Group Title: 7th International Conference on Multiphase Flow - ICMF 2010 Proceedings
Title: 2.7.5 - Demonstation of a Non-wetting Water Droplet Sustained by a Pressure-Driven Interstitial Air Flow
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 Material Information
Title: 2.7.5 - Demonstation of a Non-wetting Water Droplet Sustained by a Pressure-Driven Interstitial Air Flow Interfacial Flows
Series Title: 7th International Conference on Multiphase Flow - ICMF 2010 Proceedings
Physical Description: Conference Papers
Creator: Gibson, J.
Sumner, L.
Publisher: International Conference on Multiphase Flow (ICMF)
Publication Date: June 4, 2010
 Subjects
Subject: non-wetting
droplet
lubrication
air channel
two-phase
free surface
 Notes
Abstract: The steady non-wetting of a quasi two-dimensional water droplet pinned to one side of a narrow channel is demonstrated. An air flow pulled through the channel maintains an interstitial fluid preventing the droplet from wetting the opposite side establishing a two-phase flow scenario possibly relevant to the liquid management issues of flow-through Proton Exchange Membrane fuel cells. Lubrication theory typically explains non-wetting although in this case a pressure gradient drives the interstitial flow rather than shear on a boundary. An experimental apparatus controls droplet volume, air flow rate, and channel height. Results from this study reveal the deformed profile of droplets in a state of non-wetting, provide evidence of a pressure increase inside the interstitial fluid, and include a preliminary mapping of the non-wetting region in terms of a Reynolds number and channel-to-droplet height ratio. Finally, the experiments reveal an instability in which pronounced oscillations in droplet shape are observed.
General Note: The International Conference on Multiphase Flow (ICMF) first was held in Tsukuba, Japan in 1991 and the second ICMF took place in Kyoto, Japan in 1995. During this conference, it was decided to establish an International Governing Board which oversees the major aspects of the conference and makes decisions about future conference locations. Due to the great importance of the field, it was furthermore decided to hold the conference every three years successively in Asia including Australia, Europe including Africa, Russia and the Near East and America. Hence, ICMF 1998 was held in Lyon, France, ICMF 2001 in New Orleans, USA, ICMF 2004 in Yokohama, Japan, and ICMF 2007 in Leipzig, Germany. ICMF-2010 is devoted to all aspects of Multiphase Flow. Researchers from all over the world gathered in order to introduce their recent advances in the field and thereby promote the exchange of new ideas, results and techniques. The conference is a key event in Multiphase Flow and supports the advancement of science in this very important field. The major research topics relevant for the conference are as follows: Bio-Fluid Dynamics; Boiling; Bubbly Flows; Cavitation; Colloidal and Suspension Dynamics; Collision, Agglomeration and Breakup; Computational Techniques for Multiphase Flows; Droplet Flows; Environmental and Geophysical Flows; Experimental Methods for Multiphase Flows; Fluidized and Circulating Fluidized Beds; Fluid Structure Interactions; Granular Media; Industrial Applications; Instabilities; Interfacial Flows; Micro and Nano-Scale Multiphase Flows; Microgravity in Two-Phase Flow; Multiphase Flows with Heat and Mass Transfer; Non-Newtonian Multiphase Flows; Particle-Laden Flows; Particle, Bubble and Drop Dynamics; Reactive Multiphase Flows
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Volume ID: VID00070
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Resource Identifier: 275-Gibson-ICMF2010.pdf

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Paper No 7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010


Demonstration of a Non-wetting Water Droplet Sustained by a pressure-driven Interstitial
Air Flow


Joshua Gibson and Loren Sumner

School of Engineering, Mercer University
1400 Coleman Ave, Macon, GA, 31207, USA
Sumner LB i@mercer.edu


Keywords: non-wetting, droplet, lubrication, air channel, two-phase, free surface




Abstract

The steady non-wetting of a quasi two-dimensional water droplet pinned to one side of a narrow channel is demonstrated. An
air flow pulled through the channel maintains an interstitial fluid preventing the droplet from wetting the opposite side
establishing a two-phase flow scenario possibly relevant to the liquid management issues of flow-through Proton Exchange
Membrane fuel cells. Lubrication theory typically explains non-wetting although in this case a pressure gradient drives the
interstitial flow rather than shear on a boundary. An experimental apparatus controls droplet volume, air flow rate, and
channel height. Results from this study reveal the deformed profile of droplets in a state of non-wetting, provide evidence of
a pressure increase inside the interstitial fluid, and include a preliminary mapping of the non-wetting region in terms of a
Reynolds number and channel-to-droplet height ratio. Finally, the experiments reveal an instability in which pronounced
oscillations in droplet shape are observed.


Introduction

The physics of liquid/gas and liquid/solid interfaces
are known to dominate the mechanics of certain droplet
and thin-film scenarios. Small-scale liquid management
efforts must inevitably consider the interfacial physics that
become pronounced when dealing with relatively small
quantities of liquid in which inertia and body forces
become comparable to surface forces. Of particular
concern here, a non-wetting phenomenon, in which a
lubricating interstitial gas flow maintains separation of a
liquid droplet from a solid surface, may influence water
management issues in fuel cells. Water management is
crucial to the operation and effectiveness of Proton
Exchange Membrane (PEM) fuel cells. Fuel cells
produce electrical energy from hydrogen and oxygen gas
making hydrogen a viable secondary energy resource in the
world's efforts to manage energy.
Young (2007) mentions that the first working fuel cell
was developed in 1839 and that by the 1960's fuel cells
aided in the Apollo missions. With the advances made in
electrochemical processes, an increased range of
applications is expected in the future. Young provides a
brief history, basic operating principles, and in depth
thermofluidic modeling of the different types of hydrogen
fuel cells with a focus on the two most promising; Proton
Exchange Membrane (PEM) and Solid Oxide (SO).
In the process of producing electricity by means of a
PEM fuel cell, hydrogen fuel passes through an anode
catalyst layer where the hydrogen gas separates into
protons and electrons. The protons pass through the PEM


while the electrons pass through an external circuit
producing electricity. On the other side of the PEM at the
cathode catalyst layer, electrons and protons combine to
form water as a by product. At both the anode catalyst
layer and the cathode catalyst layer, a gas diffusion layer
serves to evenly distribute the gases in order to optimize
fuel cell performance. Gas diffusion layers contain small
channels which serve to carry reactants to the anode
catalyst layer and products (to include water) away from
the cathode catalyst layer. Water transport is crucial in that
moisture promotes good ionic conductivity but in excess
can flood the gas flow channels (Young (2007), Quan et al.
(2005)). Water often condenses in the gas diffusion
channels of the cathode catalyst layer and eventually exits
via several possible water transport modes. It is well
known that excessive liquid water can lead to a "pinch-off'
phenomenon in which the liquid coalesces across the
channel, completely blocking the gas flow, and thus
hindering the effectiveness of the fuel cell. Condensing
water concerns PEM fuel cells, which operate at 80-1000C,
rather than SO fuel cells which operate around
850-10000C.
Zhang, Yang, and Wang (2006) witnessed such a
pinch-off while conducting experiments with a transparent
PEM fuel cell. Observing the liquid water dynamics,
they identified two primary mechanisms for liquid
transport. Under some operating conditions liquid
droplets formed and subsequently migrated along the
channel surface due to the shear of the gas flow. Also, a
capillary action often caused the formation of a
core/annular film flow or slug flow. Under certain





Paper No


operation conditions, these mechanisms failed to drain
sufficient water leading to complete blockage.
Logically, the pinch-off phenomenon would begin
with the collapse of a narrowing gas stream passing by
liquid suggesting a potential non-wetting scenario.
Although this suggestion presents the arguably
controversial scenario of a pressure driven lubricating flow,
non-wetting, if possible, may provide one means to design
around pinch-off and perhaps even regulate moisture. This
work performs non-wetting experiments with such a
pressure-driven interstitial air flow in a "wind channel" or
small-scale wind tunnel. A quasi two-dimensional droplet
of distilled water (2-4 mm deep) is situated with a
stationary contact line inside the wind channel in a
sustained non-wetting scenario as shown in Figure 1. The
influences of airflow, channel height, and droplet volume
are investigated.

wind channel

airflow z



water droplet
Figure 1: Pressure-driven interstitial flow scenario over of
a droplet pinned to the side of a channel.


Background

Non-wetting is a phenomenon describing the
temporary or permanent separation of a liquid from a solid
surface caused by the lubrication of an interstitial gas flow.
Lacking the gas flow the liquid would otherwise wet the
surface. Non-coalescence is the similar interaction
between two miscible liquid bodies. In the case of
temporary non-wetting or non-coalescence, the interstitial
fluid is drained from the region between the two liquid
bodies at which time coalescence occurs. Some of the
earliest work of temporary non-coalescence, as described
by Neitzel and Dell'Aversana (2002), dates back to a series
of papers published by Lord Rayleigh. Rayleigh (1879)
observed the scattering and subsequent bouncing of
droplets exiting a spray nozzle and later in (1899)
discussed the influence of static charges on coalescence.
Also, Reynolds (1881) observed temporary non-coalescent
floating droplets. He created a splash on a body of water
and observed droplets temporarily floating on the surface.
In order to sustain permanent non-wetting, the
lubricating fluid must be continuously replaced.
Mechanisms responsible for creating and sustaining the
lubricating gas include evaporation, thermocapillary
convection, and isothermal forced gas flows.
Non-wetting by evaporation can be observed by dropping a
cooler liquid droplet onto a hotter surface. In this case, heat
from the surface causes evaporation of the droplet and thus
producing the required lubricating layer of gas. An
example of this mechanism can be observed by sprinkling
water droplets on a hot skillet. If the skillet is sufficiently
hot, the droplets will appear to bounce or dance around
above the surface of the skillet.


7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010

Thermocapillarity is a mechanism resulting in fluid
motion along the surface of a liquid due to variations in the
temperature-dependent surface tension. Bulk fluid
motion inside the liquid and surrounding gas result from
the presence of an externally induced temperature gradient
along the liquid surface. Thermocapillary convective
non-coalescence was documented in 1985 during an
experiment on a space shuttle in a microgravity
environment, as described by Dell'Aversana and Neitzel
(1998). The phenomenon occurred after a liquid bridge
was accidentally broken and an attempt was made to
reform the bridge while the two liquid droplets were at
different temperatures. The two droplets remained in a
non-coalescent state until the temperature difference fell
below a critical threshold.
The motion of one surface relative to another provides
one means for a shear-driven isothermal forced gas flow.
Dell'Aversana et al. (1996) performed isothermal
experiments in which a liquid droplet, suspended from a
cylindrical rod, was lowered into a rotating bath of the
same liquid. The effects of the interstitial fluid were seen
in both the rotating bath and the droplet. In the bath, a
dimple was created behind the droplet. In the droplet,
convective cells resulted from the viscous nature of both
the interstitial fluid and the droplet. Also, it was discovered
a threshold capillary number (Ca) and Reynolds number
(Re) existed such that below these threshold values
non-coalescence was not observed. These two
dimensionless parameters quantify the importance of
viscous effects compared with that of surface tension and
of inertial effects compared to viscous, respectively.
In a later paper, Dell'Aversana et al. (1997)
experimentally investigated the thickness of the lubrication
gas layer with clever use of laser interferometry. Both
thermocapillary non-wetting and isothermal
non-coalescence situations with a droplet suspended over a
rotating bath were examined. In the non-wetting
experiment, a droplet supported by a flat, warm surface
was pushed against a cold flat surface positioned above
and in parallel. The thermocapillary action on the droplet
surface pulls air from all radial directions into the crevice
between the cold surface and the liquid resulting in a
stagnation point and recirculation above the center of the
droplet. A resulting dimple was observed in the center of
the film profile. Sumner, Wood, and Neitzel (2003)
applied lubrication theory with an asymptotic analysis of
this non-wetting scenario and computed similarly shaped
droplet profiles. With a height-to-length ratio for the
droplet treated as a small parameter, they incorporate
inertia in the first correction term of the asymptotic
solution suggesting that inertia is likely the cause of the
dimple.
The isothermal non-coalescence experiment of
Dell'Aversana et al. (1997) suspended a droplet over a
rotating bath and, although not a main objective of that
paper, discovered unsteady oscillations depending on many
of the experiment parameters. It was also found that the
oscillations could be periodic and did not always lead to
coalescence.
Regardless of the presence of non-wetting, the
scenario shown in Figure 1 concerns two immiscible fluids
in which the first fluid is a droplet with static contact lines
and the second is a surrounding fluid in motion with






Paper No


respect to the droplet. The complicated physics at the
contact lines governs the relationship between contact
angle, position and possible migration and strongly
influences droplet shape in general. For droplets on
rough surfaces or bounded by a sharp corer, the contact
line position may be the appropriate mathematical model
while for a smooth surface it may be more appropriate to
enforce a specific contact angle. For smooth surfaces,
contact line hysteresis poses additional challenges in which
the contact angle may assume one of many values within a
range between receding- and advancing-contact-line
thresholds. Dussan (1979) documents experimental and
analytical achievements made in the area of static and
dynamic contact lines. Although migration may be of
interest in fuel cell design, the current investigation focuses
on non-wetting and avoids droplet migration by pinning
the contact line with sharp corer features.
Several previous works analyze the situation of a flow
over a droplet situated on a flat surface without addressing
non-wetting specifically. Li and Pozrikidis (1996)
compute three-dimensional shapes of a liquid drop subject
to a shear-driven passing fluid, and investigate the
influence of the shape of the contact line which is assumed
to be either circular or elliptical. Critical capillary
numbers are found marking the onset of contact line
motion.
Dimitrakopoulos and Higdon (1997) compute
two-dimensional profiles for a droplet in a shear-driven
passing fluid assuming a low-Reynolds number flow.
They investigate profiles while enforcing a specific contact
angle on one end of the droplet and pinning the contact line
position on the other. Thus, the length of the droplet is
found as part of the numerical solution. Variations of the
viscosity ratio, Bond and capillary numbers, as well as the
advancing and receding contact angles are considered.
Also, gravitational forces are found to be influential.
Schleizer and Bonnecaze (1999) used the
boundary-integral method to compute transient simulations
of the flow and droplet profiles for a two-dimensional drop
subject to a pressure-driven passing flow as well as
considering a shear-driven passing flow. The simulations
neglected inertial and gravitational forces. The droplet was
first studied under pinned contact lines, then under mobile
contact lines using the Navier slip model.
Simulations by Schleizer and Bonnecaze discovered
that increasing the capillary number, and consequently
decreasing the surface tension forces relative to viscous
forces, resulted in a more deformed droplet as logic would
suggest. The same was found upon increasing the droplet
size. The effects of increasing the viscosity ratio,
influencing pressure and shear stresses on the droplet
surface, again resulting in a more deformed droplet.
Furthermore, increasing the viscosity ratio decreased the
critical capillary number required for a steady droplet
shape.
The experiments herein intend to complement a
two-dimensional mathematical model of flow much like
that of Schleizer and Bonnecaze (1999) considering the
Navier-Stokes equations and continuity coupled with the
deformable interface boundary conditions applied at the
liquid/gas interface. A kinematic constraint maintaining a
constant volume of liquid in the droplet is also necessary
when the droplet shape is part of the investigation. Figure


7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010

2 shows the flow domain for a potential two-dimensional
analytical investigation where the upstream air follows
plane Poiseuille flow, H defines the position of the upper
channel wall, L specifies the surface length wetted by the
droplet, and h(x) marks the droplet profile. Following the
pinned contact line of the experiments preventing
migration, the contact-line is assumed fixed at x = 0, L.


Poiseuille Gas Flow
/ yA


1- -L I1
Figure 2. Flow domain for a two-dimensional analytical
investigation


Experimental Facility

The experiments demonstrate this two-dimensional
non-wetting scenario by stretching a water droplet laterally
across the bottom side of a wind-channel. The
wind-channel apparatus, shown conceptually in Figure 3,
has been designed to visually examine the dynamics of a
water droplet under permanent non-wetting conditions
sustained by a pressure-driven interstitial airflow. A
test-section platform supports the droplet from below and
pins the contact line forcing the droplet to stretch
uniformly across the air stream imposing a quasi
two-dimensional flow. Experiments vary airspeed,
channel height, and droplet volume searching for
conditions that sustain non-wetting.


z-positionir
plates


-- entrance -


g
diffuser


droplet test section fan


Figure 3. Wind-channel apparatus maintaining interstitial
flow over droplet


The wind-channel has a 60-mm-wide rectangular
cross-section less than 10-mm high as specified by
situating the top wall. A long entrance region establishes
fully developed, laminar airflow delivered to the test
section. The test section holds the droplet platform
designed with sharp edges to pin the liquid/solid contact
line and impose a uniform droplet profile across the
channel. The test section is followed by a diffuser and
fan controlling the wind speed. The position of the top
wall is adjustable from 0 to 10 mm via two manual
z-positioning plates. A syringe pump controls the volume
of liquid in the droplet. Constructed from translucent
acrylic, the wind channel allows droplet visualization with
sufficient back lighting. A high-speed digital video






7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010


camera records a side view of the droplet during the
experiments. Additionally, flow visualization techniques
discussed below measure the liquid volume and the air
speed inside the channel. With these features, the
apparatus design accomplishes three main objectives:
1) Create and sustain and interstitial air stream entering the
test section as fully developed, plane Poiseuille flow.
2) Vary and measure the air speed through the wind
channel, the volume of the water droplet, and the distance
between the top and bottom surface of the wind channel.
3) Visually record the shape and dynamics of the water
droplet through the use of a high-speed digital video
camera. Critical concepts of the design include an
entrance length, as removable test-section base plate,
diffuser, and z-positioning plates.
One-meter of entry length before the test section
establishes fully developed, laminar flow. The Reynolds
number for the air flow based on the hydraulic diameter of
the channel never exceeds 1000 suggesting fully developed
conditions within 0.86m. With a 1-meter entry length, the
entire apparatus spans 1.219m.
A typical diffuser of a wind tunnel diverges at an angle
of 100 300 to accommodate the size difference between
the test section and the fan while preventing flow
separation. According to Mehta and Bradshaw (1979),
the proper angle for an optimum pressure drop is between
5 100 included angle. Accordingly the wind channel
incorporates a diffuser with an included angle of 10.
The water droplet is situated on a removable base
plate inserted inside the test section of the wind channel.
This base plate has the overall dimensions of 60mm x
60mm x 6.35mm. Figure 4 shows the base plate and
thel5mm x 60mm foot print of the droplet. The grooves
cut into the base plate constrain the wetting area of the
droplet establishing a pinned contact line and preventing
droplet migration.


grooves "

Figure 4. Water droplet
area imposes pinned contact
profile


z-plate frame


Figure 5. Wind channel apparatus cross-section at
z-positioning plate

Measurement Techniques
Digital imaging assists in the measurement of channel
height, upstream airspeed and droplet volume. Channel
height is taken directly from scaled images referring to the
known 15-mm-wide droplet base. The uncertainty in
channel height was estimated to be +0.036 mm with the
channel height set at 4 mm and is typically 0.03mm
during the experiments. Correlations were developed for
estimates of upstream airspeed and droplet volume.
The incoming airspeed estimates utilized a flow
visualization technique tracking the motion of vapor
structures introduced into the air stream. While vapor from
a water atomizer passes through the channel, the distance
traveled between frame intervals for an identified vapor
structure is marked, and the airspeed is estimated as the
ratio of the distance traveled to the time interval between
frames.
Figure 6 contains a typical pair of sequential frame
images marking the leading edge of a vapor structure.
Based on the resolution of the meter-stick, the uncertainty
for the measurement of the distance traveled between
frames was limited to 0.5mm. Uncertainty in the
measurement of the time interval strictly dealt with the


base. Sharp edge of wetted
lines and a uniform droplet


leading edge of structure


The top surface of the wind channel moves as a single
rigid component spanning from over the inlet nozzle to the
fan. Two z-positioning plates raise and lower the top
surface while imbedded ring seals prevent air seepage. A
frame surrounds each z-positioning plate as shown in
Figure 5. One complete rotation of the adjustment knob
correlates to a 0.5mm change in plate height.


Figure 6. Example images analyzed in correlating airspeed
to channel height and fan voltage.


Paper No






7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010


internal operations of the camera through the variable
frames per second (fps) setting. The uncertainty in fps
was assumed to be one percent of the manually prescribed
value. Estimating the time interval as the reciprocal of
the fps setting implies an equal 1% uncertainty in the time
interval. Following the technique of Kline and
McClintock (1953), the airspeed uncertainty was found to
be inversely proportional to the time interval estimate.
Consequently, higher airspeeds contain more uncertainty
due to the need for higher fps settings required to keep
vapor structures within the field of view. Furthermore,
the uncertainty of the distance measurement proved to be
more influential and dictate the airspeed uncertainty.
Measurements of the airspeed for numerous
combinations of channel height and fan voltage settings
provided a correlation, shown in Figure 7. Estimates of
airspeed during non-wetting experiments interpolate
between these correlations. Consequently, the local
contribution of the droplet on the overall flow resistance in
the channel is neglected. Error bars in Figure 7 show the
increase in uncertainty with increasing airspeed as
explained above.


0 05 1 15 2 25 3 35 4 45
Height (nm)
Figure 8: Droplet volume dependence on static droplet
height (R2 = 0.9947).


Nomenclature

H height of channel
L streamwise width of droplet base
A aspect ratio, 2H/L
h, maximum height of static drop
S height ratio, H/h,
Re Reynolds number


Results and Discussion


02 mm
x 3 mm
A 4mm
E 5 mm


4 5 6 7 8 9 10 11 12
Fan Voltage (V)


Figure 7. Airspeed vs. fan voltage correlations for different
channel heights.

A syringe pump operated by a stepper motor
controlled the amount of liquid in the droplets. Rather
than monitoring the discharge of the syringe pump, droplet
volume was correlated to the maximum height of static
droplet profiles. Water droplets appropriately positioned
on the base plate were weighed on a mass scale and a
digital image of the droplet profile revealed the height.
Data in 0.1-g increments of liquid provide the linear
regression shown in Figure 8. Droplet volumes range
from 1300 to 3000 mm3. Combining the 95% confidence
interval of 75.94 mm3 for the regression with 25 mm3
due to the height measurement uncertainty indicates a total
uncertainty of 80.9 mm3 for the volume estimates.


The demonstration of non-wetting consists of
introducing a substantial passing airflow and lowering the
top surface until the droplet is thought to be in a state of
non-wetting. The air flow rate is then decreased
incrementally until the droplet wets the top surface
verifying a prior state of non-wetting and thus indicating
the boundary of the non-wetting region or critical wetting.
Figure 9 displays four images of droplet profiles from a
single non-wetting demonstration. Image 1 shows the
initial droplet shape under static conditions. Image 2
displays the droplet under the conditions of non-wetting at
the maximum fan speed. Image 3 displays the droplet
after the airspeed has been reduced to a near-critical value
and thus just before the occurrence of wetting. Image 4
shows the resulting liquid bridge formed upon wetting of
the top surface. In each image, the dark obstruction
below the droplet is merely the water hose to the base
plate.
Continuing to employing this procedure to mark
critical wn cin li the critical upstream airspeed for varying
channel heights was investigated. The results for two
specific droplet volumes are shown in Figure 10 where
each data point represents the channel height and upstream
airspeed at the onset of wetting. The dashed vertical lines
corresponding to 2.96 and 3.55 mm indicate the maximum
height of the static droplets.
The results of Figure 10 show that wetting occurred at
lower airspeeds for larger channel heights and, in all cases,
at channel heights significantly larger than the static
droplet heights. For the cases of no airflow, a comparison
of the critical channel height to the static-droplet height
shows that the droplets jumped across an air gap of 0.48
and 0.32 mm to wet the top surface. The data does
suggest then that the presence of air flow permits the top
surface to be lowered beyond this static-wetting threshold
into a scenario of non-wetting. Lowering the top surface


Paper No






Paper No


further or reducing the airflow will eventually lead to
wetting. These bounds mark a region of non-wetting to
be below the static-wetting threshold and above the curve
mapped out by the critical wetting points. This
non-wetting region is indicated in the figure and expands
with increasing airspeed. With larger airspeeds, the flow
appears to tolerate more "squeeze" induced by the top
surface.


Image 1 initial static droplet


-w r1


Image 2 non-wetting droplet at max airspeed









Image 3 near critical non-wetting droplet


----- r


Image 4 coalesced droplet at ci


Figure 9. Images captured from a non-wetting experiment.
(Airflow is from left to right.)


120 Critical Wetting Droplet
0 2027 cubicmm
100 2529cubic mm
Static Droplet Height
80 2 96mm (2027 cubicmm)
S 3 55 mm (2529 cubicmm)


2 75 2 95 3 15 3 35 3 55 3 75
Channel Height (mm)


3 95 4 15


Figure 10. Critical wetting conditions for two droplet
volumes showing that airspeed must increase as channel
height decreases for non-wetting conditions.


7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010

Additionally, the airflow is found to influence the
shape of and the flow within the droplet. A dynamic
droplet deforms in such a way as to raise the peak height of
the profile above that of the static droplet. Figure 11
compares static and dynamic droplet profiles for a
common droplet volume. Images 2 and 4 on the right
side of the figure show deformed profiles due to an
airstream passing from right to left. The top wall in
image 2 is positioned above the static-wetting threshold
and, in image 4, below this threshold and within the
non-wetting region. The deformed droplets are not
symmetric and tilt in the streamwise direction. The peak
height increases and shifts aft relative to the static situation
shown in images 1 and 3. A horizontal dashed line
referencing the static droplet height h, appears below the
dynamic-droplet height. The lubricating-air gap jumped
upon wetting under dynamic conditions is not measured
but observed to be substantially less than that suggested by
a comparison between the channel and the static droplet
height observable in Figure 10.


Image 1 -Static State Image 2- Outside Non-Wetting Region


Image 3- Static State


Figure 11. Droplet profile images illustrating that the
maximum droplet height increases as the top surface is
lowered closer to the droplet.

Comparing channel height relative to the size of the
droplet provides a means to quantify a "squeeze" effect by
the top surface and thus an implied resistance to wetting.
Defining a height ratio, S H l and quantifying flow
dynamics in general with the Reynolds number based on
the fluid properties of water but referencing the average
upstream air speed in the channel, Figure 12 shows a
comprehensive collection of critical wetting conditions for
droplets of various aspect ratios, A H/L. The data
shows that in general, a smaller height ratio S and thus
more squeeze can be achieved at higher Reynolds numbers.
Although the aspect ratio, Reynolds number, and S do not
constitute a complete parameter set (both a Froude number
and a capillary number could be influential) and so these
data cannot necessarily be expected to collapse to a single
curve, the graph of Figure 12 begins to distinguish a region
of potential non-wetting above the trend from a region
void of non-wetting below.
Revealing the greatest challenge of the experiments,
two critical wetting conditions were found unrepeatable
and are marked with enclosing circles. Extraneous
influences, varying in significance between experiments,
appear to alter the adhesive forces affecting the occurrence
of wetting.






Paper No


3000 AA= 0473
XA= 0 43
2500
OA= 0 394
2000 OA= 0 337
A O
S 1500

1000
X
500 U


1 00 1 02 1 04 1 06 1 08 1 10 1 12 1 14
S
Figure 12. Critical Re dependence on S showing that
higher air flow sustains more squeeze.


Logically a separation pressure between the droplet
and solid surface must increase as S decreases, in order to
maintain non-wetting. The separation pressure is
provided by the presence of the interstitial fluid and again
following lubrication theory increases with the velocity of
this fluid which is actually a consequence of the resulting
increased curvature in the velocity profile across the gap.
Accordingly, a severely deformed non-wetting droplet
associated with a low S value would requires a high Re
number, while a mildly deformed droplet could be
maintained with a lower Re number value suggesting a
negative sloping trend. Such a negative trend can be
inferred from Figure 12 supporting the lubricating layer
hypothesis as in previous research efforts described above.
The primary extraneous effect was discovered to be
electrostatic charging of the top surface by the passing air.
Seemingly more prevalent with dry surrounding air
conditions, this influence of electrostatic forces was
reduced dramatically by coating the top surface with a thin
ply of electrically grounded aluminum. Repeatable
results required this grounding of the top surface. Droplet
deformation due to electrostatic forces can be found in the
thesis by Gibson (2008). Other contributing factors could
possibly be: an unleveled apparatus, vibrations transferring
through the apparatus from the building, surfactants in the
droplet changing the surface tension, or residual water
molecules clinging to the top surface after it had been
wiped clean. Figure 13 reveals the variation in
liquid/solid attraction with the top surface electrically
grounded showing the size of the air gap measured just
prior to static-wetting for various droplet sizes. The air
gap jumped upon wetting could be a large as 0.48 mm or a
small as 0.16 mm. Liquids other than distilled water
could better resist electrostatic influences although distilled
water was selected here due to its convenience and direct
relevance to PEM fuel cells.
Although the maximum height of a droplet was found
to increase upon initiating a passing airflow, this doesn't
preclude the possibility of lowering the value of S to less
than unity during extreme non-wetting conditions.
However, such low values of S were never achieved during
testing. Figure 14 presents a graph of the critical-wetting
channel heights H for various static droplet height h, under
both static and dynamic conditions referring to the absence
and presence of a passing airflow respectively. In all


7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010

cases, static conditions yield larger S values than dynamic
conditions verifying that the top surface was, in fact,
lowered closer to the droplet in the presence of a passing
airflow permitting the claim of non-wetting. Furthermore,
S never takes on a value less than unity. This may be due
to limitations of the experimental apparatus which cannot
forcefully direct the entire volume of airflow into the
lubrication region of increased pressure.


060

050
E
S040

S030

. 020

0 10


000
2


40


260 280 300 320 340
Initial Droplet Heght (mm)


360 380


Figure 13. Air gap upon static wetting between liquid and
top surface for various droplet heights illustrating a
variance much larger than the instrument uncertainty.


4 00






C 3 00
4 ,
a


200 --
2 00


2 50 300 3 50 400
h,


Figure 14. Critical channel height verses the initial droplet
height (hs) illustrating that the height ratio S H i
remained greater than unity and that critical channel
heights for dynamic conditions remain less than that for
static conditions.

Experimental Observations
Several observations during the experiments helped to
guide the interpretation of and complement the
non-wetting results. Observations are made about the
flow field of the liquid in the droplet, evidence of a
pressure increase above the droplet, evaporation, and
droplet oscillations due to instability.

Flow Field of the Droplet
The flow field inside the droplet was revealed upon
observing the motion of inadvertent dust particles inside
and on the surface of the liquid. A diagram representing
the path of the particles in Figure 15 shows multiple
recirculation cells. The non-uniformity at the lateral


T


t






Paper No


extents of the droplet near the channel side walls causes a
small horizontal recirculation cell at each end of the
droplet where the contact line forms a semi-circle. These
small cells appear to kinematically drive a broad interior
cell on each side of the droplet center line. These liquid
paths suggest that a significant portion of the incoming air
(being coupled to the liquid motion on droplet surface) is
diverted around the droplet instead of passing
unidirectionally down the channel. The recirculation
cells suggests that the flow was not two-dimensional as
hoped even far from the end effects near the channel
sidewalls. Although the lack of unidirectional flow over
the droplet may severely limit the range of achievable S
values, a region marking conditions for permanent
non-wetting was found.

Front view of droplet air flowing into page
observed path
of dust particles






Boundaries of
wind channel


Top view of droplet


Boundaries of
wind channel
Figure 15. Illustration of Multiple Convective Cells on
Droplet Surface. Nature of cells suggests that a significant
portion of incoming air is diverted around the droplet
instead of passing over the droplet.


It is expected that a significant portion of the incoming
airflow passes around the droplet instead of above and thus
fails to contribute to the interstitial fluid required for
non-wetting. Thus, the volumetric air flow in the channel
does not quantify the portion to attribute to non-wetting.


7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010

Within the conditions of non-wetting, the airflow above the
droplet appeared to increase upon increasing the channel
air flow.

Evidence of a Pressure Increase
An auxiliary experiment was conducted to
demonstrate the occurrence of two conditions that must
arise for non-wetting to be achieved. First, a portion of the
incoming air must pass over the droplet, and second, the
pressure in the air above the droplet must increase with
increasing air speed. The experiment illustrated in Figure
16 begins by placing a sustained droplet spanning the
halfwidth of the channel. Airflow was introduced, and
the top surface was lowered slowly toward the droplet.
As the top surface moved into close proximity of the
droplet, the droplet profile deforms to tilt downstream as if
the result of an interfacial shear. As the top surface was
lowered still closer to the droplet, its height decreased as
the width (transverse to the air stream) increased. This
deformation demands an increase in air pressure directly
above the droplet.

Front view original droplet shape spanning halfwidth of channel


Droplet


Channel


Side view deformed droplet provides evidence that a significant
portion of air is passing over droplet and not around it


Original droplet shape


Deformed droplet shape


Front view deformed droplet shape provides evidence
that air pressure above droplet has increased

Original droplet shape Deformed droplet shape





Figure 16. Illustration describing evidence that air is
passing over the droplet and that the air pressure over the
droplet is increasing.


Droplet Evaporation
The potential for the reduction in droplet volume due
to evaporation was quantified and considered negligible.
Under static conditions, a droplet was found to lose 77.25
+ 75.97 mm3of liquid over 40 minutes. This is 0.030% +
0.029% of the initial droplet volume of 2612 mm3. A
droplet subject to the maximum channel airflow
experienced a loss of 98.47 84.89 mm3 which is a slight
increase from the static case at a 0.035% + 0.030%


c t


All,





Paper No


decrease in liquid volume. Recall that droplet volumes in
the study ranged from 1500 mm3 to 2800 mm3. An
experimental trial run typically lasted 20 minutes.

Droplet Oscillations Due to Instability
Some experiments encountered a droplet stability
issue. For relatively large droplet volumes, sometimes
unsteady oscillations in the droplet shape appeared. The
oscillations seemed to occur within a channel height range
for a constant airspeed or within an airspeed range for a
constant channel height. An investigation of this
instability was not pursued and may be the focus of future
research. However, digital video captured the oscillations
and still images from the video are presented in Figure 17.
Image 1 was captured before the oscillations occurred,
while the droplet was stable. Images 2 through 5 were
captured in sequence, while the oscillations were most
severe. The camera was set at 346 fps, so the images were
captured approximately every 2.89 ms. The droplet
surface vibrates profusely seemingly with a pronounced
bulge continuously shifting position.


image z image J


Figure 17. Images captured every 2.89 ms showing droplet
oscillations occurring for relatively large droplet volumes.


Conclusions

Experiments demonstrate the existence of non-wetting
of a droplet in a channel in which a water droplet is pinned
to one side of the channel and resists wetting the opposite
side due to an interstitial pressure driven channel flow of air.
Failure to acquire a complete set of repeatable results
suggests considerable sensitivity in this unusual case of a
pressure driven and necessarily lubricating flow.
Significant three-dimensional flows are observed although
the original intent of the experiments was to isolate a region
where the flow might remain two-dimensional flow through
the droplet cross-section. The existence of the
three-dimensional or secondary flows may actually be
responsible for the existence of non-wetting in this unusual
case and also for the repeatability issues noted in Figure 12.
More research is suggested that would focus on a modified
wind-channel apparatus that would allow the droplet to
protrude past the width of the channel cross-section and thus
reduce the end effects and resulting secondary flows.


7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010


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