Q2. What are the contributions in this paper?
Odukoya et al. this paper investigated the evaporation and de-pinning rates of micro-droplets of deionized ( DI ) water and toluene on lead zirconate titanate ( PZT ) substrates.
Droplet evaporation and de-pinning in rectangular microchannels
TL;DR: In this paper, the effects of channel width and depth on the evaporation and de-pinning rates of embedded micro-droplets of deionised (DI) water and toluene on lead zirconate titanate (PZT) substrates are presented and compared for both fluids.
About: This article is published in International Journal of Heat and Mass Transfer.The article was published on 2013-01-01 and is currently open access. It has received 3 citations till now. The article focuses on the topics: Evaporation & Microchannel.
Summary (2 min read)
Jump to: [1. Introduction] – [2. Problem Formulation] – [2.1 Droplet evaporation model] – [2.2 Droplet de-pinning model] – [3. Experimental Apparatus and Procedure] – [3.1 Fabrication of rectangular microchannel] – [3.2 Experimental measurement and uncertainty] – [4. Results and Discussion] and [5. Conclusions]
1. Introduction
- Various ways have been invented and commercialized to harness energy from water, such as hydroelectricity, tidal energy, among others.
- Heat recovery by electrical components in MEMS devices can be used to generate voltages that power individual electrical components within microchips.
- In order to predict the dynamics of the evaporation, the hydrodynamics of droplet spreading must be well understood.
- This paper investigates droplet spreading in a rectangular microchannel.
- The constant change in contact angle leads to a variation in the advancing and receding contact angles.
2. Problem Formulation
- The evaporation of a droplet in a rectangular channel has three major thermophysical processes, namely mass transfer of the bulk fluid into the gas phase, heat transfer as a result of natural convection and Marangoni convection due to temperature gradients.
- The mass transfer and natural convection are assumed to be the major transport phenomena that affect the evaporation of the droplet.
- Heat addition was not implemented in the current experimental studies, hence the temperature gradients are neglected during the evaporation process.
2.1 Droplet evaporation model
- The droplet can either have a concave or convex meniscus with respect to the substrate of the channel.
- The model in this paper is developed for the hydrophobic case, as per the experiments.
- The model can also be extended to the hydrophilic case, since the main difference is the contact angle and volume associated with the concave meniscus.
- Combining equations (1) and (6), the combined effect of diffusion and convection of the vapor from the surface will give the total effect of evaporation on the width of the droplet.
- The experimental results show that a thin layer exists between the main part of the droplet and the wall.
2.2 Droplet de-pinning model
- This separation occurs along the contact line of the main droplet.
- Unlike the evaporation process, the de-pinning process starts from the center of the channel and progresses in both directions simultaneously towards the wall.
- The phenomenon is a complex process to predict accurately.
- The volume of the pinned film can be estimated as the volume of the spherical cap of the droplet and the cuboid along the channel length.
- A value of 0.3 was used for DI-water and a value of 0.6 was used for toluene, based on a similar asymptotic analysis performed previously by Cachile et al. [8].
3. Experimental Apparatus and Procedure
- Fabrication steps of the MHE are illustrated in Fig. 4. The MHE is fabricated with PZT wafers.
- Three sets of wafers of different thicknesses were examined for the fabrication (100µm, 80µm and 60µm).
3.1 Fabrication of rectangular microchannel
- The PZT substrates of different thicknesses were cleaned with an RCA 1 cleaning procedure.
- It was difficult to completely dry the fragile substrate; hence before proceeding to the next step, the substrate was heated to 120oC for two minutes on the vacuum hot plate and allowed to cool.
- SU-8 Developer form Microchem was used to process the pattern after post exposure baking.
3.2 Experimental measurement and uncertainty
- A 10µl syringe was used to dispense the droplet into a microchannel with the aid of a stereo microscope in the experimental measurements.
- The images were recorded at a frequency that varied between 25 and 32 frames per second (fps).
- The evaporation and de-pinning processes of the droplet were recorded by Stream Pix III imaging software, which allows for digitization and characterisation of the images.
- The single sample uncertainty measurement allowed this set of data to be discarded during the analysis of the experimental data.
- The following section highlights results from the analytical modeling and experimental results.
4. Results and Discussion
- Experimental and analytical results of the evaporation and de-pinning of the toluene and DI-water will be reported in this section.
- Smaller channels were observed to have larger separation distances, which indicate a higher surface tension in smaller channels.
- This occurs due to the separation distance between the bulk fluid and the pinned film as shown in Fig. 6(a).
- The effects of contact angle and channel width on the evaporation rate are reported in Fig. 12.
- The rate of de-pinning is significantly increased across the width after about 9.04s (Fig. 14(c)).
5. Conclusions
- This paper examined the use of a PZT substrate in microfluidic transport of droplets.
- New experimental and analytical results have been presented for these droplet transport processes.
- Internal recirculation was observed during the evaporation process.
- Threedimensional printing and other MEMS applications could benefit from the experimental and analytical results in this study.
- The results also have relevance in biomedical applications where small particles of solute can be distributed through complex meshes.
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Figures (17)
Fig. 4: Fabrication of SU-8 microchannels using photolithography and sealing of the microchannel with a Bungard dry film laminator. (a) Deposition of SU-8 on PZT subtrate and mask used to pattern the SU-8 channel during photolithography. (b) SU-8 channel after wet etching of a patterned surface. (c) Laminted MHE with Bunduard film laminator. 
Fig. 3: Schematic of the de-pinning process in a closed rectangular microchannel, where the change in width of the film is ∆w. The depinning process proceeds in both directions. The contact angle θc is the measured angle made by the pinned film with the surface of the channel. 
Fig. 1: Schematic of problem configuration in the MHE 
Fig. 2: Schematic of the evaporation process in a closed rectangular microchannel. The change in droplet width for either end of the channel is ∆w. The model represents half of the channel width. The contact angle θc is the angle made by the bulk fluid with the surface of the channel. 
Fig. 11: Bulk and pinned film contact angle measurement using UTHSCSA image tool. 
Fig. 12: Effects of contact angle and width on evaporation of the bulk fluid 
Fig. 10: Comparison of experimental and analytical results of evaporation of toluene in a rectangular microchannel of different depths. 
Fig. 9: Comparison of experimental and analytical results of evaporation of DI-water in a rectangular microchannel of different depths 
Fig. 14: Initial de-pinning of DI-water droplet after evaporation of bulk fluid at time t=0s. (b) End of simultaneous de-pinning across the length and width of the film with maximum spreading of the bulk fluid at time t=1.16s. (c) Significant increase in de-pinning rate at time t = 2.96s. (d) End of de-pinning at time t = 4.42s (Magnification is ×5). 
Fig. 13: Initial de-pinning of toluene droplet after evaporation of bulk fluid at time t=0s. (b) Increase in de-pinning rate across the length and width of the droplet simultaneously at time t=1.33s. (c) Decrease in de-pinning rate across the length of the droplet at time t = 2.67s. (d) End of de-pinning at time t = 5.56s (Magnification is ×10). 
Fig. 16: Comparison of experimental and analytical results of de-pinning of toluene 
Fig. 15: Comparison of experimental measurements and analytical predictions of de-pinning 
Fig. 8: Comparison of experimental and analytical results of evaporation in the microchannel 
Fig. 7: (a) Initial wetting of toluene on a substrate at time t=0s. (b) Beginning of separation of a bulk fluid and pinned film at time t=0.76s. (c) Reduction in the evaporation rate at time t = 2.76s. (d) End of the evaporation of a bulk fluid at time t=3.76 (Magnification is × 10). 
Fig. 17: Effect of microchannel width on de-pinning of the bulk fluid 
Fig. 5: Fabricated SU-8 2075 80µm microchannel viewed at 5× magnification of a Reichert Austria stereo microscope. 
Fig. 6: (a) Initial separation of a DI-water droplet and pinned film at time t=0s. (b) Maximum spreading of the bulk fluid at time t=0.92s. (c) Reduction in evaporation rate at time t = 3.32s. (d) End of the evaporation of the bulk fluid at time t = 6.08s (Magnification is ×5).
Citations
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01 Jan 2014
TL;DR: In this paper, a review of early kinetic models of droplet evaporation is presented, based on numerical solutions to Boltzmann equations for vapour and air, and two regions of gas above the surface of an evaporating droplet are considered: the kinetic and hydrodynamic regions.
Abstract: The validity of the assumption used in the previous chapters that both liquid and gas phases can be treated as a continuum is no longer obvious when the interface between liquid droplets and the ambient gas is modelled, even when the gas pressure is well above one atmosphere. The chapter begins with a review of early kinetic models of droplet evaporation. Then more rigorous models, based on numerical solutions to Boltzmann equations for vapour and air, are discussed. Two regions of gas above the surface of an evaporating droplet are considered: the kinetic and hydrodynamic regions. Vapour and air dynamics in the first region are described by the Boltzmann equations, while the conventional hydrodynamic analysis is applied in the second region. Collisions between molecules are assumed to be inelastic in the general case. The evaporation coefficient is estimated based on molecular dynamics analysis of n-dodecane molecules, using the united atoms model (bonding between hydrogen and carbon molecules is assumed to be much stronger than bonding between carbon molecules).
3 citations
Dissertation•
01 Jan 2015
TL;DR: In this article, a general method to make nanoplasmonic devices on a flexible membrane structure, which can be free standing, extremely thin (less than the wavelength of visible light), but retains the ability to be manipulated without loss of optical function, is presented.
Abstract: Nanoplasmonics has provided a way to control light with extremely high precision, into nanoscale volumes. In many circumstances, the nanoplasmonic devices which can be realised are fabricated using processing techniques which rely on planar technologies. This thesis provides a general method to make nanoplasmonic devices on a flexible membrane structure, which can be free standing, extremely thin (less than the wavelength of visible light), but retains the ability to be manipulated without loss of optical function. These devices are very pliant and conformable. Flexibility allows the integration of nanoplasmonic devices into many new applications where curved surfaces or the ability to conform to another object is required, as well as providing a route for post-fabrication tunability. Two specific applications are considered: lab-on-fibre technology and surface enhanced Raman spectroscopy. Lab-on-fibre technologies have been advancing the ability to miniaturise experiments which would normally require a whole laboratory. Fabricating a membrane and then later applying it to the fibre decouples the choice of fibre from the design of the device. Surface enhanced Raman spectroscopy is a powerful diagnostic tool which can uniquely identify an optical fingerprint of different molecules. The technique has been held back from widespread clinical adoption because of the difficulty of reproducibility of the substrates used. A repeatable and reliable rigid substrate is demonstrated, which can identify the concentration of a three component mixture of physiologically relevant biomolecules. This same design is then shown in a flexible form factor, which is applied to a non-planar landscape where it can identify the locations where a molecule of interest has been deposited. This thesis details the development of the fabrication protocol, the construction of experimental apparatus for characterisation, and the use of numerical modelling to advance the flexible nanoplasmonic membrane platform. Candidate’s declarations: I, Peter Reader-Harris, hereby certify that this thesis, which is approximately 40,000 words in length, has been written by me, and that it is the record of work carried out by me, or principally by myself in collaboration with others as acknowledged, and that it has not been submitted in any previous application for a higher degree. I was admitted as a research student in September 2011 and as a candidate for the degree of Doctor of Philosophy in September 2011; the higher study for which this is a record was carried out in the University of St Andrews between 2011 and 2015. Date Signature of candidate Supervisor’s declaration: I hereby certify that the candidate has fulfilled the conditions of the Resolution and Regulations appropriate for the degree of Doctor of Philosophy in the University of St Andrews and that the candidate is qualified to submit this thesis in application for that degree. Date Signature of supervisor Permission for publication: In submitting this thesis to the University of St Andrews I understand that I am giving permission for it to be made available for use in accordance with the regulations of the University Library for the time being in force, subject to any copyright vested in the work not being affected thereby. I also understand that the title and the abstract will be published, and that a copy of the work may be made and supplied to any bona fide library or research worker, that my thesis will be electronically accessible for personal or research use unless exempt by award of an embargo as requested below, and that the library has the right to migrate my thesis into new electronic forms as required to ensure continued access to the thesis. I have obtained any third-party copyright permissions that may be required in order to allow such access and migration, or have requested the appropriate embargo below. The following is an agreed request by candidate and supervisor regarding the publication of this thesis: PRINTED COPY No embargo on print copy ELECTRONIC COPY No embargo on electronic copy Date Signature of candidate Signature of supervisor
2 citations
Cites background from "Droplet evaporation and de-pinning ..."
...This is a common effect in microfluidic systems [226]....
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01 Jan 2022
References
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Journal Article•
7,568 citations
TL;DR: In this article, the authors ascribe the characteristic pattern of the deposition to a form of capillary flow in which pinning of the contact line of the drying drop ensures that liquid evaporating from the edge is replenished by liquid from the interior.
Abstract: When a spilled drop of coffee dries on a solid surface, it leaves a dense, ring-like deposit along the perimeter (Fig 1a) The coffee—initially dispersed over the entire drop—becomes concentrated into a tiny fraction of it Such ring deposits are common wherever drops containing dispersed solids evaporate on a surface, and they influence processes such as printing, washing and coating1,2,3,4,5 Ring deposits also provide a potential means to write or deposit a fine pattern onto a surface Here we ascribe the characteristic pattern of the deposition to a form of capillary flow in which pinning of the contact line of the drying drop ensures that liquid evaporating from the edge is replenished by liquid from the interior The resulting outward flow can carry virtually all the dispersed material to the edge This mechanism predicts a distinctive power-law growth of the ring mass with time—a law independent of the particular substrate, carrier fluid or deposited solids We have verified this law by microscopic observations of colloidal fluids
5,553 citations
"Droplet evaporation and de-pinning ..." refers methods in this paper
...The evaporation rate of the droplet has been predicted by Deegan [15], Cachile et al....
[...]
...This is the technology used for inkjet printers [15] as the carrier liquid evaporates and patterns are deposited on the paper....
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...The equation of the average velocity over the width can be expressed as 0 1( , ) ( , )o w xu w t j w t dw A tρ ∂ = − + ∂ ∫ (8) The evaporation rate of the droplet has been predicted by Deegan [15], Cachile et al. [8] and Poulard et al. [11] to be proportional to the change in pinning radius based on the instantaneous time and final time....
[...]
...Deegan [15] used this transport phenomenon to explain the pattern of satins deposited by a drop of coffee....
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...The separation of these two layers of the liquid was used to transfer solid particles in a liquid droplet to a substrate in a previous study by Deegan [10]....
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TL;DR: In this article, the surface forces that lead to wetting are considered, and the equilibrium surface coverage of a substrate in contact with a drop of liquid is examined, while the hydrodynamics of both wetting and dewetting is influenced by the presence of the three-phase contact line separating "wet" regions from those that are either dry or covered by a microscopic film.
Abstract: Wetting phenomena are ubiquitous in nature and technology. A solid substrate exposed to the environment is almost invariably covered by a layer of fluid material. In this review, the surface forces that lead to wetting are considered, and the equilibrium surface coverage of a substrate in contact with a drop of liquid. Depending on the nature of the surface forces involved, different scenarios for wetting phase transitions are possible; recent progress allows us to relate the critical exponents directly to the nature of the surface forces which lead to the different wetting scenarios. Thermal fluctuation effects, which can be greatly enhanced for wetting of geometrically or chemically structured substrates, and are much stronger in colloidal suspensions, modify the adsorption singularities. Macroscopic descriptions and microscopic theories have been developed to understand and predict wetting behavior relevant to microfluidics and nanofluidics applications. Then the dynamics of wetting is examined. A drop, placed on a substrate which it wets, spreads out to form a film. Conversely, a nonwetted substrate previously covered by a film dewets upon an appropriate change of system parameters. The hydrodynamics of both wetting and dewetting is influenced by the presence of the three-phase contact line separating "wet" regions from those that are either dry or covered by a microscopic film only. Recent theoretical, experimental, and numerical progress in the description of moving contact line dynamics are reviewed, and its relation to the thermodynamics of wetting is explored. In addition, recent progress on rough surfaces is surveyed. The anchoring of contact lines and contact angle hysteresis are explored resulting from surface inhomogeneities. Further, new ways to mold wetting characteristics according to technological constraints are discussed, for example, the use of patterned surfaces, surfactants, or complex fluids.
2,501 citations
"Droplet evaporation and de-pinning ..." refers background in this paper
...6 Past studies [5] have conflicting information about the behaviour of water droplets on the micro/nano-scale....
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...The change in contact line elastic force has an effect on the de-pinning rate [5]....
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...Bonn [5] also indicated the complexity of these phenomena remained a challenge in accurately predicting the de-pinning process....
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TL;DR: A theory is described that predicts the flow velocity, the rate of growth of the ring, and the distribution of solute within the drop that is driven by the loss of solvent by evaporation and the geometrical constraint that the drop maintain an equilibrium droplet shape with a fixed boundary.
Abstract: Solids dispersed in a drying drop will migrate to the edge of the drop and form a solid ring. This phenomenon produces ringlike stains and occurs for a wide range of surfaces, solvents, and solutes. Here we show that the migration is caused by an outward flow within the drop that is driven by the loss of solvent by evaporation and geometrical constraint that the drop maintain an equilibrium droplet shape with a fixed boundary. We describe a theory that predicts the flow velocity, the rate of growth of the ring, and the distribution of solute within the drop. These predictions are compared with our experimental results.
2,051 citations
"Droplet evaporation and de-pinning ..." refers background or methods in this paper
...Past studies have generally assumed a spherical droplet [7, 9, 11, 14], but with the existence of a film, which is...
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...Secondly, the other method of evaporation occurs where the contact radius decreases while the contact angle remains constant [14]....
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...Firstly, the droplet radius remains approximately constant, while the contact angle of the liquid-substrate contact angle decreases [14]....
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...The authors developed a method by assuming an equivalent contact angle, based on the change in volume of the droplet and proportional to an exponential function of time [14]....
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Book•
01 Jan 1969
TL;DR: In this article, a unified treatment of momentum transfer (fluid mechanics), heat transfer and mass transfer is presented, with a focus on modern applications of the basic material, and many new homework exercises at the end of each chapter.
Abstract: Providing a unified treatment of momentum transfer (fluid mechanics), heat transfer and mass transfer. This new edition includes more modern applications of the basic material, and to provide many new homework exercises at the end of each chapter.
1,973 citations