Hydrodynamic interaction of a nonvolatile droplet with a planar surface of evaporating liquid

Hydrodynamic interaction between a nonvolatile droplet and an infinite planar surface of an evaporating or condensing liquid is studied theoretically with allowance for effects that are linear with respect to the Knudsen number. The motion of the droplet in the direction normal to the planar liquid surface is considered at low Reynolds numbers and gradients of a gaseous medium temperature and the concentration of the substance evaporating or condensing on the planar liquid surface given at an infinitely large distance from the droplet. The presence of a temperature gradient in the liquid is taken into account in the analysis. The problem is solved in a bispherical coordinate system. The velocity of the steady motion of a castor oil droplet is numerically estimated near the planar surface of evaporating water.     

Hydrodynamic interactions of evaporating droplet with plane liquid surface

The hydrodynamic interactions between freely evaporating or growing droplet suspended in gas and the infinite plane liquid layer is theoretically studied with allowance for effects that are linear with respect to the Knudsen number. It is assumed that substances comprising droplet and liquid layer are identical, and it is taken into account that these substances can contain dissolved nonvolatile component whose concentration is so low that its presence should necessarily be accounted for only in the calculation of the concentration of saturated vapor. Vapor pressure at large distance from the droplet was assumed to be equal to the pressure of saturated vapor above the plane liquid surface. Results of numerical calculations of the rate of steady motion of water droplet evaporating or growing in the air are reported.     

Evaporation of two solution droplets and a droplet located near a flat liquid surface

The mutual influence of two moderate-sized droplets of a dilute nonvolatile substance solution on the processes of their evaporation or condensation is theoretically analyzed under the assumption of a uniform concentration distribution inside the droplets. The conditions for the applicability of this approach are revealed. The evaporation or condensation of a droplet near a flat liquid surface is considered as a limiting case. The fluxes of water molecules to and from the surface of aqueous glycerol solution droplets occurring in air are numerically estimated depending on the droplet radii, distances between their surfaces, and air humidity. Analogous estimates are obtained for an aqueous glycerol solution droplet growing near a flat water surface.     

On the evaporation and motion of a volatile droplet near a volatile liquid surface

A problem concerning the free evaporation or condensation growth of a droplet near an infinite planar surface of the same liquid is solved. The behavior of the droplet is considered at vapor temperature and concentration gradients preset at an infinite distance from it. The boundary conditions take into account effects that are linear with respect to the Knudsen number. Equations are derived for the rate of variations in the radius of the droplet and the velocity of its steady motion induced by nonuniform temperature and concentration of the vapor. Dependences of the rate of variations in the radius and the velocity of the steady motion of the droplet on the distance from the planar surface are presented for a droplet 1 ??m in radius suspended in air.     

Thermophoretic motion of a solid spherical particle near a solid planar surface

The thermophoretic motion of a solid spherical aerosol particle directed normally to an infinite planar solid surface is analyzed. The solution is performed in a bispherical coordinate system with allowance for linear corrections in the Knudsen number. The finite thermal conductivity of a solid body is taken into account in the analysis.     

硬脂酸钠在蓖麻油/水界面上自组装动力学的研究

以电沉积铜为探针,循环伏安法研究硬脂酸钠在蓖麻油/水界面上自组装的动力学.在涂有蓖麻油的石墨粉-环氧树脂固态电极上,硬脂酸钠自组装膜形成过程可由电沉积铜阳极峰监测,遵从高斯函数生长动力学,生长速率常数为km=0.0006292(±0.0000294)s-1.硬脂酸钠自组装膜能较好地控制铜粒子的球形生长和生长尺度,形成硬脂酸钠自组装-铜纳米粒子复合膜.铜粒子在石墨粉-环氧树脂固态电极上为半球形生长,而在涂油和自组装电极上为球形生长.与蓖麻油涂层相比,石墨粉-环氧树脂固态电极与沉积铜间存在弱相互作用(ΔG0=3.86kJ/mol),而硬脂酸钠羧基与沉积铜也有较弱的相互作用(ΔG0=-2.412kJ/mol).     

Self-assembly of spherical particles on an evaporating sessile droplet

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

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.     

On the solidification of a supercooled liquid droplet lying on a surface

We model the solidification and subsequent cooling of a supercooled liquid droplet that is lying on a cold solid substrate after impact. It is assumed that solidification occurs for a given fixed droplet shape. The shapes used by the model are a sphere, truncated spheres, and an experimentally registered droplet shape. The freezing process is conduction-dominant and is modeled as a one-phase Stefan problem. This moving boundary problem is reformulated with the enthalpy method and then solved numerically with an implicit finite-difference technique. The numerical results for the simple case of a spherical droplet touching a surface are similar to those of a freely freezing spherical droplet and are well confirmed by the 1D asymptotic analytical model of Feuillebois et al. (J. Colloid Interface Sci. 169 (1995) 90). A freezing water droplet is considered as an example. The numerical results for full freezing time, subsequent cooling time, and last freezing point coordinate for the various droplets shapes are fitted by analytical functions depending on supercooling, thermal resistance of the target surface (expressed by Biot number), and spreading parameter. These functions are proposed for direct application, thus avoiding the need to solve the full freezing and cooling problem.     

Engineering superlyophobic surfaces as the microfluidic platform for droplet manipulation

We propose robust engineering superlyophobic surfaces (SLS) as a universal microfluidic platform for droplet manipulation enabling electric actuation, featured with characteristics of highly nonwetting, low adhesion, and low friction for various liquids including water and oil. To functionalize SLS with embedded electrodes, two configurations with continuous and discrete topologies have been designed and compared. The discrete configuration is found to be superior upon comparison of their fabrication, microstructures and nonwetting performances. We also present new formulation of SLS pressure stability for linear, square and hexagonal pattern layouts, and propose a criterion for three wetting states (the Cassie-Baxter, partial Cassie-Baxter and Wenzel states) by introducing two dimensionless parameters, which are supported by our experimental data. Droplet manipulation experiments including deformation and transport on electrode-embedded SLS were performed, showing that present SLS reduce adhesion and flow resistance of oil droplets respectively by 98% and 73% compared with a smooth hydrophobic surface, and the excellent hydrodynamic performances are applicable for a wide range of droplet velocity. Simulation of an oil droplet electrically actuated on SLS predicts the significantly increased droplet motion for a low solid fraction and a relatively large droplet size.     

Regular self-motion of a liquid droplet powered by the chemical marangoni effect

We describe here our recent work on spontaneous regular motion of liquid droplet powered by the chemical Marangoni effect under spatially symmetric conditions. It is shown that a spontaneously crawling oil droplet on a glass substrate with a nonequilibrium chemical condition of cationic surfactant exhibits regular rhythmic motion in a quasi-one-dimensional vessel, whereas irregular motion is induced in a two-dimensionally isotropic environment. Such behavior of a droplet demonstrates that spontaneous regular motion can be generated under fluctuating conditions by imposing an appropriate geometry. As another system, we introduce alcohol droplet moving spontaneously on water surface. The droplet spontaneously forms a specific morphology depending on its volume, causing specific mode of translational motion. An alcohol droplet with a smaller volume floating on water surface moves irregularly. On the other hand, a droplet with a larger volume undergoes vectorial motion accompanied by deformation into an asymmetric shape. This result suggests a scenario on the emergence of regular motion coupled with geometrical pattern formation under far-from-equilibrium conditions.     

Thermophoretic force acting on an evaporating particle suspended in a rarefied plasma

Analytical results of the thermophoretic force on an evaporating spherical particle immersed in a rarefied plasma with a large temperature gradient are presented for the extreme case of free-molecule regime and thin plasma sheath. It has been shown that the existence of a temperature gradient in the plasma causes a nonuniform distribution of the local heat flux density on the sphere surface with its maximum value at the fore-stagnation point of the sphere, although the total heal flux to the whole particle is independent of the temperature gradient existing in the plasma. This nonuniform-distribution of the local heat flux density causes a nonuniform distribution of the. local evaporated-mass flux and related reaction force around the surface of an evaporating particle, and thus causes an additional force on the particle. Calculated results show that the thermophoretic force on an evaporating particle may substantially exceed that on a nonevaporating one, especially for the case of a metallic particle (with infinite electric conductivity). The effect of evaporation on the thermophoretic force is more pronounced as the evaporation latent heat of the particle material is comparatively low and as high plasma temperatures are involved.     

Mechanism and Kinetics of Hexamethyldisilazane Reaction with a Fumed Silica Surface

An analytical study is presented on the thermocapillary migration of a fluid sphere within a constant applied temperature gradient in an arbitrary direction with respect to a plane surface. The Peclet and Reynolds numbers are assumed to be small so that the Laplace and Stokes equations, respectively, govern the temperature distributions and fluid velocities inside and outside the droplet. The asymptotic formulas for the temperature and the velocity fields in the quasi-steady situation are obtained by using a method of reflections. The plane surface can be a no-slip solid wall and/or a perfect-slip free surface. The boundary effect on the thermocapillary migration is found to be weaker than that on the motion driven by a body force. Even so, the interaction between the plane and the droplet can be very significant when the gap thickness approaches zero. For the motion of a droplet normal to a solid wall, the effect of the plane surface reduces the translational velocity of the droplet; however, this solid wall can be an enhancement factor on the particle migration as it is translating parallel to the wall. On the other hand, in case of a droplet migrating close to a free surface due to thermocapillarity, the droplet velocity can be either greater or smaller than that which would exist in the absence of the plane surface, depending on the relative thermal conductivity and the surface properties of the particle and its relative distance from the plane. Furthermore, the interacting thickness of the affected region by the presence of the plane is discussed by considering the droplet mobility. Generally speaking, a free surface exerts less influence on the particle movement than does a solid surface. Copyright 2000 Academic Press.     

Droplet size effects on film drainage between droplet and substrate

When a droplet approaches a solid surface, the thin liquid film between the droplet and the surface drains until an instability forms and then ruptures. In this study, we utilize microfluidics to investigate the effects of film thickness on the time to film rupture for water droplets in a flowing continuous phase of silicone oil deposited on solid poly(dimethylsiloxane) (PDMS) surfaces. The water droplets ranged in size from millimeters to micrometers, resulting in estimated values of the film thickness at rupture ranging from 600 nm down to 6 nm. The Stefan-Reynolds equation is used to model film drainage beneath both millimeter- and micrometer-scale droplets. For millimeter-scale droplets, the experimental and analytical film rupture times agree well, whereas large differences are observed for micrometer-scale droplets. We speculate that the differences in the micrometer-scale data result from the increases in the local thin film viscosity due to confinement-induced molecular structure changes in the silicone oil. A modified Stefan-Reynolds equation is used to account for the increased thin film viscosity of the micrometer-scale droplet drainage case.     

Droplet evaporation near a flat wall

The problem of the free evaporation of a droplet of moderately large size occurring near an infinite flat wall is solved. The cases in which the wall surface is impenetrable to an evaporating substance and vapor concentration remains unchanged at the surface are considered. The temperature of the wall surface is assumed to be constant and equal to the gas temperature at a large distance from the droplet. A set of algebraic equations is derived for molecular fluxes and the temperature and the concentration of gaseous components. Dependences of the evaporation rate of a water droplet suspended in air on its radius and distance from a wall are determined.     

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.     

On the evolution of a multicomponent droplet during nonisothermal diffusion growth or evaporation

A set of equations has been derived for the size, composition, and temperature of a multicomponent droplet of a nonideal solution during its diffusion nonisothermal condensation growth or evaporation in a multicomponent mixture of vapors with an incondensable carrier gas. In addition to complete equations for material and heat transfer in the vapor-gas medium surrounding the droplet, the derived set, in the general case, describes the nonstationary growth or evaporation of the droplet under arbitrary initial conditions (initial size and temperature of the droplet and the concentrations of the nonideal multicomponent solution in it) and the establishment of the stationary values of the composition, temperature, and the rate of variations in the size of the droplet with allowance for heat effects and diffusion and thermodiffusion material transfer, Stefan flux, motion of the droplet surface, and the nonideality of the solution in the droplet. A simplified set of equations obtained without taking into account the contributions from the flow, cross effects, and thermal expansion in the equations of the material and heat transfer in the vapor-gas medium has been considered. Equations describing growth/evaporation in the stationary regime have been analyzed for droplets of ideal multicomponent solutions.     

New approach to the kinetics of heterogeneous unary nucleation on liquid aerosols of a binary solution

The formation of a droplet on a hygroscopic center may occur either in a barrierless way via Kohler activation or via nucleation by overcoming a free energy barrier. Unlike the former, the latter mechanism of this process has been studied very little and only in the framework of the classical nucleation theory based on the capillarity approximation whereby a nucleating droplet behaves like a bulk liquid. In this paper the authors apply another approach to the kinetics of heterogeneous nucleation on liquid binary aerosols, based on a first passage time analysis which avoids the concept of surface tension for tiny droplets involved in nucleation. Liquid aerosols of a binary solution containing a nonvolatile solute are considered. In addition to modeling aerosols formed through the deliquescence of solid soluble particles, the considered aerosols constitute a rough model of "processed" marine aerosols. The theoretical results are illustrated by numerical calculations for the condensation of water vapor on binary aqueous aerosols with nonvolatile nondissociating solute molecules using Lennard-Jones potentials for the molecular interactions.     

Mechanistic studies of droplet electrophoresis: A review

Electrophoresis (EP) of droplets is an intriguing phenomenon that has applications in biological systems, separation strategies, and reactor engineering. Droplet EP is significantly different from the classic particle EP because of droplet characteristics such as a mobile surface charge and the nonrigidity of the interface. Also, the liquid–liquid system, where there is an interplay between the hydrodynamic and electrokinetic forces in both phases, adds to the complexity of electrophoretic motion. Due to the vast amount of potential applications of droplet EP, a mechanistic understanding of the droplet motion in the presence of an external electric field is crucial. This review provides a background on the mechanism of droplet EP and summarizes the intrinsic interplay between the different relevant forces in these systems. The review also describes the key differences between droplet EP and particle EP, and the impact of these differences on droplet mobility. Additionally, we schematically summarize the effects of key parameters on droplet EP mobility, such as electric double layer polarization, the development of internal flow inside a droplet and boundary effects.     

Sliding Water Droplet on Oil Impregnated Surface and Dust Particle Mitigation

Self-cleaning of surfaces becomes challenging for energy harvesting devices because of the requirements of high optical transmittance of device surfaces. Surface texturing towards hydrophobizing can improve the self-cleaning ability of surfaces, yet lowers the optical transmittance. Introducing optical matching fluid, such as silicon oil, over the hydrophobized surface improves the optical transmittance. However, self-cleaning ability, such as dust mitigation, of the oil-impregnated hydrophobic surfaces needs to be investigated. Hence, solution crystallization of the polycarbonate surface towards creating hydrophobic texture is considered and silicon oil impregnation of the crystallized surface is explored for improved optical transmittance and self-cleaning ability. The condition for silicon oil spreading over the solution treated surface is assessed and silicon oil and water infusions on the dust particles are evaluated. The movement of the water droplet over the silicon oil-impregnated sample is examined utilizing the high-speed facility and the tracker program. The effect of oil film thickness and the tilting angle of the surface on the sliding droplet velocity is estimated for two droplet volumes. The mechanism for the dust particle mitigation from the oil film surface by the sliding water droplet is analyzed. The findings reveal that silicon oil impregnation of the crystallized sample surface improves the optical transmittance significantly. The sliding velocity of the water droplet over the thick film (~700 µm) remains higher than that of the small thickness oil film (~50 µm), which is attributed to the large interfacial resistance created between the moving droplet and the oil on the crystallized surface. The environmental dust particles can be mitigated from the oil film surface by the sliding water droplet. The droplet fluid infusion over the dust particle enables to reorient the particle inside the droplet fluid. As the dust particle settles at the trailing edge of the droplet, the sliding velocity decays on the oil-impregnated sample.