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

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

Dependence of the structure of ring-shaped deposits resulting from evaporation of dispersion droplets on initial contact angle

Experiments have been performed on the formation of ding-shaped deposits upon the evaporation of dispersion droplets on different substrates accompanied by the coffee ring effect. The main attention has been focused on studying the structure of a formed deposit as depending on the initial contact angle of a droplet. It has been established that the deposit structure may vary from ring-shaped to disc-shaped with a decrease in the contact angle. For certain systems, as the initial contact angle is varied, the scenario of droplet evaporation may change and, in some cases, acquire a combined character. Before the onset of pinning, menisci of droplets that are evaporated on modified polymer substrates may initially move not only toward the droplet center, but also in the opposite direction.     

The influence of gravity on the distribution of the deposit formed onto a substrate by sessile, hanging, and sandwiched hanging drop evaporation

The focus of the present article is the study of the influence of gravity on the particle deposition profiles on a solid substrate during the evaporation of sessile, hanging and sandwiched hanging drops of colloidal particle suspensions. For concentrations of nanoparticles in the colloidal solutions in the range 0.0001-1 wt.%, highly diluted suspensions will preferentially form rings while concentrated suspensions will preferentially form spots in both sessile and hanging drop evaporation. For intermediary concentrations, the particle deposition profiles will depend on the nanoparticle aggregation dynamics in the suspension during the evaporation process, gravity and on the detailed evaporation geometry. The evaporation of a drop of toluene/carbon nanoparticle suspension hanging from a pendant water drop will leave on the substrate a circular spot with no visible external ring. By contrast, a clear external ring is formed on the substrate by the sessile evaporation of a similar drop of suspension sandwiched between a water drop and the substrate. From the application viewpoint, these processes can be used to create preferential electrical conductive carbon networks and contacts for arrays of self-assembled nanostructures fabricated on solid substrates as well as on flexible polymeric substrates.     

Sessile nanofluid droplet drying

Nanofluid droplet evaporation has gained much audience nowadays due to its wide applications in painting, coating, surface patterning, particle deposition, etc. This paper reviews the drying progress and deposition formation from the evaporative sessile droplets with the suspended insoluble solutes, especially nanoparticles. The main content covers the evaporation fundamental, the particle self-assembly, and deposition patterns in sessile nanofluid droplet. Both experimental and theoretical studies are presented. The effects of the type, concentration and size of nanoparticles on the spreading and evaporative dynamics are elucidated at first, serving the basis for the understanding of particle motion and deposition process which are introduced afterward. Stressing on particle assembly and production of desirable residue patterns, we express abundant experimental interventions, various types of deposits, and the effects on nanoparticle deposition. The review ends with the introduction of theoretical investigations, including the Navier–Stokes equations in terms of solutions, the Diffusion Limited Aggregation approach, the Kinetic Monte Carlo method, and the Dynamical Density Functional Theory. Nanoparticles have shown great influences in spreading, evaporation rate, evaporation regime, fluid flow and pattern formation of sessile droplets. Under different experimental conditions, various deposition patterns can be formed. The existing theoretical approaches are able to predict fluid dynamics, particle motion and deposition patterns in the particular cases. On the basis of further understanding of the effects of fluid dynamics and particle motion, the desirable patterns can be obtained with appropriate experimental regulations.     

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

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

Effect of temperature on ring-shaped-deposit formated at evaporation of droplets of silver-nanoparticle dispersions

The effect of temperature is studied on the geometric parameters and conductivity of ring-shaped deposits formed at evaporation of droplets of dispersions of silver nanoparticles on hydrophilic (glass) and hydrophobic (copper) substrates. It has been shown that increasing temperature leads to substantial changes in the deposit profile. Therewith, the effects of temperature on droplet evaporation on glass and copper substrates are different. It has been found that the lateral conductivity of a ring-shaped deposit formed on a glass substrate increases stepwise similarly to a percolation transition at a droplet-evaporation temperature of 58°C. It has been suggested that the reason for the temperature effect is related to a change in the ratio between the rates of physicochemical processes occurring at different stages of droplet evaporation.     

Effect of nanoparticle sizes and number densities on the evaporation and dryout characteristics for strongly pinned nanofluid droplets

A microfabricated linear heater array operating in a constant voltage mode has been used to study the effect of nanoparticle size on the evaporation and dryout characteristics of strongly pinned nanofluid droplets. Four different nanofluids have been tested, containing 2-nm Au, 30-nm CuO, 11-nm Al2O3, and 47-nm Al2O3 nanoparticles, each of 5-muL droplets with 0.5 vol % in water. Nanofluid droplets show strong pinning along the droplet perimeter and, upon evaporation, leave a ring-shaped nanoparticle stain. Particle size is seen to have a clear and strong effect on the dryout stain pattern, while heater temperature seems to have little effect. With the assumption of axi-symmetry, tomographic deconvolution of measured data from the linear heater array allows for examination of the spatially and temporally resolved temperature and heat flux characteristics of the evaporating nanofluid droplets.     

Convective rolls and hydrothermal waves in evaporating sessile drops

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

Evaporation and Marangoni driven convection in small heated water droplets

Evaporation dynamics of small sessile water droplets under microgravity conditions is investigated numerically. The water-air interface is free, and the surrounding air is assumed to be quasisteady. The droplet is described by Navier-Stokes and heat equations and its surrounding water/air gaseous phase with Laplace equation. In the thermodynamic conditions of the simulations presented herein, the evaporative mass flow is nonlinear. It shows a minimum that indicates the existence of qualitative changes in the evaporative regimes although the droplet is sessile. Due to temperature gradients on the free interface, Marangoni motion occurs and generates inside the droplet convection cells that furthermore exhibit small fluctuating motion as evaporation goes on.     

Controlling coffee ring structure on hydrophobic polymer surface by manipulating wettability with O2 plasma

A simple and novel method is firstly reported for controlling coffee ring structure on polystyrene (PS) film surface by O₂ plasma. O₂ plasma treatment leads to the wettability change of PS surface from hydrophobic to hydrophilic. For hydrophilic PS surface the coffee ring structure is avoided relying on the motion of contact line (CL) while SiO₂ microspheres are left. The motion of the CL is produced based on the viscosity and Marangoni effect with the addition of polymer additives. For hydrophobic PS surface coffee ring structure still persists even with polymer additives because SiO₂ microspheres transfer with the motion of the CL at the beginning of droplet evaporation and accumulate at the droplet edge at late stage with the pinning of the CL. As a result, uniform and macroscale SiO₂ microspheres deposition without coffee ring structure and SiO₂ microspheres deposition with coffee ring structure are controlled by O₂ plasma. This method provides a new way to tune coffee ring structure with smart surface and may be potentially useful for a range of application at material deposition and diagnosing diseases.     

Recent progress in experiments for sessile droplet wetting on structured surfaces

Wetting of a sessile droplet on structured or patterned surface can be found in a broad range of applications. The researchers have been promoted to keep working on the topic. The review is on the basis of the recent experimental advances on the sessile droplet wetting on the hydrophobic, hydrophilic, or combined hydrophobic and hydrophilic surfaces under isothermal conditions, and on heating or cooling substrates having nonisothermal conditions. More attention has been paid on the wetting configuration between the sessile droplet and the structured substrate; the research gap has been discussed on identifying the three-phase line shape. Further, the three-dimensional measurement for the sessile droplets on the patterned surfaces with focusing more on the contact line of sessile droplets might reveal new physical insights. This review targets at building a holistic overview on the sessile droplet wetting behaviors on the structured substrate in the past 2 years.     

Behavior of evaporating droplets at nonsoluble and soluble surfaces: Modeling with molecular resolution

Liquid droplets in equilibrium with vapor are simulated at solidlike surfaces using the cooperative motion algorithm (CMA). These droplets behave like real droplets, i.e., the densities of the coexistent liquid and vapor phases obey empirical relations such as rho l - rho v proportional, variant (1 - T/Tc)(1/3). Droplet evaporation was studied under various interaction conditions, i.e., nonsoluble and soluble substrates. In the last case, substrate particles migrate toward the liquid-vapor interface to minimize the droplet surface energy. This leads to the formation of a microwell surrounded by a ringlike deposit on the substrate surface. It is shown that the ring formation in the first stages of evaporation results in pinning of the droplet contact area.     

Fast evaporation of spreading droplets of colloidal suspensions

When a coffee droplet dries on a countertop, a dark ring of coffee solute is left behind, a phenomenon often referred to as the coffee-ring effect. A closely related yet less-well-explored phenomenon is the formation of a layer of particles, or skin, at the surface of the droplet during drying. In this work, we explore the behavior of a mathematical model that can qualitatively describe both phenomena. We consider a thin axisymmetric droplet of a colloidal suspension on a horizontal substrate undergoing spreading and evaporation. In contrast to prior work, precursor films (rather than pinned contact lines) are present at the droplet edge, and evaporation is assumed to be limited by how quickly molecules can transfer out of the liquid phase (rather than by how quickly they can diffuse through the gas phase). The lubrication approximation is applied to simplify the mass and momentum conservation equations, and the colloidal particles are allowed to influence the droplet rheology through their effect on the viscosity. By describing the transport of the colloidal particles with the full convection-diffusion equation, we are able to capture depthwise gradients in particle concentration and thus describe skin formation, a feature neglected in prior models of droplet evaporation. The highly coupled model equations are solved for a range of problem parameters using a finite-difference scheme based on a moving overset grid. The presence of evaporation and a large particle Peclet number leads to the accumulation of particles at the liquid-air interface. Whereas capillarity creates a flow that drives particles to the droplet edge to produce a coffee ring, Marangoni flows can compete with this and promote skin formation. Increases in viscosity due to particle concentration slow down droplet dynamics and can lead to a reduction in the spreading rate.     

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

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

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

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

Effect of nonionic surfactant on wetting behavior of an evaporating drop under a reduced pressure environment

The evaporation of sessile drops at reduced pressure is investigated. The evaporation of water droplets on aluminum and PTFE surfaces at reduced pressure was compared. It was found that water droplets on an aluminum surface exhibit a 'depinning jump' at subatmospheric pressures. This is when a pinned droplet suddenly depins, with an increase in contact angle and a simultaneous decrease in the base width. The evaporation of sessile water droplets with a nonionic surfactant (Triton X-100) added to an aluminum surface was then studied. The initial contact angle exhibited a minimum at 0.001 wt% Triton X-100. A maximum in the evaporation rate was also observed at the same concentration. Droplets with low surfactant concentrations are found to exhibit the 'depinning jump.' It is thought that the local concentration of the surfactant causes a gradient of surface tension. The balance at the contact angle is dictated by complex phenomena, including surfactant diffusion and adsorption processes at interfaces. Due to the strong evaporation near the triple line, an accumulation of the surfactant will lead to a surface tension gradient along the interface. The gradient of surface tension will influence the wetting behavior (Marangoni effect). At low surfactant concentrations the contact line depins under the strong effect of surface tension gradient that develops spontaneously over the droplet interface due to surfactant accumulation near the triple line. The maximum evaporation rate corresponds to a minimum contact angle for a pinned droplet.     

The Factors Determining Formation Dynamics and Structure of Ring-Shaped Deposits Resulting from Capillary Self-Assembly of Particles

The influence of different physicochemical parameters, such as particle concentration and size, droplet volume, dispersion medium composition, and substrate hydrophilicity, on the structure of deposits resulting from evaporating sessile droplets of colloidal dispersions has been studied. Parameters enabling one to targetedly control the structure of a deposit have been determined. The possibility of obtaining deposits having the shapes of thin rings and monolithic disks has been shown. The conditions have been found under which monolayer and multilayer deposits with ordered arrangement of particles are formed.     

Dual-frequency electrowetting: application to drop evaporation gauging within a digital microsystem

This paper addresses a method to estimate the size of a sessile drop and to measure its evaporation kinetics by making use of both Michelson interferometry and coplanar electrowetting. From a high-frequency electrowetting voltage, the contact angle of the sessile droplet is monitored to permanently obtain a half-liquid sphere, thus complying perfectly with the drop evaporation theory based on a constant contact angle (Bexon, R.; Picknett, R. J. Colloid Interface Sci. 1977, 61, 336-350). Low-frequency modulation of the electrowetting actuation is also applied to cause droplet shape oscillations and capillary resonance. Interferometry allows us to measure a time-dependent capillary spectrum and, in particular, the shift in natural frequencies induced by drop evaporation. Consequently, diffusive kinetics of drop evaporation can be properly estimated, as demonstrated. Because of coplanar electrode configuration, our methodology can be integrated in open and covered microsystems, such as digital lab-on-a-chip devices.     

Mechanisms of equilibrium shape transitions of liquid droplets in electrowetting

Liquid droplets bridging the gap between two dielectric-coated horizontal electrode plates suffer breakup instabilities when a voltage applied between the electrodes exceeds a threshold. Interestingly enough, broken liquid bridges (i.e. a pair of a sessile and a pendant drop) can spontaneously rejoin if the voltage is still applied to the electrodes. Here we study the electro-hydrostatics of the liquid bridges in the joined or broken state and we illuminate the mechanisms of the shape transitions that lead to bridge rupture or droplet joining. The governing equations of the capillary electro-hydrostatics form nonlinear and free boundary problems which are solved numerically by the Galerkin/finite element method. On one hand, we found that capillary bridges become unstable at a turning point bifurcation in their solution space. The solutions past the turning point are unstable and the instability signals the bridge rupture. On the other hand, the separate droplets approach each other as the applied voltage increases. However, solutions become unstable past a critical voltage at a turning point bifurcation and the droplets join. By studying the relative position of the turning points corresponding to bridge rupture and droplet joining, respectively, we define parameter regions where stable bridges or separate droplets or oscillations between them can be realized.     

Re-shaping the coffee ring

Not your cup of tea? "Coffee rings" of spherical colloidal particles are left behind after water droplets resting on surfaces have dried out. This controlled evaporation of colloidal solutions can be exploited to deposit material in regular patterns. It is now shown that if spherical colloids are replaced by slightly elongated ones, the coffee ring is not formed and is replaced by an even more uniform deposition.