, plate temperature, and temperature difference between plate and air all have significant effect on the initial evaporation rate. For the studied conditions, relative humidity is the most significant factor while the magnitude of the velocity and type of internal flow are insignificant within a 95% confidence interval. Validerad;2019;Nivå 2;2019-04-10 (johcin)

Evaporating sessile functional droplets act as the fundamental building block that controls the cumulative outcome of many industrial and biological applications such as surface patterning, 3D printing, photonic crystals, and DNA sequencing, to name a few. Additionally, a drying single sessile droplet forms a high-throughput processing technique using low material volume which is especially suitable for medical diagnosis. A sessile droplet also provides an elementary platform to study and analyze fundamental interfacial processes at various length scales ranging from macroscopically observable wetting and evaporation to microfluidic transport to interparticle forces operating at a nanometric length scale. As an example, to ascertain the quality of 3D printing we must understand the fundamental interfacial processes at the droplet scale. In this article, we review the coupled physics of evaporation flow-contact-line-driven particle transport in sessile colloidal droplets and provide methodologies to control the same. Through natural alterations in droplet vaporization, one can change the evaporative pattern and contact line dynamics leading to internal flow which will modulate the final particle assembly in a nontrivial fashion. We further show that control over particle transport can also be exerted by external stimuli which can be thermal, mechanical oscillations, vapor confinement (walled or a fellow droplet), or chemical (surfactant-induced) in nature. For example, significant augmentation of an otherwise evaporation-driven particle transport in sessile droplets can be brought about simply through controlled interfacial oscillations. The ability to control the final morphologies by manipulating the governing interfacial mechanisms in the precursor stages of droplet drying makes it perfectly suitable for fabrication-, mixing-, and diagnostic-based applications.

Interaction between sessile droplets and solid surfaces is a fundamental science and engineering problem, with ubiquitous presence in various applications. In this paper, we study the effect of imposing vertical and horizontal ultrasonic vibration (40 kHz) on dynamics (oscillations) and evaporation of sessile droplets of dimethylformamide (DMF), isopropyl alcohol (IPA) and water on Teflon and glass substrates. There is no or very few works considering dynamics and evaporation aspects of excited droplets, simultaneously. The theory concerning the force balance and pinning/depinning in pristine and excited sessile droplet systems is elucidated. Time varying left and right contact angles and contact radius are measured for the duration of the droplet lifetime, where the stick-slip phenomena are observed and interpreted for various liquids. Imposing substrate vibration results in significant decrease in droplet lifetime and affects the behavior of the stick-slip mechanism. Droplets excited by horizontal vibration have the shortest lifetime. It is also experimentally shown that in the case of vertical vibration, the left and right contact angles oscillate in-phase, whereas in the case of horizontal vibration, there is 180° phase difference between left and right contact angles.

Numerical study has been conducted to study the fluid convection inside sessile and pendant evaporating droplets of aqueous NaCl solution placed on a superhydrophobic surface. Evaporation from the droplet surface leads to increase in the solute concentration at the evaporating liquid–air interface generating concentration gradient inside the droplet. Concentration gradient inside the droplet induces Rayleigh convection. Fluid with higher concentration in the liquid–air interface region moves downward along the interface and lighter fluid rises upward along the central region of the droplet like a plume. The average concentration, evaporation rate and the maximum velocity inside the sessile droplet on a superhydrophobic surface is higher than that on a hydrophobic surface. Both sessile and pendant droplet configurations have been investigated. Fluid near the interface moves towards the substrate in case of sessile droplet, where as the fluid moves away from the substrate along the interface for the pendant droplet configuration. Two counter rotating recirculation bubbles are observed in both sessile and pendant droplets. The magnitude of maximum convection velocity and circulation strength of the recirculation bubbles for pendant droplet is smaller than that of sessile droplet at the same evaporation conditions. This may be attributed to the stratification of higher density fluid for the pendant droplet configuration which suppresses the Rayleigh convection. The effect of initial solute concentration on the strength of convection is stronger for sessile droplet configuration compared to that of pendant droplet. The present study establishes strong influence of superhydrophobicity and orientation on the internal convection inside a droplet of aqueous solution.

Protein self-assembly is fundamental to nanotechnology. Self-assembling structures are produced under static in vitro conditions typically forming over hours. In contrast, hydrodynamic intracellular environments employ far shorter time scales to compartmentalize highly concentrated protein solutions. Herein, we exploit the radial capillary flow within a drying sessile droplet (the coffee ring effect) to emulate dynamic native environments and monitor an archetypal protein assembly in situ using high-speed super-resolution imaging. We demonstrate that the assembly can be empirically driven to completion within minutes to seconds without apparent changes in supramolecular morphology. The model offers a reliable tool for the diagnosis and engineering of self-assembling systems under nonequilibrium conditions.

The coalescence between a free droplet and a sessile droplet on wettable substrate is numerically studied. The axisymmetric lattice Boltzmann method for two-phase flows is used in modeling. Here the contact angle hysteresis (prescribed by advancing angle [Formula: see text] and receding angle [Formula: see text]) is taken into account. The effects of Ohnesorge number ( Oh), contact angle and its hysteresis, and the radius of the free droplet on the coalescence dynamics are investigated in detail. The Oh numbers ranging from 0.02 to 0.15 here makes the radius of the liquid bridge r and the time t follow power law. Also, Oh has remarkable impact on the development of capillary wave and on the amount of kinetic energy released from coalescence. It is found that the curve of the wetting radius varying with time includes several plateau stages, which is a typical characteristic for the effect of contact angle hysteresis. The larger window of contact angle hysteresis would result in smaller steady wetting radius after coalescence. Compared with the existence of contact angle hysteresis, the absence of contact angle hysteresis makes the droplets system release more kinetic energy during the coalescence but the released kinetic energy decays more rapidly and soon reduces to zero. Oppositely, if the contact angle hysteresis exists, the released kinetic energy would oscillate for a period of time before approaching zero.

Surface wettability plays an important role in droplet formation, removal, and resistance to fouling. The sessile droplet profile is one of the most important parameters characterizing surface wett...

International audience; Motivated by the space project EFILE, a 2D axisymmetric numerical model in the framework of ALE method is developed to investigate the coupled physical mechanism during the evaporation of a pinned drop that partially wets on a heated substrate. The model accounts for mass transport in surrounding air, Marangoni convection inside the drop and heat conduction in the substrate as well as moving interface. Numerical results predict simple scaling laws for the evaporation rate which scales linearly with drop radius but follows a power-law with substrate temperature. It is highlighted that thermal effect of the substrate has a great impact on the temperature profile at the drop surface, which leads to a multicellular thermocapillary flow pattern. In particular, the structure of the multicellular flow behavior induced within a heated drop is mainly controlled by a geometric parameter (aspect ratio). A relationship between the number of thermal cells and the aspect ratio is proposed。