A robust algorithm for the simultaneous parameter estimation of interfacial tension and contact angle from sessile drop profiles

The pendant and sessile drop profile analysis using the finite element method (PSDA-FEM) is an algorithm which allows simultaneous determination of the interfacial tension (gamma) and contact angle (theta(c)) from sessile drop profiles. The PSDA-FEM algorithm solves the nonlinear second-order spherical coordinate form of the Young-Laplace equation. Thus, the boundary conditions at the drop apex and contact position of the drop with the substrate are required to solve for the drop profile coordinates. The boundary condition at the position where the drop contacts the substrate may be specified as a fixed contact line or fixed contact angle. This paper will focus on the fixed contact angle boundary condition for sessile drops on a substrate and how this boundary condition is used in the PSDA-FEM curve-fitting algorithm. The PSDA-FEM algorithm has been tested using simulated drop shapes with and without the addition of random error to the drop profile coordinates. The random error is varied to simulate the effect of camera resolution on the estimates of gamma and theta(c) values obtained from the curve-fitting algorithm. The error in the experimental values for gamma from sessile drops of water on acrylic and Mazola corn oil on acrylic falls within the predicted range of errors obtained for gamma values from simulated sessile drop profiles with randomized errors that are comparable in magnitude to the resolution of the experimental setup.     

A method for correcting the contact angle from the θ/2 method

The θ/2 method, a widely used technique on measuring the contact angle of a sessile drop, assumes that the drop profile is part of a sphere. However, the shape profile of a sessile drop is governed by the Young–Laplace equation and is different from a sphere, especially for drops with a large bound number (e.g. large volume or small surface tension). The spherical assumption, therefore, causes errors on evaluating the contact angles. The deviation of contact angle from the θ/2 method is evaluated from a theoretical calculation in this work. A simple means is given for correcting the measurement error. The corrected angle results from the drop volume, surface tension, liquid density and the contact angle from θ/2 method. An algorithm for finding the correct contact angle without knowing the density and surface tension is also given. At the end, two examples of pendant drops are given for the illustration.     

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.     

Estimation of trace vapor concentration-pathlength in plumes for remote sensing applications from hyperspectral images

A novel approach for quantification of chemical vapor effluents in stack plumes using infrared hyperspectral imaging are presented and examined. The algorithms use a novel application of the extended mixture model to provide estimates of background clutter in the on-plume pixel. These estimates are then used iteratively to improve the quantification. The final step in the algorithm employs either an extended least-squares (ELS) or generalized least-squares (GLS) procedure. It was found that the GLS weighting procedure generally performed better than ELS, but they performed similarly when the analyte spectra had relatively narrow features. The algorithms require estimates of the atmospheric radiance and transmission from the target plume to the imaging spectrometer and an estimate of the plume temperature. However, estimates of the background temperature and emissivity are not required which is a distinct advantage. The algorithm effectively provides a local estimate of the clutter, and an error analysis shows that it can provide superior quantification over approaches that model the background clutter in a more global sense. It was also found that the estimation error depended strongly on the net analyte signal for each analyte, and this quantity is scenario-specific.     

Onset of Marangoni convection for evaporating sessile droplets

We have generated stability parameters using a linear stability analysis to predict the onset criteria for Marangoni convection in evaporating sessile droplets for two types of substrates, insulating and conducting. The stability problem was formulated with boundary conditions that allow for a temperature discontinuity at the liquid-vapour interface and the inclusion of an expression for the evaporation flux that considers this temperature discontinuity. We introduce no fitting coefficients; therefore, the stability parameters we generate contain only physical variables. The results indicate that spherical sessile droplets evaporating on insulating substrates are predicted to have a similar onset criteria with sessile droplets evaporating on conducting substrates. The onset prediction for sessile droplets evaporating on insulating substrates is found to be considerably different than the case of liquids evaporating from conical funnels constructed of insulating materials owing to the modification of the boundary condition from the geometrical shift and the corresponding retention of modes in the solution. A parametric analysis demonstrates how the input variables impact the stability of evaporating sessile droplets.     

小角躺滴法测定低界面张力

在测定界面张力,特别是测定低界面张力的各种方法中,躺滴法占有相当重要的位置。但一般的躺滴法都要求获得赤道半径(图1中的x_e)数据.故躺滴与基底之间的接触角必须大于90°.这在低界面张力体系中常常难以实现,致使躺滴法的应用受到限制。本文提出一种新的躺滴法,它不依赖于接触角的大小,只需测定躺滴轮廓线上两个相关点的坐标,根据所给数值表即可计算出界面张力,从而为躺滴法应用于低界面张力,特别是     

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.     

Carbon nanotube network formation from evaporating sessile drops

Fabrication of single-walled carbon nanotube (SWNT) networks using evaporation of SDS-SWNT sessile drops on a hydrophobized silicon substrate is reported. It is suggested that the organization of nanotubes during evaporation is controlled by aggregates (in the SDS-SWNT dispersion) and hydrophobicity of the substrate. On hydrophobic substrates, the evaporation of SDS-SWNT sessile drops proceeds through constant contact area. On hydrophilic substrates, nanotube aggregates in SDS-SWNT dispersion stop the contact line from moving, resulting in the formation of "coffee-stains". The (partial) removal of aggregates by centrifugation is essential for a freely moving contact line leading to the organization of nanotubes into a network of homogeneously distributed nanotubes on the most hydrophobic substrate. The evaporation of sessile drops was characterized by microscopic, spectroscopic, and topographical techniques.     

Evaluation of the surface tension measurement of axisymmetric drop shape analysis (ADSA) using a shape parameter

A quantitative criterion called “shape parameter” to evaluate the quality of surface tension measurement of Axisymmetric Drop Shape Analysis (ADSA) is presented. ADSA is a powerful technique for the measurement of interfacial tensions and contact angles of pendant drops, sessile drops, and bubbles. Despite the general success of ADSA, deficient results may be obtained for drops close to spherical shape. Therefore, the “shape parameter” was used to determine the range of drop shapes in which ADSA succeeds or fails. The “shape parameter” is a dimensionless parameter that expresses quantitatively the difference in shape between a given experimental profile and an inscribed circle. The surface tension measurements of ADSA were evaluated for both pendant drop and constrained sessile drop configurations using the shape parameter. Different shapes of the pendant drop were studied using different sizes and materials of holders. For each drop configuration, a “critical shape parameter” was defined based on the minimum value of the shape parameter that guarantees an error of less than ±0.1 mJ/m². Furthermore, the effects of the type of liquid and constellation on the “critical shape parameter” were studied.     

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.     

Sessile droplet de-pinning: new life for gravimetric data

Using three different types of surfaces as exemplars, we report a gravimetric method as a viable tool for studying the de-pinning process. Namely, the de-pin time, tau(d) (the time required for a horizontal sessile droplet to de-pin at the triple phase line on a given substrate), is estimated without using a time consuming and expensive video imaging system. This is made possible by deciphering the non-linear portion of mass vs time data of an evaporating sessile droplet. Typical gravimetric glass-substrate evaporative mass loss vs time data has two regimes: a long, linear regime followed by a short, non-linear regime. Traditionally, researchers extract only the evaporation rate of a droplet from the linear regime but discard (by truncating the data) or ignore (thus deriving no information from) the non-linear regime. The origin of the linear to non-linear transition, found almost universally in gravimetric data, persists unremarked upon. By constructing three very different types of surfaces and comparing gravimetric data with video imaging data taken simultaneously, we report the transition is correlated to the onset of the de-pinning event in each case. This realization enables us to measure the de-pin time, tau(d), with gravimetric data only; i.e., without the video system, gathering more information from gravimetric data than previously considered. The method has application in estimating the de-pin time of a droplet deposited on a substrate that yields poor top-view contrast for videography, such as a water droplets on silicon wafers or glass substrates. Finally, gravimetric data is more accurate for evaporation modeling when substrate/droplet interaction areas are not circular.     

Evaporation dynamics of a binary sessile droplet: Theory and comparison with experimental data on a droplet of a sulfuric-acid solution

Diffusion evaporation of a sessile binary droplet in an atmosphere of a noncondensable carrier gas has been considered. For a droplet consisting of two infinitely miscible liquids, a relation between the current values of solution concentration and volume of the droplet has been derived in an explicit form under the ideal solution approximation. It has been shown that the volume of a sessile binary droplet may, as well as the volume of a free binary droplet, vary nonmonotonically with time. The evaporation of a droplet of an aqueous sulfuric-acid solution has been considered in detail taking into account the nonideality of the solution. Time variations in the volume, base area, and contact angle have been experimentally measured for the sessile droplet of an aqueous sulfuric-acid solution on a hydrophobized substrate. The experimental data obtained at different initial humidities of water-vapor and droplet-solution concentrations have been analyzed within the theory of the stationary isothermal diffusion evaporation of a sessile binary droplet.     

Influence of surface orientation on the organization of nanoparticles in drying nanofluid droplets

The influence of droplet orientation on the flow directed organization of nanoparticles in evaporating nanofluid droplets is important for the efficiency of foliar applied fertilizers and contamination adhesion to the exterior of buildings. The so called "coffee ring" deposit resulting from the evaporation of a sessile nanofluid drop on a hydrophilic surface has received much attention in the literature. Deposits forming on hydrophobic surfaces in the pendant drop position (i.e. hanging drop), which are of importance in foliar fertilizer and exterior building contamination, have received much less attention. In this study, the deposit patterns resulting from the evaporation of water droplets containing silica nanoparticles on hydrophobic surfaces orientated in the sessile or pendant configuration are compared. In the case of a sessile drop the well known coffee ring pattern surrounding a thin nanoparticle layer was formed. A deposit consisting of a thin coffee ring surrounding a bump was formed in the pendant position. A mechanism involving flow induced aggregation at the droplet waist, settling, orientation dependant accumulation within the drop and pinning of the contact line is suggested to explain the findings. Differences in the contact area and adhesion of deposits with surface orientation will affect the efficiency and rainfastness of foliar fertilizers and the cleanliness of building exteriors.     

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.     

Digital optical memory devices based on polymer-dispersed liquid crystals films: appropriate polymer matrix morphology

ABSTRACT

Permanent memory effect (PME) in polymer dispersed liquid crystal (PDLC) allows a greater applicability range than traditional PDLCs. One of the most interesting application could be the possible storing of optical information, the so-called Digital Optical Memory (DOM) devices. To test this application it would be required a display structure having an array of pixels addresses. Each pixel was filled with PDLC film with PME and electric field can be independently applied to different PDLC elements to define on/off pixel states (transparent or scattering states).PDLC films were obtained from a mixture of E7 nematic liquid crystal and poly(ethylene glycol) dimethacrylate with 875 g mol^-1oligomer as precursor of the polymeric matrix. The effect of the curing temperature and the UV light intensity as well time exposure during the polymerisations on the electro-optical performance of PDLC films were investigated. In this way, a high transparency state (T_OFF=55%) for a long period of time at room temperature even after the applied voltage has been switched off were obtained, started from an opaque state (T₀=0%) and after reaching a transparent state (T_MAX=75%), which causes 73% PME. The application to an 8x8 passive matrix using PDLC with PME is also demonstrated as proof-of-principle.     

An External Matrix-Assisted Laser Desorption Ionization Source for Flexible FT-ICR Mass Spectrometry Imaging with Internal Calibration on Adjacent Samples

We describe the construction and application of a new MALDI source for FT-ICR mass spectrometry imaging. The source includes a translational X-Y positioning stage with a 10×10 cm range of motion for analysis of large sample areas, a quadrupole for mass selection, and an external octopole ion trap with electrodes for the application of an axial potential gradient for controlled ion ejection. An off-line LC MALDI MS/MS run demonstrates the utility of the new source for data- and position-dependent experiments. A FT-ICR MS imaging experiment of a coronal rat brain section yields ～200 unique peaks from m/z 400-1100 with corresponding mass-selected images. Mass spectra from every pixel are internally calibrated with respect to polymer calibrants collected from an adjacent slide.     

Relation between contact angle and the cross-sectional area of small, sessile liquid drops

In this theoretical study, the cross-sectional areas of small, sessile drops were calculated for solid surfaces with a wide range of wettability. These areas were then used to estimate obstruction of rectangular gas flow channels by sessile liquid drops. Our findings suggest that even a small improvement in wettability (i.e., a lower contact angle) will lead to a substantial decrease in blockage. This work has implications for small channels that contain two-phase flow, such as those found in fuel cells.     

Real-space observation of internal ordering configurations of sessile liquid crystal micro-droplets

In this study, we report a simple method to determine the internal ordering configurations of sessile liquid crystal (LC) micro-droplets. We studied the ordering of LC micro-droplets under perpendicular, tangential and hybrid boundary conditions, using a polarised microscope equipped with a full-wave retardation plate. Four types of internal ordering configurations were found in sessile LC micro-droplets: two different types of dark cross configuration, a four-petal configuration and a three-petal configuration. These findings provide valuable information for further characterisation and analysis of the optical images of LC droplets and their corresponding configurations.     

使用一维机械模板的高分辨阿达玛变换显微图像探测技术研究

阿达玛变换（HT）是一种类似于傅里叶变换（FT）的光谱调制技术,具有多通道同时检测和多通道成像能力等优点,但两者的数学模型、对光信号的调制方法和调制手段都不一样。由于HT仅涉及四则运算,而FT涉及较为复杂的三角函数和复数运算,所以HT的解码速度快于FT。在成像技术方面,HT具有直接成像的能力,而FT只能对通过其它方式获取的图像进行加工处理。     

Implementation and examination of a new drop shape analysis algorithm to measure contact angle and surface tension from the diameters of two sessile drops

The performance of a new algorithm developed to measure contact angle and surface tension of sessile drops is examined. To calculate the contact angle and surface tension, the new algorithm (ADSA-TD) requires the radius (contact or equatorial) and volume of two sessile drops of different sizes that are placed on the same surface. Initially, the algorithm was tested using synthetic drops (synthetic or theoretical drops are produced by numerical integration of the Laplace equation). The radii and volumes of synthetic drops were used as ADSA-TD inputs. The calculated contact angle (θ) and surface tension (γ) by ADSA-TD matched perfectly the assumed values of θ and γ used to produce the synthetic drops, confirming theoretically the validity of the new algorithm. In the next step, the sensitivity of the algorithm to input errors was examined. It was shown experimentally that both calculated contact angle and surface tension are affected by the errors in volume and radius. Besides the error in input values, it was shown that the size difference between the paired drops and the differences in their contact angles would affect the output of ADSA-TD. As it turns out, the calculated surface tension is so sensitive to the above factors that ADSA-TD does not appear to be promising as a surface tension measurement technique. However, ADSA-TD produced acceptable contact angle values as compared to measurements made by other proven techniques such as axisymmetric drop shape analysis-profile. Thus, ADSA-TD may be of interest as a contact angle measurement technique which does not require the liquid surface tension as input.