Mea

sure

men

ts o

f Sur

fact

ant

Sque

eze-

out U

sing

Mag

netic

ally

-Le

vita

ted

Liqu

id B

ridge

s

Cha

rles

Ros

enbl

att

Dep

artm

ent o

f Phy

sics

Cas

e W

este

rn R

eser

ve U

nive

rsity

Wor

k pu

blis

hed

in C

ollo

ids a

nd S

urfa

ces A

218

, 65

(200

3)

https://ntrs.nasa.gov/search.jsp?R=20060014068 2018-06-25T21:30:14+00:00Z

Liqu

id B

ridge

s•

Liqu

id b

ridge

s: C

olum

ns o

f liq

uid

supp

orte

d by

two

solid

surf

aces

—Th

ese

are

gene

rally

opp

osin

g rig

ht c

ircul

ar

cylin

ders

in 0

g.

•Fo

r a c

ylin

dric

albr

idge

of l

engt

h L

and

diam

eter

d, i

n ze

ro g

, the

max

imum

sl

ende

rnes

s rat

io Λ

[L/d

] = π

[R

ayle

igh]

•In

the

pres

ence

of g

ravi

ty th

e cy

lindr

ical

sh

ape

of a

nax

isym

met

ricbr

idge

tend

s to

defo

rm (s

ee o

ur w

ork

J. C

oll.

Int.

Sci.

213,

592

(199

9))

Prin

cipl

es o

f mag

netic

levi

tatio

n(s

ee o

ur w

ork

inPh

ys. F

luid

s 10,

220

8 (1

998)

)

•Fl

uid

has a

vol

umet

ric m

agne

tic su

scep

tibili

ty χ

. O

n ap

plyi

ng fi

eld

H:

•En

ergy

per

uni

t vol

ume

is U

= -½

χH2

•Fo

rce

per

unit

volu

me

is F

= -∇

U =

½χ∇

H2

= χΗ

∇H

. T

his f

orce

can

be

orie

nted

to

coun

tera

ct g

ravi

ty.

•D

isso

lve

para

mag

netic

man

gane

se c

hlor

ide

tetra

hydr

ate

in w

ater

or g

lyce

rol t

o cr

eate

hig

hly

para

mag

netic

flui

d th

at c

an b

e co

ntro

lled

with

a

re

lativ

ely

smal

l fie

ld.

Thus

the

effe

ctiv

e bo

dy fo

rce

on th

e co

lum

n m

ay b

e co

ntro

lled

by v

aryi

ng th

e cu

rren

t in

the

mag

net—

as

a fu

nctio

n of

tim

e!

App

arat

usTo

p vi

ew

End

view

-3-2-1012

3 x

107

|Hx ∂zHx| (G2 cm

-1)

0.5

0.0

-0.5

-1.0

-1.5

-2.00.

5

0.6

0.7

0.8

0.9

1.0

1.1

1.2

x 10

4

Hx (G)

z (

cm)

H a

nd H

∇H

pro

files

“Far

aday

pol

e pi

eces

” cr

eate

un

iform

forc

e

Reg

ion

of q

uasi

-uni

form

fo

rce

We

have

look

ed a

t sta

bilit

y is

sues

0.0

0.1

0.2

0.3

0.4

1.6

1.8

2.0

2.2

2.4

2.6

2.8

3.0

3.2

Axi

al

Late

ral

Slenderness Ratio Λ

Bon

d N

umbe

r1.

41.

61.

82.

02.

22.

42.

62.

83.

03.

20.

4

0.6

0.8

1.0

1.2

1.4

B =

0.3

55B

= 0.

205

B =

0.0

15

Reduced Volume Vr

Sle

nder

ness

Rat

io Λ

Stab

ility

of c

ylin

dric

al b

ridge

s (V

r=1)

vs.

Bon

d nu

mbe

rSt

abili

ty c

urve

s as f

unct

ion

of V

rat

fixe

d B

ond

num

ber(

s)

Bon

d nu

mbe

r: (

)σ∇χ

−ρ

≡4

dH

21g

B2

2

Rat

io o

f gra

vita

tiona

l for

ce

to su

rfac

e fo

rces

Stab

le b

elow

the

line,

uns

tabl

e ab

ove

the

line)

(Hor

izon

tal b

ridge

)

(Ver

tical

brid

ge)

Gly

cero

l+ m

anga

nese

chl

orid

e te

trahy

drat

e

We

have

look

ed a

t col

laps

e dy

nam

ics

Sequ

ence

of i

mag

es o

f a g

lyce

rol b

ridge

afte

r the

upw

ard

mag

netic

forc

e is

redu

ced

sudd

enly

. B

ridge

col

laps

es o

ver t

ime

due

to g

ravi

ty.

t cor

resp

onds

to ti

me,

in se

cond

s

Mov

ie m

ay b

e vi

ewed

at

http

://liq

-xta

l.cas

e.ed

u/V

ideo

s.htm

We

have

look

ed a

t res

onan

ce b

ehav

ior

Firs

t, se

t tim

eav

erag

edB

ond

num

ber

Bo ef

fby

app

lyin

g ap

prop

riate

d.c

. cu

rren

tio,

and

ther

efor

e Η

∇Η

……

.

Then

, mod

ulat

e m

agne

t cur

rent

. Fo

rce

∝(i o

+δi

sin

ωt)2 ,

and

δBef

f∝

2io

δix

sin

ωt

+ O

(δi2 )

sin2

2ωt

Var

y th

e to

tal b

ody

forc

e si

nuso

idal

ly a

t fre

quen

cy ω

and

exam

ine

the

resp

onse

.

Mov

ie m

ay b

e vi

ewed

at

http

://liq

-xta

l.cas

e.ed

u/V

ideo

s.htm

Mot

ivat

ion:

Inv

estig

ate

“res

pira

tory

dis

tress

sy

ndro

me”

in n

eona

tes.

•D

urin

g re

spira

tion

alve

oli t

o gr

ow a

nd sh

rink

perio

dica

lly•

This

requ

ires d

ynam

icva

riatio

n of

surf

ace

tens

ion

to b

alan

ce

•Pr

emat

ure

infa

nts h

ave

not m

anuf

actu

red

suff

icie

nt su

rfac

tant

(e.g

.,ph

osph

atid

ylch

olin

e).

Thus

thei

r pul

mon

ary

fluid

can

not r

espo

nd

prop

erly

dur

ing

brea

thin

g.

Dyn

amic

surf

ace

tens

ion

RP

σ2=

∆

The

chan

ge o

f sur

face

tens

ion

with

tim

e as

surf

acta

nt m

olec

ules

mov

e be

twee

n th

e su

rfac

e an

d bu

lk

As a

func

tion

of su

rfac

tant

co

ncen

tratio

n:

Rap

idly

redu

ce b

ridge

leng

th in

ze

ro g

ravi

ty

Exam

ine

the

elec

tric

al re

sist

ance

vs

. tim

eof

the

brid

ge w

hen

the

late

ral a

rea

of th

e br

idge

is

redu

ced

sudd

enly

. (I

n ze

ro

effe

ctiv

e gr

avity

the

only

re

leva

nt fo

rce

is su

rfac

e te

nsio

n)

Top

Vie

w

Side

Vie

w

Use

hor

izon

tal b

ridg

e to

det

erm

ine

“squ

eeze

-out

tim

e” o

f sur

fact

ant f

rom

surf

ace.

•M

ixtu

res o

f pa

ram

agne

tic li

quid

(MnC

l 2 . 4H

2O/W

ater

)

•A

dd D

odec

yl tr

imet

hyla

mm

oniu

m c

hlor

ide

(cat

ioni

c su

rfac

tant

)

0 ≤

X ≤

1.5

wt.

%.

•C

ritic

al M

icel

le C

once

ntra

tion

(CM

C) i

s det

erm

ined

from

su

rfac

e te

nsio

n m

easu

rem

ents

usi

ng c

apill

ary

rise

tech

niqu

e.

(Abo

ve C

MC

add

ition

al m

olec

ules

tend

to fo

rm m

icel

les r

athe

r th

an a

dsor

b at

the

surf

ace)

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

01020304050607080

CM

C

Surface Tension (dynes/cm)

Con

cent

ratio

n(w

t%)

•Fo

r eac

h co

ncen

tratio

n X

of s

urfa

ctan

t, br

idge

s of Λ

= 2.

5 ar

e cr

eate

d.

•A

rapi

d ch

ange

of l

engt

h (1

.3 m

m in

500

ms)

forc

es it

to

assu

me

a ne

w sh

ape. Fi

nal s

hape

as t

→ ∞

Mov

emen

t of s

uppo

rt ro

d

Inst

anta

neou

s sha

pe

Ther

e is

a tr

ansi

ent b

uckl

ing

of th

e su

rfac

e af

ter t

he b

ridge

is “

squi

shed

” in

or

der t

o ac

com

mod

ate

the

surf

acta

nt

that

has

not

yet

gon

e fr

om th

e su

rfac

e in

to th

e bu

lk.

As s

urfa

ctan

t is

sque

ezed

-out

into

bul

k, th

e su

rfac

e ar

ea

of th

e br

idge

is re

duce

d to

the

final

eq

uilib

rium

shap

e

Cre

nella

tions

are

due

to:

Indu

ced

capi

llary

wav

es d

urin

g “s

quis

hing

”A

ccom

mod

atio

n of

surf

acta

nt th

at c

anno

t be

sque

ezed

out

from

surf

ace

inst

anta

neou

sly

whe

n th

e br

idge

are

a is

redu

ced

durin

g “s

quis

hing

”

The

rela

xatio

n tim

e of

the

cren

ella

tions

for l

arge

X

is re

late

d to

the

sque

eze-

out t

ime

of th

e su

rfac

tant

, and

ther

efor

e to

the

resp

onse

tim

e of

the

(dyn

amic

) sur

face

tens

ion.

This

rela

xatio

n tim

e is

det

erm

ined

ex

peri

men

tally

by

the

rela

xatio

n of

ele

ctri

cal

resi

stan

ce a

cros

s the

bri

dge

R =

ρL/

A

zr

dz

r fin(

z)

δr(z

,t)

dzz

rR

finL zfin

fin∫ =

=0

2)

(π

ρ

[]dz

tz

rz

rR

finL zfin

inst

∫ =+

=0

2 ),

()

(δ

πρ

Fina

l res

ista

nce:

Inst

anta

neou

s res

ista

nce:

L fin

1. E

ven

orde

r ter

ms a

ll ha

ve p

ositi

ve c

oeff

icie

nts

2.Fr

om v

olum

e co

nser

vatio

n, lo

cal n

egat

ive

δr(z

) ter

ms

are

larg

er

than

loca

l pos

itive

δr(

z) t

erm

s

R ins

t> R

fin

We

can

see

that

Rin

st>

Rfin

:Ex

pand

Rin

stin

pow

ers o

f δr(

z,t),

from

whi

ch

dz

zr

tz

rz

rt

zr

zr

tz

rz

rt

zr

zr

zr

dzR

finfinfin

finL z

fin

L zfin

inst

finfin

+−

+

−

+

+

−

+=

∫∫

==

...)

()

,(

5)

()

,(

4

)(

),

(3

)(

),

(2

)(

)(

432

02

02

δδδ

δ

πρ

πρ

Res

ista

nce

vs. T

ime

05

106.

2

6.4

6.6

6.8

7.0

7.2

7.4

500

ms

trans

latio

n tim

e

Sha

pe re

laxa

tion:

Thi

s is

whe

re th

e ph

ysic

s is

!

Resistance (a.u.)

Tim

e (s

ec)

R =

ρL/A

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

0.8

0.9

1.0

1.1

1.2

1.3

1.4

1.5

1.6

1.7

CM

C

Time (s)

Con

cent

ratio

n (w

t%)

τvs

. XFo

r eac

h co

ncen

tratio

n w

e ob

tain

th

e re

laxa

tion

time

For

low

con

cent

ratio

ns, X

< C

MC

(τ

~ 1.

1 s)

Surf

ace

area

dec

reas

eson

tran

slat

ion

of ro

d. I

ncre

ased

surf

acta

nt

dens

ity a

t sur

face

can

be a

ccom

mod

ated

by

surf

ace

due

to it

s sm

all

surf

ace

dens

ity.

Ther

e is

no

need

for s

urfa

ctan

t to

be p

ushe

d in

to b

ulk.

Fast

cap

illar

y w

aves

(> 8

Hz)

are

indu

ced

by th

e vi

brat

ion

durin

g sq

uish

ing

and

resu

lt in

hig

h el

ectri

cal r

esis

tanc

e. (

We

mea

sure

the

enve

lope

dec

ay)

As c

apill

ary

wav

es d

ecay

, ele

ctric

al re

sist

ance

dec

reas

es to

fina

l eq

uilib

rium

val

ue (a

ssoc

iate

d w

ith fi

nal e

quili

briu

m sh

ape)

So, f

or sm

all X

, we

mea

sure

the

deca

y of

cap

illar

y w

aves

, not

of

surf

acta

nt sq

ueez

e ou

t

For

larg

e co

ncen

trat

ions

X >

CM

C (τ

~ 1.

7 s)

Cap

illar

y w

aves

are

dam

ped

very

rapi

dly

for X

> C

MC

, and

do

not

cont

ribu

te to

mea

sure

d si

gnal

dur

ing

deca

y.

Whe

n ro

d tra

nsla

tes,

surf

ace

cann

ot ra

pidl

y ac

com

mod

ate

the

high

er su

rfac

tant

den

sity

su

rfac

e ar

ea is

tem

pora

rily

> eq

uilib

rium

su

rfac

e ar

ea.

Surf

ace

area

rela

xes f

rom

nea

r equ

ilibr

ium

to e

quili

briu

m sh

ape

as

surf

acta

nt is

sque

ezed

out

from

surf

ace.

Res

ista

nce

rela

xes w

ith

surf

ace

topo

grap

hy, w

here

τis

the

sque

eze-

out t

ime

of su

rfac

tant

.

This

is n

ota

diff

usio

n lim

ited

proc

ess,

whi

ch is

abo

ut fo

ur o

rder

s of

mag

nitu

de fa

ster

.

Tak

e ho

me

mes

sage

:M

agne

tic le

vita

tion

has n

umer

ous a

pplic

atio

ns in

stud

ies

of fl

uids

, “so

ft” a

nd “

hard

” co

nden

sed

mat

ter p

hysi

cs,

and

biop

hysi

cs

1.“D

ial i

n” a

ppro

pria

te g

ravi

tatio

nal f

ield

, e.g

., M

artia

n,

Luna

r

2.Th

e fie

ld c

an b

e m

aint

aine

d in

defin

itely

3.Fi

eld

can

be v

arie

d w

ith ti

me

Col

labo

rato

rsPh

ilip

Tayl

orJ.

Iwan

D. A

lexa

nder

Lev

Slob

ozha

nin

Mili

nd M

ahaj

anSh

iyon

g Zh

ang

Neh

a (B

hatt)

Pat

elM

. Rez

a D

odge

Supp

orte

d by

NA

SA u

nder

gra

nts N

AG

3-18

64an

d N

AG

8-17

79