NASA-Ci_-2044_2
r
Non-Coalescence
Effects (NAG
Performance 17 June
3-1894)
Report 1996
in Microgravity
for the period
- 16 June
Submitted
1997
to:
Dr. Ray Skarda Microgravity Fluids Branch, Mail Stop 500/102 NASA Lewis Research Center 21000 Brookpark Road Cleveland, OH 44135
by
Prof. G. Paul Neitzel, Principal The George
Investigator
W. Woodruff School of Mechanical Georgia Institute of Technology Atlanta, GA 30332-0405
May,
1997
Engineering
I.
Summary
Non-coalescence between
liquid
investigations Research
drops being
and
surfaces
of
(1996)
additional
data.
Interferometry
a
glass
Parametric
dimensional
Center,
constructed
and contact
flow
and
convection
to
the two liquid
free
the
visualization
solid
(contact
experiments
and quantitative
in
measurements
droplet
A preprint
to Physics
of Fluids
apparatus
load
threshold
for
value
by the MARS as Exhibit
of
group
B of the
to this report. being
made
to allow
Obviously,
gas film will reach
associated
values
phenomenon.
on non-coalescence.
the lubricating
the
by a solid
an absolute
is presently
gas pressure zero,
replaced
is included
as the Appendix
to obtain
to interrogate
contact-suppression
of this paper
the
of being
of yielding
Banavar
modified
devised
are capable
to the MARS
toward
has been
has been
the
appears
to sustain
drops
is capable
investigate
by Dell'Aversana,
with
different
droplet states
a point
deformation. of
surrounding
examine
quasi-two-
deformation.
case,
who
between
reported
system
submitted
determine
Tech,
in these
non-coalescence
surface
of two liquid
which
tends
an
non-coalescence
two-dimensional
free
experiments
of surrounding
able
will
At Georgia
MARS
report,
modification
longer
and droplet
employed
recently
gas pressure
studies
the Microgravity
of thermocapillary
geometries
in the latter case
of the influence
it is no
to
of this.
performance
as the absolute
and
of parallel
case in both geometries.
the lower
plate
examples
An additional
pressure
and
A paper
detailed
Both
include
an interferometry
measurements
the film thickness.
where
to date
of the axisymmetric
droplets as
drop
two-dimensional
Specifically,
such
assessment
the
on the non-coalescence
air film between
subgrantee's
between
a pair
of Technology
Italy.
of contact
Research
The apparatus & Koplik
Institute
suppression
through
gas (air) into the space
in the contact-suppression
Discussion
and the
studied
the mechanism
performed
and (nearly)
of film thickness
provides
exploiting
or
Experiments
is being
in Naples,
film of surrounding
both axisymmetric
surface
surfaces
Center
by
(non-coalescence)
suppression).
of the same liquid
at the Georgia
(MARS)
are achieved
drive a lubricating
bodies
solid
conducted
and Support
suppression
II.
of two
but
and contact the
experiments. visited
for this apparatus
apparatus
drop
been
suppression.
sizes
With
Georgia
has
are
quite
the assistance Tech
in March,
as well, permitting
2
constructed Both
to
effects
small
for
of Pasquale
can be achieved the
silicone Dell'Aversana
an interferometry
film thickness
oils
determination
setup
in the being of the
has
been
as described
above for the axisymmetriccase. Some preliminary parametric studies have been performedwith this apparatus,includingan examinationof behavioras the load between the two dropsis increased.In somecases,the dropsareobservedto coalesceinto a twodimensionalliquid bridge, while in others,thepinnedcontactline holding the drop to the copperheatergivesway, allowingliquid to spill overthe sideof the heater. Visualizationof the highly employ
curved
smoke
flee
the flow field surface
visualization
drops.
The motion
consists
toward
the gap between
within
at the ends
the two-dimensional
of the drops.
to investigate
the flow
of a vigorous
inflow
the droplets
cold drop.
In the region
just outside
vortex
is formed.
Flow in the gap between
However,
is difficult,
we have
in the air immediately along
accompanied
lower,
drop
the surface
by an outflow
the convergence the two drops
been
be observed
to
to the hot drop
the surface
of the two drops,
cannot
able
adjacent
of the upper, along
due to
of the
a standing
at the present
time.
Finally, transition
in both
to time-dependent
quantified.
This
thermocapillary states
which
two-dimensional flow
and
is observed
time-dependence
axisymmetric
under
is periodic
certain
in nature,
convection
in liquid
bridges.
A study
was originally
proposed
therefore
appears
in a subsequent III.
the
cases,
conditions
which
reminiscent of the
interesting
are yet to be
of the instability
stability
to be in order
an
properties
of
of these
and will be conducted
year of this grant.
Reference
Dell'Aversana,
P.,
shear
and temperature
IV.
Project
at Georgia
Banavar,
J. R. & Koplik,
gradients.
Physics
J.
of Fluids
1996 8, 15.
Personnel
Tech:
G. Paul Neitzel,
Professor,
John C. Nalevanko, at the MARS
Graduate
Principal
Investigator
Research
Assistant
Center:
Luigi Carotenuto,
Researcher
Dario Castagnolo,
Researcher
3
Suppression
of coalescence
by
PasqualeDell'Aversana,Researcher V.
Publications
Dell'Aversana, and wetting:
Nalevanko,
the shape
G.
P.
Invited
Kansas
City, MO,
Castagnolo,
Russian
Design
1997
Georgia
Institute
P.
March
and non-coalescing
1997
Suppression
to Physics
for investigation
of coalescence
of Fluids.
of 2-D
liquid drop
non-
of Technology.
When
liquids
of Liquid
Drops
stay
dry.
Invited
paper
in
Today.
Non-Coalescence
talk presented
L.
Submitted
1997
in Physics
at the March
Meeting
and
Suppression
of the American
of Surface
Physical
Society,
17-20.
D., Dell'Aversana,
Symposium
film.
of an apparatus
P. & Dell'Aversana,
Wetting.
wetting
1997
for publication
G.
V. & Carotenuto,
of the interstitial
M.S. thesis,
preparation
Neitzel,
Presentations
P., Tontodonato,
J. C.
coalescence,
Neitzel,
and
P., Tontodonato, drops.
on Physical
V. & Neitzel,
To be presented Sciences
at the Joint
in Microgravity,
15-21.
4
P.
St.
1997 Xth
Features European
Petersburg,
of nonand
Russia,
Vith June
Appendix MARS CenterPerformance Report
5
MicrogravityAdvanced
Research
Non-Coalescence
and
Support
Center
Effects in Microgravity
Performance
Report
for the period June
17,
1996
through
Subgrantee's
Subgrant
number:
Center Subgrantee
Principal
Prime
address:
Investigator:
grant number:
Grantee: Principal
Date:
1997
part
Advanced
Research
and
(MARS)
Via Comunale
Tavernola,
80144,
Italy
Napoli,
Phone:
+39-81-234-4580
Fax:
+39-81-234-7100
Dr. Luigi
Carotenuto
NAG3-1894 Georgia
Investigator:
16,
E-25-L43-G1 Microgravity
Subgrantee:
April
Institute
of Technology
Prof. G. P. Neitzel
16 April
1997
uigi Carotenuto (General
Manager)
Support
Non-Coalescence
Effects
in Microgravity
Non-Coalescence
Effects
Performance
The
present
the first year liquids
document
of a study
1. The work
reports
is being
executed
jointly
out over
a four year
period.
be completed
by June
16,
They
Stable
and even
defined surprising
behavior
moving, liquids.
and thus their
understanding
investigate
more
of the
the phyisical
application,
has been
and
evolution
wetting
are
or exploiting
theory,
which
numerical
surfaces.
owing
representing
a different
has
been
also
unsteadiness. have
The
in close
reason
of such
possibly,
the forces
the
contact
is to achieve
description
and,
that,
between
an actual
year project
well
surfaces
medium
a quantitative
where
to what
as long as certain
preventing
of to find
concerned
a
it, to some
assume
nature
been formulated.
A theoretical
are presently
has
been
of the same
being
worked
parameters extended
liquid/solid
lubrication
of non-coalescence
on preliminary
measurements.
to be more suitable
evidenced
based
fluid-dynamic
In facts,
aspect
the interpretation
previously
study
to the same
resulted
The
was
relevant The
non-wetting
have
reported,
simulations
most
stressed.
of solid
systems
force
systems,
microgravity,
by interferometric
of the
systems
of non-coalescing
brought
of the liquid
The aim of this four to give
to be
surrounding
a lubricating
phenomenon,
of the period
confirmed
outlined,
of the
85%.
to
than on ground.
In the course of lubrication
a film
and
are expected
to about
mantained.
to an action
between
according
merge,
for
of Technology
performed
without
ascribed
exert
Institute
liquids
are
performed
non-coalescence
A] and completed
of some
being
of the first year
being
surfaces
coalescence.
limits
terrestrial
relevance
to drag
film would
now
one another,
tentatively
be able
Such
are
of their
had been
may
of the liquids full
conditions
of stable
The activities
ability
against
activities
with the Georgia
[Exhibit
is the
squeezed
dynamical
involved
of work
non-coalescence
proximity,
when
1997.
in the statement
Subgrantee's
the phenomenon
will be carried
announced
Report
on the
concerning
in Microgravity
systems,
mechanisms problem
experimental
results,
explanation
has been
out to consider
of the
also
to the from
problem
hand,
that non-coalescing
systems,
of such unsteadiness
is being
of the lubricating even
being
investigated
may
hand,
stable,
the the
of nonundergo
non-coalescence
- and, on the other
for the study
when
investigation
one
producing
in terms
- so
liquid/solid
film shapes. may
and some
undergo
hypotheses
It
Non-Coalescence
Effects
Different interest
been
interferometric
in order
coalescing
to reveal
liquids
means
to yield
with
variation thickness,
instead,
more
interfaces;
for this reason film
becomes
unsteady.
unsteady
flows
parameters
between For
occurs
modes
The
results
counterintuitive have
wetting:
threshold
The
been
in the
B]. This
conditions
environment.
Some
the experimental
received
technique
developed
both
and to analyze
of
highly
has
the
the film
fringes
are,
deformed
characteristics when
observed
the
that
the
of
system onset
of
thermo-fluid-dynamical been
used
to simulate
the images
to monitor
the
interference
containing
fringe
the information
system.
discussed
in terms
of
lubrication
of the lubricating
of the new findings manuscript
entitled
theory
and
some
film as the system
film"
manuscript
the NASA
for
of the pressure on loan from
cell. The remaining
in the course
is
of the period
of coalescence
by P. Dell'Aversana,
V. Tontodonato,
has been
support
coalescence
achieved "Suppression
which
part to be still performed
temperature
been
been
of the interstitial
experimental
been
from
and explained.
discussion
acknowledging
field
liquid
in the relevant
such as the thickening
been evidenced
[Exhibit
of Fluids",
deflection
same
the
has been
far
the dynamical
by
simplifies
to measure
features
of the
it has
that
The
situations.
have
behaviors,
the shape
Carotenuto
already
a certain
have
is found
a bath
when
of the drop/bath
An exhaustive concerned,
and
system
A beam
found
used to reveal
drop/bath
3-D film profiles
the oscillations
been
been
has
shape
of light,
possible
geometrical
the
softwares
for given
the
a drop
in unsteady
Dedicated patterns
they have
is overcome.
oscillation
loaded,
to monitor
It has
film
interferometry
of incidence
it has been
non-
convection.
greatly
near field
of
apparatus
on the
interface
the angle
order,
of its shape.
appropriate
lubrication
about
besides
of a flat
shifting
experimental
information
In particular,
of the interference
The
separating
of thermocapillary
to yield
the presence
to the cases
of the thin air film
and a solid.
suitable
and,
set out and adapted
by means
patterns.
configurations
absolute
liquid
because
been
features
also non-wetting
of the interference such
have
geometrical
is more
of interferometry
consequent
the
the
configuration
interpretation used
techniques
or a non-wetting
configured
liquid/solid
in Microgravity
as
submitted allowed
concerns
for publication the execution
sensors,
needed
Georgia
Tech,
to perform successfully
of
pressure
and L.
of the work.
of critical in
the
outer
such measurement, tested,
parts of the cell are completed,
of
in "Physics
the measurement
a function
and
and integrated
including
have in
the liquid
Non-Coalescence
Effects
injection/suction
system,
device,
which
pressure
have
sensors
board,
after
which
is also
and
signal
pressures
inside
from
that
inside
velocity
experimentally
The Dell'Aversana
Neitzel
City,
using
of a data
from
the
acquisition
SCXI
a Labview
to monitor
system,
software.
temperatures
out. A numerical
to simulate
suspended
at a solid
A and
heating
condition
has been
technique
based
the thermocapillary
coordinate
to prepare
the argument
presentation
1997,
disk.
The
motion calculated
for the simulation
transformation
employed
scientific
experiment
his APS talk,
of the
based
to solve
at the Joint
"Features
a one
on the
the problem
with
a talk
Tech-Mars
joint
Solids).
After
magazine Tech,
a Prof.
Xth St.
together European
Petersburg,
of non-wetting
P. Dell'Aversana,
week
Physical
visit
Society given
Today"
Prof.
in
graduate
and Vlth Russia, and
Russian 15-21
non-coalescing
V. Tontodonato,
conference G. P.
(session
04:
Neitzel
was an
held a seminar student
collaborated
with him, another
Dr,
to contribute
Dr. Dell'Aversana Neitzel's
of
by Prof.
research
his talk,
"Physics
on non-coalescence,
and outlined,
in Microgravity,
by D. Castagnolo,
and
helped
for
the American
his stay at Georgia
for a 2-D
used
in coincidence
in Fluids
and non-wetting,
is entitled
been
of the Georgia
of the monthly
to be given
Sciences
20,
During
has
and to attend
Motion
on this topic.
interferometer
travel
the first results
article
on non-coalescence
Tech
on March
by the Editor
prepared
carried
utilized
deflection
for
to Georgia
to illustrate
Physical
been
An orthogonal
surface
allotted
invited
Neitzel
signals
Instruments
in order
used as a boundary
channel.
Surface-Tension-Driven
the
pressurization
geometry.
budget
in Kansas
drop
has been
measured
this complex
have
has been
a liquid
in a deformed
in real time realised
The
by means
National
the
cell simultaneously.
method
profile
analysis
has been
simulations
volume
air film
data
and
structure.
are read
in an integrated
the experimental
on the control
mechanism,
in a pre-existing
the thermocouples,
interface
numerical
displacement
integrated
to perform
man-machine
surface
drop
conditioning,
able
develops
the
been
software
Some
in Microgravity
to set up with
Prof.
presentation
on
Symposium
on
June
1997. drops"
Such and
is
and P. Neitzel.
References 1p. Dell'Aversana, and temperature
J. R. Banavar gradients,"
Phys.
and J. Koplik: Fluids
"Suppression
8, 15-28, (1996).
of coalescence
by shear
Non-Coalescence
Effects (Subcontractor
in Microgravity Part)
L. Carotenuto, D. Castagnolo and P. Dell'Aversana Microgravio, Advanced Research and Support Center Via Comunale Tave,vTola 80144.
Statement
of Work
Napoli,
ITALY
and Budget Year 1
Explanation
According to the recommendations given in the final proposal review and in order to cope with the budget available, some changes have been operated with respect to the originally proposed studv. The entire study will now concentrate on the sole coalescence topic, which is one of the two issues addressed in the original proposal. The MARS Center part of the work has been agreed with the Principal Investigator, Professor G. Paul Neitzel of the Georgia Institute of Technology in Atlanta. It will consist in an experimental activitv, complementary,' to that to be carried out at Georgia Tech. and in a numerical simulation, to be conducted in collaboration with the group in America. Experimental activity The case where a non-coalescing system is surrounded by a gas will be investigated. The nature and the density of the gas are expected to affect the resistence of the interfaces between the non-coalescing liquids. In particular, we will see how the critical temperature difference between two liquids to hinder their coalescence depends on the outer gas pressure. An already existing cell will be adapted in order to change and monitor the gas pressure, to set the proper sample temperatures and to introduce the liquid and the gas indepedently from one another. The interpretation of the stable non-coalesce effect in terms of elasto-hydrodynamic theory of lubrication can be experimentally backed by interferometric measurements which are able to reveal the presence, between the liquids, of a thin interstitial film of the external medium. Preliminary results in this sense have already been achieved at the MARS Center. In the course of this project, the experimental technique will be improved to determine the exact shape of the film in steady conditions. The results of these measurements will provide the surface contours to be used in the numerical simulations. Numerical simulation A numerical model for a non-coalescing system will be set out in collaboration with Georgia Tech using boundary conditions and parameter values which are consistent with the experiments. The disjoining pressure which we expect to find over the contact area will be used in cross checks with the experimental and theoretical results. The numerical results are also intended to help in determining the limits of validity of some assumptions and of the use of the Navier-Stokes equations to describe the flows within the thin film separating the non-coalescing liquids. This activity will be carried out in Italy: the original intent to have a researcher from Mars resident at Georgia Tech as a postdoctoral research associate, has had to be changed.
MARS
Center Year
Budget I
The budget share, also agreed with the Professor Neitzet, for the subcontract to the MARS Center for the first vear of the project is $ 35,083. In addition, one trip to Georgia Tech, of approximately ! '.veek duration is foreseen, whose cost has been estimated at $ 2,500. About S 200 have zeen allotted for miscellaneous supplies, needed to support the experimental activitv to be performed at MARS. The budget explanation is summarised below.
Subcontract
to MARS
($ 88 / man-hour
$ 35,083
for vear
1" 2.3 man-mo
Travel
$ 2,500
Miscellaneous
TOTAL
/ yr)
FIRST-
$ 200
Supplies
YEAR
COST
$ 37,783
/
Suppression
of Coalescence
the Shape
P. Dell'Aversana
and of Wetting:
of the Interstitial
-J. V. Tontodonato
._lars CdJz_er. _'ia C_)munale
Film
b) and L. Carotenuto
Tm'ernola
, 80144
c)
Napoli,
Italy
ABSTRACT The shape and a solid
of the interstitial
SUl-face is detected
are exploited particular,
to reveal the
that stable
resting
light
detect
the
of the
calculated.
The
procedure
of a specific
uncouple
numerical
exploiting
code The the
the stress-balance
only the latter
film
technique,
The
results
equations
based
steady
upon
image
related
herewith
data
at the interfaces
behavior. method,
conditions
are
is explained
are explained
and the lubrication
explicitly
fringe
which
to
with the aid
in terms
conditions
show
is exploited
spectra
interference
In
in the
reflectometry,
analysis,
Fourier
the
as boundary
shift
a drop
techniques
and time-dependent
with
to simulate
presented
experimental
of an angle
of the film thickness
is able
optical
and its dynamical
bv means
coupled
unsteadiness.
which
thickness
both under
and between
A.Iternative
experiments,
for the determination
by thin films.
lubrication,
deflection
liquids
mterferometrv.
further
mav be realised
interfaces..-_
non-coalescing
and absolute
on a solid surface:
non-coalescence
features
of laser
of the film is measured,
of the
generated
bv means
the film profile
thickness
case of a drop
air film between
patterns
of theory allow
equations
of
one
to
and solve
ones.
I. INTRODUCTION In a paper where
that
two liquids,
achieving phenomenon
a stable occurs
was
separated
previously
published
bv an air film.
non-coalescence in the presence
in this Journal
can be brought
configuration. of liquid
In that
surface
I some
in close paper
motions,
cases proximity
it was whereas
were
described
of each
discussed coalescence
other
how
this
would
readily
occur
liquid
in the absence
surface
liquids
motions
provided
overcome.
main
are able to drag
distance
where
molecular
contact
results,
temporary
The
the
present
As
air
is able
lubricated
bearings)
prevents,
in principle,
conditions
are
Generalising
including
liquid/liquid
the relative
study
technological forces,
sticking
of spray
benefit
from 4.
between
already
surface
wetting
'self-lubricated
and liquid/solid
formation,
paints
systems, than being systems
in this used
combustion
in the
and
clean
by
systems' where supplied can
as development
on smooth
progresses
result
bearing"
rather
between
of solid
"self-acting
such
pressure
liquid/liquid
of self-lubricated
the
was
(stable
a qualitative
motion
rain
paper
two
is
surfaces to the
liquids
at a
the liquids
in
new experimental
strongly
the presence
liquids
the hindering
applications
surface
film
liquid
contribution the
that
two
configuration)
to drive
support
the
of the interstitial
air
observed
can now be generalised
a disjoining
we use the term
tangential
The
to create
term
here
presented
confirm
This
keep
the
for the
for the new
cases
of
liquid/liquid
here described.
and
bearings,
liquids.
would
In the present are
definitively
lubrication
how
between
was that the running
not be sufficient
of coalescence.
no matter
on the specific
force
may
that,
the coalescence
a constant
lubrication
and its presence
set. In fact, the
this behavior
measurements,
non-coalescing
systems
(depending
interaction
results
also outlined
to prevent
so generating
the primer
non-coalescence
and liquid/solid
inhibition
der Waals
by interferometric
above.
between
van
to explain
a permanent
and cause
yielded
hypothesis film
the
velocity
the liquids
Thus,
It was
it is possible
surface
hypothesis
air between
pressure.
motions.
are generated,
that a threshold
The
disjoining
of such
sense
understanding
by a liquid, has
if proper
been
presented
by an external
of the
Also,
dynamical recently
2.
all the particular
cases,
film is supplied
by
source.
dampers,
of aerosols,
nothing
of gas
in a series and
gas
classification
the gas lubricating
etc.
in common
non-coalescence)
to indicate
of bearings
surfaces,
(as
Gross 3 in the
be relevant
efficiency
solids
of fields
coalescence
in
measurement
composite studies
and
materials,
in rheology process
of
and
will its
Basic studiesin gaslubrication may get aheadthanksto the powerful tool laser interferometry
gaining
about
to parameter
their
response
In order pressure,
to assess
parameters
theoretical
many
involving
differences
in the
of a lubricated
means
to gain deep insights has
Mason 9. 10 to reveal suface
the novelty
liquid
more
dynamical
accurate
behavior
unsteadiness
not undergo observed same
for the
that
imply
which
The
relevance
of experiments
have
shown
dramatic
and
different that
small
differences
interferometry
for
liquid
offers
of the film
example,
toward
in the
a well
suited
layered
film
thickness
technique
in particular,
how
or aperiodic starts
changing
lead to coalescence.
shape. has been
This
in time even
The unsteadiness
for the case of a silicone
oil drop
and
rising
toward
a
where
a drop
interface.
Here, applied
This configuration
the air flows
oscillations.
Charles
has been
surface.
and
was still unknown,
two
liquids
the liquid-liquid
a solid
separating
by Allan,
of a bubble
interferometric
drop against
film, which
that would regard
studies
leads to coalescence
of the
It is shown,
to the disjoining
Sixties 6, 7, with
observation
exploited,
by a liquid
in the film shape
and
and thickness.
used
give rise to periodic
here with special
In addition,
the
investigated
for
in the film
may
is reflected
though
by the
the film does
in the film shape
placed
upon
is
a bath of the
liquid. In parallel
been
formed
of the interstitial
the rupture
thickness
a load 8. Laser
the lighter
determinations
and
These
and
in the
in the case of two immiscible
through
in general
and thickness.
by a number
bearings.
by the fact that a refined
configuration.
to be steady
related
falls
confirmed early
It was
the film thinning
systems
a liquid/liquid cease
liquids.
is represented
to self-lubricated yields
been
systems
contribution
the gap shape
performed
on the gap shape
and the film thinning
of the heavier
shape
to support
already
non-coalescing
about
solid
film
system
Interferometry
liquid
of which
lubrication
of the lubrication
and has been
common,
ability
temporary
importance
is well known
of lubricated
by
in the lubricant.
5 to gain information
calculations,
configurations
on the features
variations
the relative
it is essential
of these
new insights
offered
developed
with the experimental to simulate
work
the interference
presented fringes
herein,
produced
a specific
numerical
by a thin film.
code
It has been
has used
hereto supportthe interpretationof the interferencepatternsobtainedin the experimentswith air films.
II.
EXPERIMENT
DESCRIPTION
The experiments thermal
Marangoni
the only way exploiting very
surface
Three which
measurements
behavior
drop
lateral
direct
surface
A. Measurement
surface whilst the
would case
way
complicate where
a drop
Marangoni
tension
to set. Furthermore,
The
actuator,
gives
is not
choice
of
can produce
thermal
Marangoni
thus, the samples
are free
observations. first
one
produces
a drop and a solid surface far-field
fringes
curvatures
the third experimental a beam
gradients
to as
effect
states 1, 12, 13. The
surface
mechanical
on the main
near-field
and are used to perform that are projected
of the involved configuration
deflection
fringes,
surfaces
onto and
is used to detect
technique
coupled
with
a on
the
image
of the air film oscillations.
film between fringes.
an antireflection
the
through
shape
the interpretation is pressed
against
a drop and a reference
Fig. 1 depicts
with a flatness
is made
to observe
easy
(also referred
and thickness
flat is machined with
The thermal
because
realised.
setup
measurements
of near-field
the observation
best
been
exploiting
of the lubricating
is treated
convection
the interferometric
the second
oscillations
of shape
by means
the optical
have
situations;
to yield indirect
revealed
any external
information
in unsteady
The shape
is made
compromise
of thickness;
their
coalescence.
are relatively
without
setups
thermocapillary
and the non-wetting
on the thin film between
and yield
analysis,
which
that would
are focused
screen
flows
different
11 to prevent
convection
is established
vibrations
exploit
the non-coalescing
thermocapillary
convection
described
convection)
to achieve
regular
from
here
better
than
coating.
The
the coated
of the fringe a curved
the interferometer
drop
The
surface,
upon
liquid/solid because
This
is
One surface
of
the flat
surface
configuration
other
would
or the
of glass
nm) and the opposite
is loaded
channel
patterns. solid
used.
_./20 (_. = 632.8
surface.
of the lubrication
flat surface
configurations
be, for example,
case
is
of a drop
the
pressed
againstthe surfaceof anotherliquid. Whenthedropis pressedagainsta flat andrigid surface, the flat boundaryof the film is usedasa referenceandthe thicknessgradientsrevealedby the interferometricpatternsgivecompleteinformationaboutthe film profile, no otherdatabeing requiredexceptthe absolutefilm thicknessin onepoint. In orderto know the local film absolutethickness,the angleof incidenceof the light was variedto observethe correspondingvariationof the interferenceorderat a given point. The thicker the film, the larger the interferenceordervariationfor a given angleshift. Fig. 2 resumesthe situation.It sketchesthe Marangoniflows insidethe drop andthe velocity profile inducedin the air film. Besides,the figure illustratesthe variationof the light direction used to measurethefilm thickness. Other techniques are available to measurethe absolute thickness of a thin film: Newton'srings in white light give the approximatethicknessfrom classicaltableswith the color successions;sophisticatedheterodynetechniques14yield more precisemeasurements, but at the priceof morecomplexexperimentalsetups;ellipsometryis moreappropriatefor the nanometricrange15.All in all, for our purposes,the angleshift methodseemedto bethe best compromisebetweenprecisionandsimplicity. In the measurementsdiscussedhere,the angle of incidence was varied by linearly translatingthe laserheadover therange1,asshownin Fig. 1. Let A be the wavelengthof the incident light (a greenHeNe laserwas usedat 543.5 nm), nl
the refraction
and Am
the interference
thus given
respect
a
of glass,
order
no the refraction
variation
index
to be detected.
The
of air, d the unknown relation
between
Am
thickness, and d
is
by:
AmA=2dn
where
index
and/3
o
[J 1-
are, respectively,
to the normal
sin:a-
1-
the initial
of the film surface.
nl \ no/
sin2/3
and the final
(1)
angles
of incidence
of the light
with
The anglesa setup;
thus,
andfl and the refraction
the quantity
in square
indexes
brackets
are known
parameters
in eq. (1) is a known
constant,
the following: AmZ d = -2noA In order interferometer
of the experimental say A, resulting
in
(2)
to avoid
the risk
of incorrectly
has been
calibrated
using
estimating
the thickness
a film of known
thickness
to be measured,
and of the same
the
material
(air) as that of the film to be measured. The
calibration
Newton's
rings
fiat surface.
consisted
in measuring
due to a spherical
So, equation
the
interference
lens kept at a distance
(2) can be rewritten
order
of 30.0
for the calibration
head
Amo
distance
over the range
during
shift range
obtained from Am d = d o -Am 0 The
steady
technique
magnitude
better
monochromatic
and all the remaining
equations
above
than
that
used) can
the contrast
distribution
Besides,
precision
can be further
able to trace the light intensity possibility gradients,
to do, obtained
for do agreed optical
thickness.
allows
able to yield very
intensity
temperature
do :
the laser
with the expected
parameters
Thus,
by translating
were
one.
then left unchanged
the thickness
to be determined
is
(4)
the light
The
the reference
(2) and (3) yielding:
wavelength
light,
related
measured
of the unknown
being
#m (for the
variation
of Amo
illustrated
conditions,
to 100
order
1. The value
the measurement
readily
in
(3)
is the interference
The angle
obtained
_+0.1 btm from
d o = Am°Z 2noA where
variation
to control volume
one
precise
to take
measurements
with a spatial
be achievable
with
enhanced
without by means
in a well defined the relevant of the liquids,
the need
light.
pressure
Thanks
is enhanced
of image
analysis
of the
system
of the surrounding
of
in the range one to the
readout
techniques
0.1
order
of
use
of
and the analysis
for any complex
point of the interference
parameters
availability
approximately
white
figures
of the
of thickness
resolution
of the interference
is facilitated,
advantage
of
chain.
which
are
figure. under
study
medium,
- namely and degree
of liquid-to-liquid compression- without compromising their steadiness,allows one to monitor the evolution of the lubricating film featuresdue to changesin the value of such parameters.The presentpaperreportsthe changesin the film shapeproducedby increasing the compressionof a drop againsta flat surfaceof glass. Fig. 3 representsthe resultof theinterferometricanalysisasobtainedfor threedifferent deformationsof a dropof 5 cSt siliconeoil on theflat referencesurfacementionedabove.In the three casesthe volume of the liquid is kept unchangedwhile the position of the rod sustainingthe drop is varied. The diameterof the rod is 5.0 ram; a constanttemperature differenceof 35 °C is imposedbetweenthe rod andthe glassto establisha thermalMarangoni convectionin the dropsufficientto ensurestablenon-wetting(therod is kept at a temperature of 54 °C while the temperatureof the glasssurfaceis 19°C). The first thing to noteis that the channel is not parallel and flat: rather, a dimple is presentwith an almost perfect axis symmetry,reflectingthe axissymmetrybothof the dropandthe convectivecirculationwhich drivesthe lubricatingair into the gap.This fact extendsto the stablenon-coalescence casethe observationsby Allan, CharlesandMasons9, 10performedfor the transientsituations.One can observethat. as the drop is pressedagainstthe glassandthe contactareaincreases,the dimple deepensandthe exit constrictionreduces.Suchdeformationsarenecessaryto balance the increasedload.The dropdeformationasa functionof compressionis shownin Fig. 4. A numericalcodehas beendevelopedto supportthe interpretationof interferometric patternsdueto thin films of whateverrefractionindexandshape.Fig. 5 andFig. 6 havebeen obtained with this code, using the film profile of Fig. 4, caseb as input, to give a more immediateperceptionof a typical interferenceordervariationfound in the experiments.From the figures it is understoodhow the angleshift methoddescribedabovecan be usedfor the phaseunwrappingof the interferencepatterns.Providedthat the anglevariationis performed quickly enough,the methodcan alsobe usedin non-stationarysituations,wherechangesin film shapesareslow with respectto thechangesin thelight direction. In passing,it is importantto notethat the stablenon-wettingstate,in the presenceof gravity, wasobservedonly whenthedirectionof the thermalgradientandthe relativeposition
of the dropandthe solid surfacewassetin a well definedway: namely,it is necessarythatthe drop be warmer than the glassand stay above the glass.These observationsconstitute a further confirmation of the dragging action exertedby the moving liquid surfaceson the surroundingair. In fact, surfacetensiongradientshaveto drivethe surfaceflows (andthusair flows) into the gapratherthan outside.Moreover,sinceon ground,in siliconeoil, buoyancy convection prevails over thermocapillaryconvection,the drop has to stay above the glass becauseotherwise,evenwith the dropwarmerthanthe solid surface,onewould havea flow rising alongthe dropaxis andgoingdown alongthedropsurface,thusdraggingair out of the gap. So far, the drop pressedagainstthe flat glasssurfacehas been referred to as 'nonwetting'. However,it is necessaryto reportthatit is very difficult to achievethis stateunless the drop is kept in close proximity of the glasssurfacefor a while, before being pressed againstit. In otherwords,if a cleananddry glasssurfaceis used,then wettingalmostalways occursquickly. Onthe otherhand,if the hot dropis placedvery nearto the cold surfacefor a minuteor so,a thin liquid layer is seento slowly form on the surfaceitself, likely constituted by the liquid evaporatedfrom the drop and subsequentlycondensedon the solid surface. Interferometryhasshownthatevencleaningthe glasswith a dry absorbingpapermay not be sufficient to completely remove the thin oily layer which is clearly visible from the interferencefringesit generates.If the drop_sleft in this positionfor enoughtime, then it is evenpossibleto seedropletsof oil migratingon the glasssurfaceradially, moving awayfrom the suspendeddropvertex.Suchmigrationis likely dueto surfacetensiongradientsandto the air flows which arepresentin the gapseparatingthe dropfrom the glass.In somecases,one of thesesmall dropletswhich condensedon the glasswasalsoobservedto remaintrappedin the dimple formed after the suspendeddrop had beenpressedagainstthe glass.For these reasonsone should be prudentwhen referring to 'non-wetting'droplets.However, we will continue to use this term becauseit is most expressiveto refer to such particular selflubricatedsystems.
B. Measurement
of the air film oscillations
As shown unsteady shows
below,
condition.
liquid
achieved.
dealing
gradient
near-field
fringes. at a time,
point.
In these
information. curvature
good
with
In fact,
over
since
the angle
situations
far-field
bath is contained splitter
the interference camera
its axis, system.
Thus
of the film,
fringe
in the sketch figure
of the setup
to determine
the of
portion
of the interference
pattern
is
on the surface
changes
from
point
to
light may help
in giving
other
types
of
pattern
the contrast
one can
of the boundary
are the only way
used to obtain
cell to allow the laser
a screen.
to monitor
get the
interfaces
the thickness
of the figure
may not be as
the laser beam
The
fringes.
The liquid
light to be transmitted
toward
images
far-field
the contact
of the fringes
of the
to the film. The
interfaces
and transmits
are recorded
by a CCD
setup. is fixed;
the drop
in time.
by means
If the shape
even though
that can be
patterns.
deflects
toward
fringes
of the
of the film itself
of the interference
of triangulation.
far-field
in a transparent
bath container and
bv means
Fig. 7
a bath
deformations
difficult
as an
curved.
oil and
and change
and
extention
of light
in reflected
is strongly
interface
it is very
only a small
the deformation
a sketch
as in the previous The
fringes
in time,
Fig. 8 represents
interfaces,
of incidence
from
film
may lose its axis symmetry
cases,
both as a steady
a drop of silicone
of the possible
film for the whole
in such
large portions
between
deformed
of the interstitial
as for the near-field
beam
highly
of the interfaces
variation
the thin lubricating
evidence
the film shape
changes
can be achieved
non-coalescence
For example,
of the thin film
systems,
a striking
In addition,
thickness
visible
of stable
and offers
When
non-coalescence
In drop-bath
a situation
same
stable
volume
the film shape
the rod where can
be varied
can be monitored
the drop is suspended by means
can be displaced
of an injection/suction
as a function
of the drop
position,
along
pneumatic volume,
and
temperature. The kept
disk sustaining
at a temperature
the drop
of about
in Fig. 7 has a diameter
35 °C and at a constant
of 5.0 mm and the drop volume
while
the bath
is initially
is at ambient
temperature.Subsequently,thetemperatureis raisedto 70 The unusual exerted
size of the drop shown
by the bath
non-coalescing lubricating
state
volume
certain
threshold.
absolute
parameters
of the involved
of the lubricating
set. Fig.
10 shows
between
a bath and a large
A dedicated both the lateral
surface
gas
observed
films
has
drops
provided
rise
performed
of the same
might
in the
nature
as those
as liquid
threshold of
of the system,
suitable
the
to reach
it will be shown
oscillation
a
the viscosity
that
conditions
are
in a lubricating
film
the oscillations
which
affect
the non coalescing
bodies
when
that one needs
to address
In facts,
it seems
another
arise
be regarded
that
to measure
The question
to instabilities,
drops
for
was 10.0 mm.
in the drop or in the film.
give
instabilities such
been
This
The conditions
Rather,
of a periodic
diameter
is overcome.
in non-coalescing
convection
framework.
due to the
can be reached,
factor
ambient).
of the drop and the air film between
arises
may
in succession
pattern
the disk diameter,
bath,
in the present
drop whose
threshold
instability
(drop,
of Fig. 7a the
overcome.
the bath, the scale
film can be periodic,
moments
experiment
the unsteadiness
respect,
four
from
push
with the bath overcomes
was largely
the drop volume,
temperatures
conditions
interference
difference
is increased.
to the hydrostatic
in Fig. 9. Unsteadiness
threshold
the disk distance
In the
of the far-field
if the temperature
including
thanks
of the drop.
is represented
will not be analyzed
the oscillations
wide
A view
In Fig. 7d the unsteadiness
the unsteadiness
observed
steady.
of the drop,
and the bath,
values
the weight
conditions
and shape
on several
both the drop
in Fig. 7d can be achieved
balances
is still
film in steady
a given
depends
which
°C and also its volume
drops
while
possibility
encountered
bridges
the
as a result
in liquid
whose
reasonable
is that
themselves,
is whether
bottom
bridges
the that
oscillations of capillary 16, 17. In this
lays on the colder
bath
surface. The difference oscillations been
used.
transmitted
behavior
of the drop oscillations
between
the
in various
disk
experimental
The technique through
sustaining
consists
the drop,
has been observed the
conditions, of exploiting
projects
drop
and
again,
the
as a function bath.
In order
a non-invasive
a properly
focused
a light spot on a screen.
The
of the temperature to monitor
optical laser light
beam
technique which,
spot position
such has being on the
screenis very sensitive to any liquid surfacedeformation.The image acquired
by
a frame
automatically in Fig.
grabber
calculated
related
threshold
frequency
Such and,
analysis
of liquid
oscillation
indicating
the coupling
reality
the instability linear
stability The
glass
different
pattern
arises
III. DISCUSSION
toward
is similar
setup
is
is then is sketched above
12 together
the
with the
the disk sustaining
the high frequencies amplitude
to that found
of the main reasonable
peak
the
as the
also increases.
in liquid
bridges
is of the same
to suppose
transmitted
air film
has
to be analysed,
by these
measurements,
seem
a floating
zone
This subject
also
recorded
image
in the film.
theory
even
Here
the oscillation
it seems
dynamics
experiments from
moves
value
of the two oscillations
these
observations
system,
peak
is subsequentely
of the
are yielded
though
nothing
centroid
conditions
in Fig.
spot
that
18
order
of
the observed
to the air film
through
the
at the surface.
of the optical
spectra
then
and
frequency
frequency
Even
are shown
Simultaneously,
bridges,
velocity
of the interference complexity
spot
temperature
of a FFI' algorithm.
to the AT variations
in the drop
of the liquid
The
by means
that also the frequency
starts
oscillations
larger
with respect
as that
unsteadiness
obtained
of the
The experimental
different
25 °C, in this event),
is increased.
if one considers
magnitude
40 seconds.
that the main frequency
difference
a behavior
for about
position
light
of 5.0 mm.
It can be noted temperature
The
in this way for three
(about
spectra,
drop has a diameter
digitised.
and tracked
I 1; the data collected
unsteadiness
and
of the
been
with
desumed
the setup
with respect
directly, of Fig.6.
from Due
to the light spot,
but with identical
main
an
to the broader
peak
values
(see Fig. 12c). to indicate instability, should
that
the unsteadiness
the present
be further
observed
data cannot
investigated,
exclude
e.g., by means
is in that of
19, 20 made
indicate
if the amplitude
OF THE
that the same type of instability
of the oscillations
EXPERIMENTAL
1!
was much
RESULTS
occurs
also in the drop-
less in this case.
In the found
following
some
experimentally
coalescence
and
and to show non-wetting.
surface
by a silicone
to such
configuration,
where
an analogous
(where
small
description
and
than in common
bearings),
relations
starting
3 and
with mass
numbers
can be obtained from
the
apply
film
of the air film gives on the
non-wetting given
profiles
rise to nonof a glass herein
also to non-coalescence
phenomenon
the lubrication
Reynolds
dimpled
refer
of liquids,
as well.
of the
coupled
action
the
data on the film profiles
considerations
film is formed
but in practice
to discuss
will be based
as the experimental
equations,
loads
presented
discussion
but similar
the
balance
at the interfaces,
oil drop,
are
how the lubrication
The
dimpled
In principle, momentum
arguments
well
should
conservation
equations
be based
the
and with boundary
to be used
are involved
and where
with some
simplifications,
known
on
conditions
in this specific friction
problem
is by far smaller
neglecting
Navier-Stokes
energy-
equation
of
the energy momentum
conservation:
(5)
where
p
is the density,
respectively,
v is the fluid velocity,
p is the absolute
pressure
Let a case be considered This
corresponds
film
can be safely
to a situation assumed
and of the glass are much air film is considered the present (some
dynes)
where
situation
the body forces.
the air film is steady
(like in Figs.
where
also
these
the air flows because
assumptions
(the hindrance
Considering
problem
the thermal
and the viscosity can be made,
no heat is produced
can be neglected
within
than that of air. As in many
incompressible,
and practically
the
and F represents
to be adiabatic, larger
_t and [a* are the shear
of coalescence
in cylindrical
cases
_t uniform
the film;
has been produced
coordinates
and
3 and 4, for example).
the film
are steady.
conductivities
throughout loads
in addition,
the
air
films,
the
the channel.
In
are quite the body
in microgravity
expressing
The
of the liquid
of gas lubricating
since the involved
inside
and the bulk viscosity
small forces
as welll).
air velocity
v as
v = ui r +
vi o + wi:,
surviving
components
imposing
the
axis
symmetry
(0u
-)Oz )
(m. _
Ow p( .--+ Or
Ow)) w--_Z
Op (OZw 1r Ow =_--+.l-yT+---+ Oz Or
velocity
0.__ ---+_ 0p Or
film radius
Ou
small,
is two orders
dp
Or
one
can
( O:zt
axial
02w) OZ2)
observing
that
with the radial
component
the
axial
component
one (to complete
larger
its path
the
and the
than the film thickness).
to:
u
l au
8:u) +_"S-g-
Or
as a consequence
r2
of the approximation
the film does not depend At this
following
stage,
further
just
made,
one
gets
that
the
pressure
on z •
order
of magnitude
considerations
can
be made
operating
the
are introduced,
VM
normalizations:
-
being
across
air
(7)
Thus,
the
two
of the
the film radius
Oz
and
the
(6)
UP= 0
within
write
component
to go all the way forth and back along
of magnitude
:-- Or +"t-;Y. -'+r
--
compared
eqs. (6) reduce
radial
10. r.z+ 02.] OZ2 )
+ r Or
can be made
mass of air needs
Therefore
'"
simplification
is, in average,
film, a certain
problem,
of eq. (5) as:
p u--+w Or
A further
of the
aspect
ratio
the reference
pH
A = H/R liquid
.
UVjl '
surface
u ff ----; VM
and the
r F = --; R
Reynolds
velocity,
number
R the channel
z = -- -" H
Re = pVMH/_ radius,
and H the reference
height. Now,
the first of eqs. (7) can be rewritten
1"2
in a non-dimensional
form:
channel
3_ A_---= 3_
A oVfip A E { 3 2"ff 13"ff + ? o_? Re c_? + -_e (-_
In order typical
to assess
values
g/cm3;/_
the relative
of the
10 z_. ) A2 0z 2 )
importance
experiments
= 1.81.10 -3 poise;
_ _.2_
of the various
described
in the
VM = 0.5 cm/sec;
H=
= 2.10 -2 and Re = 3.3-10 -4 = A2. So, neglecting equation
(8) to its original
O_p
dimensional
form
(8)
terms
in the equation
text are assigned,
namely:
10 -3 cm; R = 5.10-2 era. With all the terms
of order
above,
p = 1.2.10 -3 these
values
A
> A 0, and transposing
one can write:
_2b/
"_F = /../-09Z2
(9)
Integrating
eq. (9) twice
the velocity
u, as anticipated
u = az 2 +bz
+c
The
the film
coefficients
interfaces,
= 0, which
most
situations,
in the expression
states
present
circumstances,
With
which
that
where
as the no-slip
molecules
yields
a parabolic
Poiseuille
profile
the liquid
the net flux
the lubricant
is equal
the constraints
along
is concerned,
as the Knudsen problem
surface
velocity
are
(Kn
number = k/H,
determined
imposing
above,
lzt
is not constant
channel
a velocity
results _, being
vanishes,
inversion
it can be observed
to ,_ 6.3.10 -2 lam at normal introduced
(which
the lubrication
does not undergo
assumption
the
of the velocity
They are: u(z = 0) = 0 and u(z = h(r)) = Ub (r), assuming
Ub (r) being
As far
characterize
the film profile
for
in Fig. 2:
of the problem.
z)dz
across
(10)
three
constraints
which
the
that
across
no-slip
ambient
eq. (10) assumes
mean
free
contrary
conditions). its explicit
form:
to
the channel.
it is verified
molecular
at
in r); fu(r,
to be < 10 -2, with the typical the
the
path
in the values of air
u=u(r,z)=3Uh(r---_)-2 h2(r)
and, together
2U_(r). h(r) _
"_-
with eq. (9), makes
(11)
it possible
to derive
the following
expression:
__ 3p = 6k t Uh(r) c_r hZ(r)
which
needs
to be integrated
h(r) has described data
(12)
been
with
measured
good
the pressure
in some
approximation
are not available
nevertheless,
to obtain
cases
it can be noted
order,
value
that it must
within
and, as reported
by a fourth
yet (its maximum
profile
has
the lubricating
in the previous
polynomial been
pages,
function;
measured
be a monotonic
air film.
funtion
it can be
for Ub(r)
to be around of r, which
precise
0.5 cm/s),
vanishes
at the
origin. As a result overpressure, film
generated
center.
This
displacement. deepening against
of eq. (12), after integration, inside
overpressure,
This,
surface,
over
a larger
It is understood deformations, with
considering liquid
surface,
the pressure, produces
that the deformation which
the dimple
even
is undergoing
a local
at the surface
Also
the
counterintuitive
when
the drop is squeezed against
the rigid,
with consequent
that its value
flat
widening
does not increase,
deformation.
to calculate
the pressure
simultaneously.
convection
flattening
if one assumes
a deeper
amplitude
forms.
in r, the
be maximum
produces
occurring
an elastic
h be constant
would
deformable,
work with the stress-balance
equations
flow,
As the drop is pressed
it undergoes
that, in order
one should
fluid-dynamic
explanation.
of wetting,
surface,
is how
readily
by the measurements,
has a qualitative
in the absence
out that, should
by the incoming
the liquid
terms,
revealed
of the film area. Therefore acting
being
in simple
of the dimple the glass,
the channel
one finds
equations That
depends
curve
at the air/liquid
would
on the local
due to temperature
accounting
be
a rather
for the surface interface
and
difficult
task,
dynamical
situation
at the
- and, thus,
surface
tension
- gradients.Fortunately,the film shapeis
an experimental
deal with the equation
the lubrication
The where
steady
conditions
the Laplace's
pressure
of momentum
exerted
of the present
force
generated
due
force
acting
wetting
tends
the
surface
(or coalescence,
to further
that the lubrication
on the involved
to lubrication,
example
interfaces. attractive
according
deformation
deform
the channel.
supplies
of such
not contrasted,
to the relevant
to just
equilibrium
opposes
a disjoining
In the absence
forces,
one
of dynamical
surface
force
this allows
channel.
are conditions
by the liquid
by the air, which
One can thus conclude total
inside
data, and
the dynamical
contribution
disjoining
would
to the
contribution
lead
the
system
to
case).
IV. CONCLUSIONS The wetting
present
work
shows
can be explained
in terms
10 in the past for temporary and non-wetting
systems.
here
separated
are actually
but it is thicker
is known pressure such
that even curves
pressure
numerical results
can
detected
method patterns.
and
bodies
The
need
small
variations
which
be obtained,
of the system
assume
accounting
for
of laser interferometry
fringes
have been
illustrated
experimental
actual
under
configuration.
technique
with the aid of numerical data,
yielded
by
|
f
such
Now,
of
which
it
in the
to calculate
more
which
of
precise has
been
conditions.
thickness is based
measurements,
shape
made 2 by means
channel,
simulations
9,
differences
film.
experimental
authors
is not flat
from
An attempt
recently
of the
the absolute The
a load.
of
investigated
this film
important
interstitial
shape
different
used to measure
of a liquid/solid
has been
the
and flat
and
and
non-coalescing
of lubrication,
may yield
has been
by other
the characteristic
theory
liquids
a parallel
medium
to sustain
found
the systems
with precision
in the film profile
of coalescence
to stable
non-coalescence,
to measure
non-coalescing
results
can be generalised
in the light of elasto-hydrodynamic
calculations
The
and that some
by a thin film of the surrounding
between
film
of the hindrance
as in temporary
and thus in the ability
by means
interstitial
Namely,
curves
Near-field
of lubrication
non-coalescing
at its center.
this film is understood
that the phenomena
and the shape upon
an angle
of the shift
of the interferometric supply
the
boundary
conditions
to solve
balance
equations,
the
provided
Measurements liquid/liquid systems
may
undergo
has been
instability unsteadiness
A possibility
fringes
behavior
the
threshold.
rupture.
in the lubricating to clarify
this point
the
at the liquid
interface surface
deflection
unsteadiness
on
such
as,
e. g.,
can be periodic
behavior
cannot
exclude
and is subsequently
is to use, for example,
is known.
technique
that the observed to the drop
of the linear
theory
instability.
ACKNOWLEDGEMENTS Part funded
by the
subgrant Grant
of the present
with
Italian
Space
the Georgia
n. NAG3-1894).
for their
work
illuminating
has Agency
been
performed
(ASI);
another
Institute
of Technology
The authors
wish to thank
suggestions
in the framework
contributed
part (GIT
7
been
Subgrant
Dr. D. Castagnolo
to section
1,,,
has
of a research supported
project
by a NASA
n. E-25-L43-G1, and Dr. Carlo
III of this paper.
in
convection
transmitted
the tools
and
of the systems
as that of the thermocapillary data
stress-
that such self-lubricated
of parameters
The oscillatory
the present
film itself
values The
to be of the same nature Nevertheless,
Ub(r)
from
data evidencing
when
a certain
them
and by a beam
quantitative
to the interface
zones.
arises
both with far-field
overcome
suspected
uncoupling distribution
have yielded
lead
in floating
equations,
that the velocity
unsteady
or volume,
not necessarily
question
bulk.
made
configurations
temperature does
lubrication
NASA Albanese
of
FOOTNOTES
AND REFERENCES
a)Electronic
mail:
[email protected]
b)Electronic
mail:
[email protected]
C)Electronic
mail:
[email protected]
1p. Dell'Aversana, temperature
gradients,"
2R. Monti with
and
Xian,
of non-coalescing
of Third
John Wiley
and H. E. H. Meijer, The
Pacific
by shear
and
liquid
China-Japan
drops
and correlation
Workshop
on Microgravity
& Sons,
(1962).
"The influence
Conference
of surfactants
on rheology
on coalescence
and polymer
processing
in (PCR
(1994). Basic
Lubrication
Science,
Wiley
& Sons (1976).
John
6A. W. Crook,
Theory,
"Elasto-hydrodynamic
7G. R. Higginson,
"A model
2nd Edition,
lubrication
experiment
Ellis
of rollers,"
Horwood
Nature
in elasto-hydrodynamic
Series
190,
in Engineering
1182 (1961).
lubrication,"
Int. J. Mech.
(1962).
8j. F. Archard J. Mech.
of coalescence
2 - 5 (1996).
5A. Cameron,
Sci. 4,205
"Suppression
(1996).
model
Proceedings
Gas Film Lubrication,
dispersions,"
Kyoto,
8, 15-28,
"Numerical
October
A. K. Chesters
liquid-liquid
and J. Koplik:
Fluids
results," China
3W. A. Gross, 4S. Abid,
Phys.
R. Savino,
experimental
Science,
'94),
J. R. Banavar
Engng.
9G. E. Charles interfaces,"
melting,"
and
S. G. Mason,
"The
for a range
and
of lubricants
under
severe
stress,"
Sci. 16, 150-165
Mass Transfer
12R. Monti
and P. Dell'Aversana,
Micrograv.
Q. 4, 2, 123-131
of liquid
drops
with
flat
liquid/liquid
(1960).
S. G. Mason,
and Ch. E. Chang,
Int. J. Heat
coalescence
Sci. 15,236-267
G. E. Charles
J. of Colloid
11W. R. Wilcox
"Film thicknesses
Sci. 6, 101 (1964).
J. of Colloid
10R. S. Allan, interface,"
and M. T. Kirk
"The approach
of gas bubbles
to a gas/liquid
(1961).
"Analysis 19,355
of surface
tension
driven flows
in floating
zones
(1976).
"Microgravity
(1994).
lo
experimentation
in non-coalescing
systems,"
13p. Dell'Aversana,
R. Monti
in microgravity," 14L. Zeng,
Adv.
and Shape
Triangulation," SPIE
Proc.
2861,
203-210
15A. Rothen, and Drude
256,
SPIE's
liquid
18R.
D.
phenomena
by Combining
for
Measuring
Interferometry Denver,
the
and Laser
8-9 August
1996,
of optical
of the present
ellipsometer,"
and thin films,
in Selected
and A. Sharmann,
papers
means,
Nat. Bureau
from
Proc.
Rayleigh
of Symp.
of Standards,
on Ellipsometry,
MS
on
Miscell.
28, Books
in
"Steady
and oscillatory
J. Fluid
Mech.
surface," instabilities
Marangoni
convection
in
126,545
in cylindrical
(1983).
thermocapillary
liquid
bridges,"
(1993).
Schwabe,
in cylindrical K.-T.
of thin films
(1991).
"Hydrodynamic
247,247
thermocapillary A 5, 108-114
of surfaces
Reprinted
Series
19G. P. Neitzel,
method
of the thickness
with free cylindrical
Velten,
Method
VIII: Applications,
and the development
D. Schwabe
Mech.
convection
2°G.
Interferometry
Laser
and coalescence
(1996).
17H. C. Kuhlmann, J. Fluid
of
7 - 21 (1964).
columns
K. Kawachi,"New
Film Simultaneously
in the measurement
16F. Preisser,
and
flows
(1995).
of a Thin
"Measurement
Milestones
"Marangoni
Res. 16, 7, 95-98
H. Matsumoto
to Langmuir,
ellipsometry Pub.
in Space
T. Ohnuki,
Thickness
and F. S. Gaeta,
A.
liquid Chang,
convection
Sharmann, bridges"
Phys.
"The Fluids
D. F. Jankowski
in a model
periodic
and
of the float-zone,
instability
A 3,267-279
(1991).
H. D. Mittelmann, crystal
of thermocapillary
growth
"Linear process,"
stability Phys.
of
Fluids
(1993).
P. Neitzel,
M. K. Smith
of energy,"
Int. J. Heat
and M. J. Bolander, Mass
Transfer
"Thermal
37, 2909-2915
instability (1994).
with radiation
by the
FIGURE CAPTIONS FIG. 1.Sketchof the experimentalsetupusedto revealthe shapeandmeasurethe thickness of the interstitial FIG. 2. When drop.
The
film between
a silicone
the drop is hotter
surface
flow
oil drop and a reference
than the solid surface
is directed
toward
the colder
surface
a Marangoni
of glass.
convection
part and it drags
develops
in the
an air film (not to scale
in the drawing). In order
to measure
to [3 to observe
the air film thickness,
the corresponding
the incident
interference
order
light direction
variation,
which
is changed
from
is proportional
ct
to the
local film thickness. FIG.
3. Drop
of 5 cSt silicone
been
pressed
by
appear;
in row
represent
100 _m
oil pressed
with
2 the displacement
respect
against
a flat glass
to the position
surface.
where
is 200 _tm; and in row
In row
the first
3 it is 300
1 the drop
interference
_tm. The
has
fringes
three
columns
respectively:
a) the drop on the reference b) the near-field c) a 3-D
fringes
view
of the
surface;
due to the thin air film between lubricating
film
shapes
the glass
as reconstructed
and the drop; from
the interference
patterns. FIG.
4. Comparison
drop
against
of the film profiles
the glass surface
as shown
obtained
for the three
different
compressions
of the
in Fig 4.
a) 100 _tm displacement b) 200 _m displacement c) 300 _m displacement FIG.
5. The
interstitial flame
near-field film
sequence
variation,
profile
interference
obtained
of Fig. 4b for different
it is possible
for a given
fringes
angle
to discriminate shift, is larger
incidence
minima where
from
a numerical angles
and maxima
the film is thicker.
simulation
of illumination. since
using
the
From
the
the interference
order
FIG. 6. Plot of the light intensity versusthe illumination direction in correspondenceof the maximum(central point) and minimum (externalpoint) thicknessof the interstitial film as obtainedfrom the simulation.Similar plotscanbeobtainedfrom the experimentsand usedto determinethe interferenceordervariation. FIG. 7. Inhibition of coalescencebetweensiliconeoil dropsof increasingvolumesanda bath of the sameliquid. Here, the disk sustainingthe drop hasa diameterof 5.0 mm, but larger sizesare possible,also in the presenceof gravity. In frame d the disk hasa temperatureof 70 °C while the bathis at ambienttemperature. FIG. 8. Sketch of the experimental setup used to monitor the time-dependenceof the interstitialfilm shapein unsteadyconditionsfor a drop/bathself-lubricatedsystem. FIG. 9. The far-field fringes producedby the interstitial film of a drop/bathsystemas they appearin steadyconditions.The dropdiameterin this caseis 10.0mm. FIG. 10. Sequenceof far-field fringes producedby the samesystemas that of the previous figure, driven to unsteadiness. Note theapparentsaddlelike shapeof the lubricatingfilm. The numbersrepresentthetime in hh:mm:ss. FIG. 11. Setupusedto track the droplateral surfacedisplacements.The datacollectedwith this techniqueconstituteanindirect measurement of the air film oscillations. FIG. 12.Oscillation amplitudes(windowed)andrelatedfrequencyspectrafor threedifferent temperaturesof a 5 mm diameter drop: a) 47.3 °C; b) 51.8 °C; c) 56.0 °C. The temperature obtained
in all cases by a direct
is fixed
analysis
at about
20 °C. The
of the interference
21
pattern
broader rotation.
spectrum
shown
bath
in c) has been
Translation
stage
I
Liquid
volume
control
Monitor
Cooling
Reference
Filter Translation Lens
Mirror
Microscope
",
objective
2
Mirror
I
)
hnage
analysis
Fig. 1
Laser
stage
2
\ no
(airfilm)
n I (glassplate) Radial
velocity
profiles
Fig.
2
_m 20-1/
16-
128 ,4
Oz -800
la)
lb)
2a)
2b)
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lc)
i_/'/_,,_-
,
_
o pm
-1---'---4
-
....
3c)
3b)
Fig. 3
_oo
_--_____[_
_
-
u
3a)
4oo
_m
400
pm
'
l
--_---i
800
_l III
25
i 2O
.....................................
15
...........
j
t
..........................
,
i
i
:
:
i
L ............ I
t ,
............
J ............. I
:
i
L ............
_ ............
J .............
'.......................... ,
i
: :.............
L
...........
e
10
..........
0 -800
.......
a .............
I
-600
,_--
-
i
-400
i
-200
0
Fig. 4
.......
i ..............
_ .........
I
I
I
200
400
600
800 _m
Om
1.0 0.9 0.8 .
0.7 0.6
__2
0.5
._'
0.4 0.3
-=
0.2 0.1 0.0
_--_--
5
6
-----{D---_-
Central
---o--
External
7
I
I
I
I
I
I
8
9
10
11
12
13 Incidence
Point Point
Fig.
6
14 angle
I
I
15
16
(degrees)
a)
b)
c)
d)
Fig. 7
Heated
drop
_
Bath
I
Beam
Laser
splitter
\
....
Video
• ''"
camera
""
""
"" ""
""
"" "':c
""'
_
Translucid
Fig.
8
screen
0_
a)
b)
c)
d)
Fig. 10
Frame
Data
grabber
Light
spot
/ /
analysis
Oscillating
/
tll Bath Optics
Translucid
screen
drop
Cell with optical
Fig.
11
walls
I
--
Laser
a)
--
20 Time
25 (sec)
30
35
40
45
-
L
_
_
L
L
1
2
3 Frequency
4 (Hz)
5
6
1
2
3 Frequency
4 (Hz)
5
6
4
5
6
0
i
i
b) 4:
i
0
5
10
15
½0 Time
25
30
35
40
45
(sec)
m
i
c)
E
tI it I
L_
'i !, iI
/ I
0
5
10
15
20
25
30
35
40
45
0
Time (sec)
'
1
I
2
3 Frequency
Fig.
12
(Hz)
7
