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Journal ArticleDOI

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)

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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Book ChapterDOI
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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References
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Journal ArticleDOI
11 Sep 2002-Langmuir
TL;DR: In this paper, a semi-empirical approach is proposed to study the dynamics of shrinking of thin alkane droplets evaporating on isothermal surfaces, where only evaporation is taken into account.
Abstract: The dynamics of shrinking of thin alkane droplets evaporating on isothermal surfaces has been studied in the case of complete wetting, where no pinning of the contact line is expected. As the resolution of the complete hydrodynamic equation is still an open problem, we propose a semiempirical approach, where only evaporation is taken into account. A careful analysis of the mathematical consequences of the form chosen for the evaporation term is given. The agreement with experiments is extremely good, suggesting that hydrodynamic contributions and Marangoni flows are probably negligible for the simple liquids considered.

95 citations


"Droplet evaporation and de-pinning ..." refers background in this paper

  • ...[8] developed a semi-empirical correlation for estimating the hydrodynamic behaviour of alkanes on a wetting surface....

    [...]

Journal ArticleDOI
06 Aug 2005-Langmuir
TL;DR: In this paper, the dynamics of evaporation of wetting droplets is investigated experimentally in an extended range of drop sizes to provide trends relevant for a theoretical analysis, which represents a first step toward the solution of a very old, complex problem.
Abstract: The dynamics of evaporation of wetting droplets is investigated experimentally in an extended range of drop sizes to provide trends relevant for a theoretical analysis. A model is proposed, which generalizes Tanner's law in the presence of evaporation. A qualitative agreement is obtained, which represents a first step toward the solution of a very old, complex problem.

85 citations

Journal ArticleDOI
TL;DR: In this paper, an experimental setup was constructed to investigate the drying process of a micro-scale polymer solution droplet deposited on homogeneous surfaces, and the average polymer concentration at which the contact line is pinned is independent of the initial solution concentration.

82 citations


"Droplet evaporation and de-pinning ..." refers background in this paper

  • ...The shape of pinned polymer films is dependent on the pinning time and distance between the bulk fluid and pinned film [16]....

    [...]

Journal ArticleDOI
TL;DR: In this article, it was shown that the wetting behavior of n−alkanes on a water surface can be predicted using the Cahn wetting theory of Cahn, together with experimental results for n-alkane vapor adsorption on water which are readily available in the literature.
Abstract: It is shown in this paper that the wetting behavior of n‐alkanes on a water surface can be predicted using the wetting theory of Cahn, together with experimental results for n‐alkane vapor adsorption on water which are readily available in the literature. The evolution of the wetting behavior with the carbon number of linear alkanes and with temperature is determined and wetting temperatures are calculated. The results agree with experimental observations at room temperature, except for pentane which appears to be a limiting case. The determination of the wetting temperature demonstrates that in order to account for the wetting behavior, additional effects of long‐range forces have to be taken into account.

40 citations


"Droplet evaporation and de-pinning ..." refers methods in this paper

  • ...The initial spreading of liquids on a solid substrate has been analysed by the Gibbs adsorption equation to estimate the change in surface tension [6]....

    [...]

Journal ArticleDOI
TL;DR: In this paper, a new method of cyclic flow control with an external heat source is developed for thermocapillary pumping of a micro-droplet in a closed microchannel.
Abstract: In this paper, a new method of cyclic flow control with an external heat source is developed for thermocapillary pumping of a micro-droplet in a closed microchannel. Unlike past studies with a moving heat source at the receding edge of the droplet, this new technique involves a stationary cyclic heat source embedded within an adjoining silicon substrate. Thermocapillary pumping of the micro-droplet is examined numerically (finite-volume method) and theoretically (slug-flow approximation). In contrast to past studies, this paper considers the solution of the full Navier?Stokes and energy equations within the droplet. Additionally, temperature boundary conditions for a stationary heat source are applied at the interface between the substrate and its surroundings, rather than along the microchannel wall. The finite-volume formulation is developed with a sliding grid in the liquid phase and an adaptive grid along the compressed air and substrate regions. Coupled pressure and velocity boundary conditions are applied along the droplet/air interface. Numerical predictions suggest that cyclic droplet displacement can be obtained with the stationary heat source. Close agreement between numerical and theoretical predictions has provided useful validation of the formulations.

31 citations


"Droplet evaporation and de-pinning ..." refers background in this paper

  • ...Earlier investigations by Glockner and Naterer [1, 2] suggested that two promising fluids for thermocapillary pumping were toluene and water....

    [...]

  • ...Earlier investigations [1, 2] showed that surface tension of water can be used for thermocapillary pumping in a microchannel....

    [...]

Frequently Asked Questions (2)
Q1. What are the future works in this paper?

Further studies would be required to determine the actual effect of the overall volume change on the de-pinning process. 

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.