Non-Coalescence Effects in Microgravity - NTRS - NASA

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Jun 17, 1996 - Fluids Branch, Mail Stop 500/102. NASA Lewis Research. Center .... When liquids stay dry. Invited paper in preparation for publication ..... rings due to a spherical ... of 30.0 _+0.1 btm from the reference ... and flat: rather, a dimple is presentwith an almost perfect axis ..... 1.81.10 -3 poise; VM = 0.5 cm/sec;.

NASA-Ci_-2044_2

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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,

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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)

-4oo

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