Flow visualization and solute transport in evaporating droplets

We have investigated the velocity field and associated particle transport in an evaporating water droplet using the tool of particle image velocimetry. Experiments were performed where single droplets containing polystyrene particles were exposed to evaporation. Our method applicable to droplets confined between two parallel surfaces differs from the conventional PIV techniques on the 3D droplets and removes many of the limitations associated with mapping of velocity field. To avoid refraction of light at the droplet surface we have studied the motion in a disc‐shaped droplet which was prepared by confining the drop between two nonwetting surfaces and its base is pinned to a wetting surface. Experiments were carried out under the conditions where Marangoni flow creates convection cells and finally leading to deposition of particles toward the pinned edge. The contact angle, height of the droplet, velocity field, and the particle concentration inside the evaporating droplet was measured and its time evolution was recorded. © 2009 American Institute of Chemical Engineers AIChE J, 56: 1674–1683, 2010     

平面上固定接触角蒸发液滴内Marangoni对流失稳现象

实验观察了水平加热基板上1cSt硅油液滴在固定接触角蒸发模式下的Marangoni对流失稳模式的演化规律,分析了接触角和基板温度对Marangoni对流不稳定性的影响。结果表明,随着基板温度的升高液滴内依次呈现热毛细对流、稳定的Bénard-Marangoni（BM）对流和不规则振荡的BM对流。对于稳定的BM对流,涡胞数随润湿半径的减小逐渐减少;当涡胞数少于5时,涡胞变为圆形;随着接触角的增大,由热毛细对流转捩为稳定的BM对流时的临界Marangoni数（Ma_c）增大;蒸发过程中,液滴内无量纲涡胞数随无量纲润湿半径的增大而线性增大,与接触角无关。     

The separation of two different sized particles in an evaporating droplet

The separation of two different sized particles during evaporation of a dilute droplet is examined both computationally and experimentally. A transport model of the evaporating droplet system was solved using the finite element method to determine the fluid velocity, pressure, vapor concentration surrounding the droplet, temperature, and both particle concentrations. Experimentally, 1 μm and 3 μm polystyrene particles were used during the evaporation of a sessile water droplet. It was determined that to accurately model particle deposition, thermal effects need to be considered. The Marangoni currents in evaporating droplets keep particles suspended in the droplet until the end of the evaporation. Previous models of particle deposition during droplet evaporation have rapid accumulation of particles at the contact line. Our experiments and the experiments of others demonstrate that this is not accurate physically. In addition, to model the separation of two different sized particles the consideration of thermal effects is essential. © 2015 American Institute of Chemical Engineers AIChE J, 61: 3547–3556, 2015     

The importance of gravity in droplet evaporation: A comparison of pendant and sessile drop evaporation with particles

As a droplet with particles evaporates, the particles deposit on the substrate surface. In this work, we show the extent of gravitational effects on the particle deposition profile and propose a new model for particle tracing in an evaporating droplet which accounts for gravitational effects. Experimentally, we compare pendant and sessile water droplets with 1 and 3 μm polystyrene particles. Numerically, the finite element method was used to create a transport model of the evaporating droplet system and particle deposition. The numerical and experimental results have excellent agreement and show that a pendant water droplet with 1 and 3 μm polystyrene spheres has significant separation of the two particle sizes. Finally, a phase diagaram was created to map different deposition profiles for various gravitational Péclet numbers (Pe_G) and ratios of Péclet number to Damköhler number (Pe/Da). © 2015 American Institute of Chemical Engineers AIChE J, 62: 947–955, 2016     

Transport and deposition patterns in drying sessile droplets

The literature on drying sessile droplets and deposition of suspended material is reviewed including the simple explanation of the “coffee ring” deposit given by Deegan et al.¹ Analytical and numerical solutions for the flow are given, including the effect of Marangoni stresses, pinning or movement of the contact line, and viscous, thermal, gravitational, and other effects. The solution space is explored using dimensionless groups governing mass, momentum, and heat transfer effects in the droplet, external gas, and substrate. The most common types of deposition patterns are summarized, including those produced by pinned contact lines, sticking‐and‐slipping contact lines, and Marangoni effects. The influence of contact‐line deposits is also reviewed, and the effects of colloidal, polymeric, and other depositing materials. Advanced applications from ink‐jet printing to disease diagnosis are discussed as well. The review helps readers take stock of what has been learned and what remains incompletely explained. © 2014 American Institute of Chemical Engineers AIChE J, 60: 1538–1571, 2014     

水平及竖直基底上微小固着液滴的蒸发特性分析

为揭示非水平表面上微小蒸发液滴的传热传质特性,本文在准稳态模型的假设下构造三维液滴模型,综合考虑了蒸气扩散、蒸发冷却以及气相域中的自然对流这3种传输机理,对水平以及竖直基底上液滴的蒸发过程进行数值研究。通过分析气液界面上温度分布、蒸发通量分布及总蒸发率的变化,重点探究了基底过热度以及重力的改变对液滴蒸发特性的影响。结果表明：与水平基底上温度的对称分布不同,竖直基底上气液界面温度分布表现出明显的非对称性,且非对称性随基底过热度的升高而增强,最低温度点不再位于液滴顶点,而向一侧偏移。此外,水平基底上气液界面局部蒸发通量呈对称分布,各截面分布相似,而竖直基底上局部蒸发通量分布则呈现出显著的非对称性以及各截面异性,非对称性随着基底过热度的升高而增强,这是重力改变后气相域自然对流发生改变的结果。与水平基底相比,竖直基底上蒸发率更高,总蒸发时间更少。最后,基底由水平变为竖直时,液滴内部流场由对称双涡转变为非对称单涡,单涡流速显著大于双涡流速,液滴内流速随基底过热度的上升而增大,单涡环流造成了气液界面温度分布的改变以及最低温度点的偏移。     

Electrospray evaporation and deposition

Electrospray transport, evaporation and deposition on a heated substrate is investigated theoretically by Lagrangian tracking of single droplets. The droplet mass and heat transfer are calculated under forced convection and compared to limited cases of electrospray transport only or droplet evaporation only. Segregation of primary and satellite electrospray droplets is observed also, in agreement with data in the literature. The arriving droplet diameter and spatial distribution at the substrate show that evaporation barely affects droplet transport. In contrast, droplet size and salt concentration can be affected significantly by evaporation. It is shown also how process parameters such as substrate temperature, initial droplet diameter and vapor transport may affect the film quality. Accounting for the Rayleigh limit of charged droplets, leads to acceleration of their evaporation when high substrate temperatures or small droplet diameters are employed.     

Deposition of Brownian particles during evaporation of two-dimensional sessile droplets

Evaporation of sessile droplets gives rise to internal flow that, in turn, affects drastically the deposition of the suspended particles on the substrate. Analytical expressions for the flow field are used to compute the local velocity inside an evaporating two-dimensional droplet as a function of position and time of evaporation. Trajectories of a sample of suspended Brownian particles are computed along the progress of the evaporation process and terminate upon collision with the solid substrate. Traveling particles are allowed to interact with the evaporating free surface and are either rebounced into the main body of the droplet or float on the surface until they are collected on the substrate. The dependence of the diffusion coefficient on the distance from the substrate is taken into account giving rise to anisotropic diffusional effects that, however, are shown to affect slightly the deposition rate profile except in the case of flow-dominated transport. Results for hydrophilic and strongly hydrophobic substrates are presented and the conditions for the development of the two-dimensional variant of the famous “coffee stain phenomenon” are investigated. Comparison of the simulated deposition profiles with the corresponding predictions of a convection-diffusion lattice–Boltzmann model revealed excellent agreement for various Peclet number values. Simulation of stick-slip evaporation leads to well-defined multiple stripes, the density of which depends strongly on the difference between the initial contact angle and the angle at which the slip step is activated.     

Influence of Plate Size on the Evaporation Rate of a Heated Droplet

The purpose of this study is to numerically investigate how the width of a plate influences natural convection around a droplet. Droplets evaporating on hot surfaces have many applications including drying of dishes and paint. Evaporation rate and deposition of particles withheld in the fluid are of great importance in both cases. As a first step to investigate how the drying rate and deposition mechanisms can be controlled, this work aims to investigate how the external flow around a water droplet influences the evaporation rate. Natural convection caused by the hot plate on which the droplet rests is considered and the effect of different widths is examined. Results show that an extension of the plate past the droplet will increase the maximum velocity in the domain due to natural convection while the flow close to the surface is decreased due to the no-slip condition and temperature gradient. A decrease of the evaporation rate is therefore observed when the plate is extended past the droplet as compared to the case when the plate and droplet have the same diameter. Simulations furthermore show that the results from the heat and mass transfer analogy only compare well to the results of Fick's law when the droplet and plate have the same width.     

高温辐射环境中液滴的沸腾效应

建立了液滴在高温对流和辐射环境中的受热和蒸发模型,结合液滴均质沸腾模型,编制了计算程序。以正十二烷液滴为例,考虑液滴的膨胀效应以及液滴与周围气流的热物性变化,数值模拟了高温辐射与对流加热下的液滴升温和蒸发过程。分析了不同对流和高温辐射条件下,液滴内部是否能够发生沸腾。研究表明,液滴在高温辐射和对流加热下,蒸发伴随热膨胀;高温热辐射加热可导致液滴内部温度高于表面温度,升温到一定程度后可达到液滴内部沸腾状态;影响液滴沸腾的因素有液滴半径、辐射温度、环境气流温度等;同时,随着液滴蒸发,高温环境中液滴的沸腾过热度逐渐增大。     

太阳能加热液滴在亲疏水表面"黏-滑"蒸发

实验研究了亲水和疏水表面上太阳能加热去离子水及金纳米流体液滴三相接触线动力学。在亲水和疏水表面滴加2μL去离子水和纳米流体液滴,用一定功率太阳能模拟器照射液滴使其蒸发,期间采用高速摄像机实时记录液滴在不同表面上的蒸发过程。由MATLAB程序处理图像得到液滴在不同表面上蒸发过程中接触角和接触圆直径的动态变化过程。发现液滴接触线在不同亲疏水表面上存在不同运动特性。去离子水液滴在亲水表面上常接触面积模式和常接触角模式依次控制蒸发过程。去离子水液滴在疏水表面上都呈现出“黏-滑”蒸发特性,即液滴先以常接触面积模式蒸发,之后接触线快速滑动,接触线固定后再以常接触面积模式蒸发,依次往复。纳米流体液滴在亲水表面上主要以常接触面积蒸发模式为主,在疏水表面上同样呈现“黏-滑”蒸发特性。从液滴表面能角度出发,对液滴接触线“钉扎”和“去钉扎”过程进行详尽分析,得出基底润湿性和纳米颗粒沉积是影响液滴接触线在表面上运动的重要因素。     

Morphology evolution and dynamics of droplet coalescence on superhydrophobic surfaces

In this work, the coalescence of two equal‐sized water droplets on superhydrophobic surfaces (SHSs) is experimentally investigated. The morphologies of droplet coalescence are observed from side‐view and bottom‐view using high‐speed camera system. The related morphology evolution and dynamics of droplet coalescence are explored. The dynamic behaviors of droplet coalescence on SHSs can be decomposed into liquid bridge growth, contact line evolution, and droplet jumping. The liquid bridge radius is proportional to the square root of time, whereas the dimensionless prefactor is decreased from 1.18 to 0.83 due to the transition of interface curvature. The retraction velocity of the contact line shows limited dependence on initial droplet radii as the retraction dynamics considered here are governed by the capillary–inertial effect. The coalesced droplet finally departs the substrate with a dimensionless jumping velocity of around 0.2. A heuristic argument is made to account for the nearly constant dimensionless jumping velocity. © 2018 American Institute of Chemical Engineers AIChE J, 64: 2913–2921, 2018     

Wetting of hydrophobic substrates by nanodroplets of aqueous trisiloxane and alkyl polyethoxylate surfactant solutions

Trisiloxane surfactants at low concentrations promote the complete and rapid wetting of aqueous droplets on very hydrophobic (hydrocarbon) substrates. This behavior has not been demonstrated by any other surfactant which explains why the trisiloxanes are referred to as superspreaders. Despite many experimental and theoretical investigations the mechanism of superspreading is not fully understood. Molecular dynamics simulations using all-atom force fields have been conducted to attempt to elucidate the mechanism of superspreading. Spherical nanodroplets containing approximately 10,000 water molecules in the bulk and 475 surfactant molecules at the liquid-vapor interface were placed in the vicinity of a graphite substrate and allowed to spread freely at room temperature. In the trisiloxane case the droplet was found to spread very little, although randomly removing 175 surfactant molecules lowered the final contact angle from 110^° to 80^°. In contrast, an alkyl polyethoxylate surfactant-laden droplet was found to spread significantly further, with the equilibrium contact angle reaching 55^°. Similar results for the two surfactant systems were found for cylindrical nanodroplets spreading on a self-assembled monolayer (SAM). The reasons for the lack of spreading in the trisiloxane case and the simulation challenges associated with these systems are discussed. In support of our arguments we demonstrate that the surfactant molecules of an initially uniform aqueous trisiloxane solution self-assemble into a bilayer in tens of nanoseconds on a graphite substrate. Lastly, in a final set of simulations, neat trisiloxane droplets at 450 K are found to arrange into a layered structure on a methyl-terminated SAM and to form a sand pile-shape on a hydroxyl-terminated SAM.     

Behavioral patterns of drop impingement onto rigid substrates with a wide range of wettability and different surface temperatures

This article concerns behavioral patterns of droplet impingement onto solid substrates covering a wide range of wettability from hydrophilic to superhydrophobic surfaces heated at different temperatures. For droplet impingement onto partial hydrophobic surfaces (mirror‐polished Cu substrate), the maximum heights of receding droplet undergoing a consecutive increment with surface temperature can be explained taking account of Marangoni flow. Also, the relation to predict the increment of droplet heights with surface temperature was manifested in the light of lubrication approximation combined with energy conservation. However, this relation is only valid for droplet impacts onto partial hydrophobic surface, because the recoiling droplet height was observed to be independent of surface temperature for both hydrophilic and superhydrophobic targets. This phenomenon was attributed to inherent wettability accompanying larger contact angle hysteresis for the hydrophilic substrate and to the presence of an adiabatic gas layer between the composite surface and impacting droplet, for the superhydrophobic target. © 2009 American Institute of Chemical Engineers AIChE J, 2009     

Transport and Removal of Expiratory Droplets in Hospital Ward Environment

The transport and removal characteristics of expiratory droplets at different supply airflow rates and “coughing” orientations were investigated both numerically and experimentally in a three-bed hospital ward setting. A Lagrangian-based particle-tracking model with near-wall correction functions for turbulence was employed to simulate the fate of the expiratory droplets. The model was tested against experimental droplet dispersion data obtained in an experimental hospital ward using Interferometric Mie Imaging and a light-scattering aerosol spectrometer. The change in airflow supply rate had insignificant effect on the transport and deposition of very large droplets (initial sizes ≥ 87.5 μm) due to the dominance of gravitational settling on these behaviors. Smaller droplets (initial sizes ≤ 45 μm) exhibited certain airborne behaviors. The effect of thermal plumes from heat sources was observed only when the supply airflow was low and when the droplet size was small, as observed in the vertical mixing patterns of the droplets of various sizes. Larger droplets tended to settle lower and lateral dispersion of the droplets became weak at the low supply airflow rate. The deposition characteristics for different surfaces in the room are described. The heat plumes seemed to obstruct small droplets from being deposited onto heated surfaces. More deposition was predicted in the lateral injection case compared with the vertical injection case. Adopting near-wall correction for turbulence in the model reduced the predicted deposition removal fraction by 25% for 1.5 μm droplets. This reduction became less significant for larger droplets due to the smaller dependence on turbulent diffusion in their deposition.     

Evaporation of a sessile water droplet subjected to forced convection in humid environment

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.     

Factors affecting the rate of deterioration in the frying quality of fats II. Type of heater and method of heating

Using a commercially prepared hydrogenated lard and heating methods simulating those currently employed in commercial fryers, it was found that the rate of fat deterioration varied inversely with the temp of the heating element. This has been attributed to differences in the rate and duration of convection circulation, a measure of the amt of fat-air contact, and therefore, thermal oxidation. When element temp were increased from 900–2400F, while thermostatically maintaining the fat temp at 375F, it was found that the rate of convection circulation increased while the duration of convection circulation decreased, and it is postulated that the overall effect of increasing element temp is one of decreasing the total amt of fat contact with the air. It was also demonstrated that mechanical circulation of fat, as required in an externally heated fat system, significantly increased that rate of fat deterioration when compared to fat heated by conventional direct gas-heat, if both were heated and maintained at 375F for identical periods of time. Presented at the AOCS Meeting in New Orleans, 1962.     

Driving liquid droplets on microstructured gradient surface by mechanical vibration

Dynamic transportation of water droplet on microstructured hydrophobic silicon substrate with a contact angle gradient is studied in this article. We propose a new type of substrate designed with microridges on a silicon wafer fabricated by photolithograph and subsequent coating with octadecyltrichlorosilane (OTS). When horizontal vibration is applied on the substrate, the water droplet can move to the direction with larger solid–liquid contact area fraction. It is found that the dynamic contact angle of the water droplet varied with the vibration direction and the speed of the substrate. The contact angle difference at the left and the right edge of the water droplet on the vibrated surface is obviously magnified compared to the contact angle difference of the droplet on the static surfaces, resulting in the increasing driving force. When the vibration amplitude of the exciter source (20 Hz) increases from 0.14 to 0.43 mm, the average velocity of 10 μL water droplet increases from 10 to 23 mm/s. The internal flow pattern of the water droplet moving on the microstructured hydrophobic surfaces is also obtained using particle image velocimetry (PIV) and particle tracking velocimetry (PTV) techniques. Both rolling and slipping motions are observed for the water droplet during its movement in the vibrated substrate.     

A Method of Determining the Contact Area Between a Particle and Substrate Using Scanning Electron Microscopy

A new technique for determining the contact radius between a micrometer size particle and a contacting substrate using scanning electron microscopy has been developed. The Contact Area Measurement (CAM) technique, which is especially suited for small surface-force-induced contact radii, involves evaporating a thin, uniform coating of a conductive material, such as aluminum, over a sample comprised of particles on a substrate while the sample is rotated slowly. The sample is examined before and after particle removal to determine both the radii of the particle and its respective contact. Where the particle contacted the substrate, no metal deposition occurred. The resulting differences in the secondary electron emissions provide a contrast mechanism that the SEM can image. The CAM technique is shown to be useful in examining rigid particles on rigid substrates, where the inherent contacts are small, making measurements difficult, and for examining irregularly-shaped particles and contact areas.