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Journal ArticleDOI

Droplet evaporation and de-pinning in rectangular microchannels

01 Jan 2013-International Journal of Heat and Mass Transfer (Pergamon)-Vol. 56, Iss: 1, pp 127-137

AbstractExperimental and numerical studies are presented for evaporation of micro-droplets of deionised (DI) water and toluene on lead zirconate titanate (PZT) substrates. The microchannels are fabricated with SU-8 2025 and 2075. The effects of channel width and depth on the evaporation and de-pinning rates of embedded micro-droplets are presented and compared for both fluids. The study reveals a partially hydrophobic nature of SU-8/PZT microchannel to DI water and a complete wetting when toluene is used as the droplet. The rate of evaporation of toluene is about double the rate of evaporation of DI water. Comparisons of the rates of evaporation and de-pinning show that the channel width has a larger effect on evaporation than the depth of the channel. The equivalent contact angle of the pinned film and bulk fluid compensated for the evaporation of the droplet. Surface roughness was also shown to have a significant effect on the pinned film in the rectangular microchannels.

Topics: Evaporation (61%), Microchannel (54%), Wetting (52%), Lead zirconate titanate (50%)

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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1
Droplet Evaporation and De-pinning in Rectangular Microchannels
A. Odukoya
1
and G. F. Naterer
2
1, 2
University of Ontario Institute of Technology, Oshawa, Ontario, Canada
Abstract
Experimental and numerical studies are presented for evaporation of micro-droplets of deionised
(DI) water and toluene on lead zirconate titanate (PZT) substrates. The microchannels are
fabricated with SU-8 2025 and 2075. The effects of channel width and depth on the evaporation
and de-pinning rates of embedded micro-droplets are presented and compared for both fluids. The
studies indicate a partially hydrophobic nature of SU-8/PZT microchannel to DI water and
complete wetting when toluene is used as the droplet. The rate of evaporation of toluene is about
double the rate of evaporation of DI water. Comparisons of the rates of evaporation and de-pinning
show that the channel width has a larger effect on evaporation than the depth of the channel. The
equivalent contact angle of the pinned film and bulk fluid compensated for the evaporation of the
droplet. Surface roughness was also shown to have a significant effect on the pinned film in the
rectangular microchannels.
Nomenclature
A cross sectional area (m
2
)
C vapor molar concentration (mol/m
3
)
D
AB
diffusion coefficient (m
2
/s)
e
v
uncertainty in voltage measurement (V)
1
Research Associate, Faculty of Engineering and Applied Science, University of Ontario Institute of Technology,
2000 Simcoe Street North, Oshawa, Ontario, Canada, L1H 7K4
2
Dean, Faculty of Engineering and Applied Science, Memorial University, St. John’s, Newfoundland, 240 Prince
Phillip Drive, St. John’s, NL Canada A1B 3X5

2
e
i
uncertainty in current measurement (A)
e
P
uncertainty in pixel measurement
e
w
uncertainty in width measurement (m)
N
F
e
uncertainty in frame number
R
F
e
uncertainty in width measurement (m)
F
N
frame number
F
R
frame rate
g acceleration due to gravity (m/s
2
)
h heat transfer coefficient (W/m
2
K)
j(w) evaporation rate per unit area (kg/m
2
)
l thickness (m)
L length (m)
M
D
mass (kg)
M
molecular weight (kg/kmol)
P pressure (N/m
2
)
R
universal gas constant (J/kmol K)
t time (s)
T temperature (
o
C or K)
ū instantaneous velocity (m/s
2
)
U uncertainty

3
V volume (m
3
)
w width of microchannel (m)
w
o
initial width (m)
Z
n
distance from neutral axis (m)
Greek
discrete change, or difference
µ dynamic viscosity (kg/m s)
ρ
density (kg/m
3
)
θ
contact angle (
o
)
φ
concentration gradient of evaporating fluid (mol/m
3
)
σ
accommodation coefficient
Subscripts
air air
app apparent
c critical contact angle
D droplet
e experiment
f friction without roughness
i initial
L left
lv liquid vapour interface

4
m meniscus
o start
R right
sub substrate
t total
v vapor
w water droplet
Abbreviations
CIRFE Center of Integrated Radio Frequency Engineering
DI Deionized
IPA Isopropyl Alcohol
LOR Lift Off Resist
MEMS Microelectromechanical System
MHE Micro Heat Engine
PZT Lead Zirconate Titanate
RCA Radio Cooperation of America
RF Radio Frequency
RIE Reactive Ion Etching
UV Ultra Violet
1. Introduction
Various ways have been invented and commercialized to harness energy from water, such
as hydroelectricity, tidal energy, among others. This paper investigates transport phenomena of
micro-droplets in micro-electromechanical systems (MEMS) for powering micro-devices. MEMS

5
generally require small quantities of energy, so generating electricity for their use can reduce their
dependence on conventional power generating systems such as batteries. Increasing the efficiency
of micro-power generating systems embedded in MEMS devices can increase their length of
operation. For example, heat recovery by electrical components in MEMS devices can be used to
generate voltages that power individual electrical components within microchips.
MEMS heat recovery can be achieved by various methods such as thermoelectric or
piezoelectric materials in MEMS devices. Thermoelectric materials have the ability to convert heat
directly to electricity, while piezoelectric materials can convert stresses in a material into electrical
voltages. This paper examines the transport phenomena associated with thermal energy conversion
for MEMS devices, in particular for a Micro Heat Engine (MHE). Earlier investigations [1, 2]
showed that surface tension of water can be used for thermocapillary pumping in a microchannel.
An MHE can use thermocapillary effects to induce stresses in a piezoelectric membrane by the
cyclic heating and cooling of a droplet in a microchannel [1 - 4].
When heat is applied to one end of the droplet in a closed microchannel, an increase in
temperature at the heat source leads to a temperature gradient across the droplet. This results in a
displacement of the droplet along the length of the channel towards the cooler end of the channel.
This process is known as thermocapillary pumping. The resulting displacement increases the
pressure at the closed end of the channel. The increased pressure is used to induce stress on a
membrane at the closed end of the channel. This induced stress results in mechanical deformation
of the membrane. The mechanical deformation of the membrane then leads to a flow of electrons
in an externally connected circuit, which yields conversion of mechanical energy to electrical
energy. Fig. 1 shows a schematic of the MHE and the forces acting within the microchannel.

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References
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Journal ArticleDOI
23 Oct 1997-Nature
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

4,980 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....

    [...]

  • ...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....

    [...]

  • ...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]....

    [...]


Journal ArticleDOI
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.

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  • ...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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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.

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Journal ArticleDOI
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.

1,874 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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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.