Wetting of fibers : theory and experiments

HAL Id: jpa-00245903

https://hal.archives-ouvertes.fr/jpa-00245903

Submitted on 1 Jan 1988

HAL is a multi-disciplinary open access

archive for the deposit and dissemination of

sci-entific research documents, whether they are

pub-lished or not. The documents may come from

teaching and research institutions in France or

abroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, est

destinée au dépôt et à la diffusion de documents

scientifiques de niveau recherche, publiés ou non,

émanant des établissements d’enseignement et de

recherche français ou étrangers, des laboratoires

publics ou privés.

Wetting of fibers : theory and experiments

David Quéré, Jean-Marc Di Meglio, Françoise Brochard-Wyart

To cite this version:

Wetting

of fibers :

_theory

and

_experiments

David

Quéré

_{(1, 2),}

Jean-Marc Di

_Meglio

₍₁₎

and

_{Françoise Brochard-Wyart}

_{(1, 3)}

(1)

Laboratoire de

_Physique

de la Matière Condensée, UA 792 du

C.N.R.S., Collège

de France, 11

_place

Marcelin-Berthelot,

75231 Paris Cedex _05,

France

(2)

ATOCHEM,

Centre

_{d’Applications}

de Levallois, 95 rue _Danton, 92203 Levallois-Perret _Cedex, France

(3)

Laboratoire de Structure et Réactivité aux

_Interfaces,

Université

Pierre-et-Marie-Curie,

4

place

Jussieu,

75231 Paris Cedex _05, France

(Reçu

le 26 octobre _1987, révisé le 18

_janvier

_1988,

_accepté

le 8 mars

₁₉₈₈₎

Résumé. 2014 Nous

rappelons

d’abord les résultats

_théoriques

d’un des auteurs

_(F.

_B.-W.)

sur la

_statique

du

mouillage

des fibres.

_Lorsqu’on

considère les interactions à

_{longue portée}

de _type Van der Waals entre le solide et le

_liquide,

on montre _{que la fibre} peut être mouillée si le

_paramètre

d’étalement S est

_{supérieur à}

une

valeur seuil

_Sc

_(Sc

= 3/2

03B3(a/b)2/3

_{avec 03B3} la tension de surface du

liquide, b

le rayon de la fibre et

a =

(A/6

_{03C0 03B3}

)1/2

où A est _une constante de Hamaker

(A

=

ASL -

ALL)).

Au-delà de _ce

seuil, l’épaisseur

du

film mouillant en contact avec une _goutte réservoir est _ec =

a2/3b1/3

(c’est

l’épaisseur

au

_seuil).

Si la fibre est

tendue verticalement du _réservoir, la situation de

_mouillage

final est _{donnée par}

_{l’équilibre}

de la

_pression

de

disjonction

avec les

_pressions

de

_Laplace

et

_{gravitationnelle,}

c’est-à-dire

_{e(h) ~}

(h + K-2/b)1/3.

Nous

présentons

ensuite des

_prédictions

_théoriques

récentes sur la

_dynamique

de ce _{processus :} comme dans le cas

de la montée d’un film

_{liquide microscopique}

le

_long

d’un mur

_vertical,

il convient de

_distinguer

deux

_{régimes :}

une

_langue

_dynamique

_{(e ~}

t/h2)

est d’abord émise du

_ménisque.

_{Elle progresse selon} un _comportement

diffusif, tout comme le film

_{statique qui}

vient la

_{remplacer. Après}

un _temps

_{caractéristique,}

il faut tenir _compte

de la

_gravité

et la

_progression

du film

_statique

obéit à une loi h ~

t3/5.

Il _rattrape donc le film

_dynamique

à la hauteur finale

_{d’équilibre}

H. Ces

_prédictions

_théoriques

sont confrontées avec une

_expérience

_originale

de

mouillage

de fibres verticales par une solution

_marquée

en

_spin,

les _{films étant détectés par RPE. La vitesse}

avec

_laquelle

le film monte est anormalement

_grande,

ce _que nous avons montré être _{dû à des rayures axiales} de la fibre. Nous pensons néanmoins que les interactions de Van der Waals contrôlent l’état final du film

liquide :

le

_{profil e(h) qui}

s’établit est

_compatible

avec la théorie.

Abstract. 2014 We first

present a

_digest

of a

_previous

theoretical

_study

of one of us

_{(F. B.)}

about the static _aspects of

_wetting

of thin fibers. This

_study

includes the effects of

_long

_{range Van der Waals interactions. Two}

_points

merit

_special

attention :

_(i)

the threshold

_{value Sc}

of the

_spreading

parameter for

_{complete wetting}

is greater

than zero

_(Sc

= 3/2 _03B3

(a/b)2/3

with _03B3 the

liquid

surface

tension, b

the fiber radius and _a =

(A/6

03C0 03B3

)1/2

where

A is a Hamaker constant

(A

=

ASL -

ALL)) ;

and

_(ii)

when S >

_Sc

and when the

_liquid

is in contact with a

reservoir of zero-curvature, the thickness of this

wetting

film is locked to _ec =

a2/3

b1/3,

i.e. the thickness for

S =

Sc.

A recent

study

about the

dynamics

of such a

_microscopic

film is then

_{presented :}

the situation of

upward creeping

of a

_liquid

on a fiber is

_specially

studied. As for the

_planar

_geometry two

_regimes

can be

distinguished :

a static

_regime,

defined

_by

the

_equilibrium

between

_disjoining

_pressure,

_Laplace

_{pressure and}

gravity : e(h) ~

(h +

K-2/b)-1/3

and a

_dynamic

_regime

where viscous terms have to be considered while

gravity

can be

_{neglected : e(h, t) ~}

t/h2.

These two

_profiles

_{first creep with diffusion}

_equations.

After a

characteristic time, the static

_profile

then follows a

_{hs ~}

t3/5 2014

law and catches the diffusive tongue up at the final

_equilibrium

_height

H. These theoretical

_predictions

are tested

by

a new set of

_{experiments using spin}

labels and electron

_spin

resonance

(ESR).

Not all our results are understood via our

_theory.

_Particularly

the

creeping velocity

is too

_large

when

_compared

to

_theory.

The

_explanation

of this

_discrepancy

is due to surface

roughness.

Nevertheless we believe that Van der Waals interactions are relevant in our

_{problem :}

the final

state seems to involve a static

_wetting

film

along

the fiber.

Classification

Physics

Abstracts

68.40 - 68.45

1024

1. Introduction.

The

_{understanding}

of

_wetting

of thin fibers

_(diameter

less than 100

_03BCm)

is crucial _{in many industrial} fields :

composite

materials

_{[1] (like}

carbon-reenforced

re-sins),

textiles

_(spinning

and

_dyeing),

_paper

_industry

and other

_growing

areas.

Wetting

of fibers is

_{peculiar especially}

when

compared

to the

_planar

_geometry

_[2]

because of the additional radius of curvature. Let us

_imagine

a fiber

covered

_by

a

_liquid

film

(Fig.1b) :

the outer free surface of the

_liquid

does not match the

_solid-liquid

contact surface. Thus a non-zero

_Laplace

_pressure

exists inside the film and will increase with the

spreading

of the

_liquid.

These

_physical

evidences will show up in both statics and

_dynamics

of fiber

wetting.

We recall in _{this paper} recent theoretical studies about statics

_[3]

and

_dynamics

_[4]

and we

present

new

_experimental

results. 2. Statics.

2.1 CRITICAL SPREADING PARAMETER AND THICK-NESS OF THE WETTING FILM. - Let

us consider the

two

_following

situations :

-

a

_large

_{unspreaded liquid}

_drop

of radius R on a fiber of radius b

_{(Fig. la) ;}

- the same fiber covered with a uniform

_liquid

film of thickness e

_(Fig.1b).

Fig.

1. -

(a) unspreaded

drop

(R > b ) ; (b) liquid

covered fiber

_{(e b ).}

The free _{energy per} unit volume of the former is :

with y the surface tension of the

_liquid,

while for the

latter we get :

the first term of

₍₂₎

_represents

the interfacial _energy

-

SA, S

being

the

_spreading

_{parameter : S}

=

ysv -y sL - y and A the wetted area. The second term is associated with the excess interfacial _{energy due} to

the curvature of the film and the last term is the

long-range

interaction term. For non-retarded Van der Waals

_{interactions,}

with

_ASL

and

_ALL

_being

respectively

the Hamaker constants for

_solid-liquid

and

_{liquid-liquid interactions}

p e - AsL - ‘4LL

(we

set

03B3a2 =

6 7T

’

typically

a = 3

A).

By

comparing

f,

i and

f 2,

we can determine the most

stable state.

The film will be stable if

_{f2 - f i}

0 and

a (f2 - fI)

= 0. The transition between the _two

states occurs when :

1T (e)

is the

_disjoining

_pressure

_{1T ( e)}

= -

’dp .

This

gives :

for S

_Sc,

the

_{unspreaded drop}

state is favored

_{[5] ;}

for S

_{= Sc, a wetting}

film of thickness _e,,

_{develops ;}

for S >

_Sc,

this

_wetting

film has a thickness

_equal

to :

like for the

_planar

case

_[2].

We should note that it is

theoretically possible

to

_imagine

a situation where 0 S

_S,,

i.e. the

_liquid

would wet a

_planar

surface but would not wet a fiber made of the same material. For a fiber of

_length

L,

the

_optimum

volume of

liquid

is 2

_{Trbeo L}

with _eo

_given

_by

_(4).

With a

_larger

volume of

_liquid

_put

on the

_fiber,

it can be

_easily

shown that the final state is a

_large

reservoir

_drop

in

equilibrium

with a

_wetting

film of thickness _ec, ec

given

by

(3).

2.2

EQUILIBRIUM

PROFILE OF A LIQUID ASCENDING ON A VERTICAL FIBER

(UPWARD

CREEPING). - The

physical

situation is a vertical fiber

partially dipped

in a

_large

_liquid

reservoir

(Fig. 2a).

The film

thick-ness

e (h )

is a function of the

height

h above the flat

surface. The free energy is :

The first two terms are associated with interfacial

energies,

the third one

_represents

_long-range

interac-tion while the last one

_{pictures gravity.}

2.2.1

_{Macroscopic regime :}

meniscus. - At the

Fig.

2. -

(a) equilibrium profile ; (b) liquid profile during

an

_upward

_creep.

stands,

we can

_neglect

the

_long-range

interaction

term. Minimization of

_{(5) by}

means of Euler-La-grange

equation

yields

a

_catenary

_profile

for

_e(h)

associated with a zero curvature :

where

i

= b

S

+

1

and

_ho

is the

_height

of the

edge

of the meniscus for S = 0. When S >

0,

e tends

towardss

b for h =

ho,

while when S 0 the

o

meniscus ends up at

_height

_{hm given}

_{by :}

where

_{0 e}

is the

_Young

contact

_angle.

2.2.2

_{Microscopic regime : wetting}

_film.

- In the

film,

|

de

|

is small and

minimization

of

₍₅₎

_gives

and we

_get

for the

profile e

(h ) :

with

K-2 =

_03B3/03C1g.

This

_wetting

film

_joins

the

_macroscopic

meniscus with an

angle 0 = 2

(

e,

1/2

and ends _{up for}

3.

_Dynamics.

A detailed

_analysis

of the

_dynamics

of

_spreading

films will be

_presented

in a

_forthcoming

_paper

_[4].

We will consider here

_only

the case of S >

_Sc.

Moreover,

the

_description

of the rise of the

macro-scopic

meniscus

_{(Eqs . (6, 7))}

will not be set out in this paper because

_currently

our

_experiments

do not

focus on this

_regime.

Let us

_just

mention that the

speed

of

_creeping

of the meniscus is

_{governed by}

the well-known Tanner’s law

_[6]:

_{03B83 ~ U/v*}

with

v* = 03B3/~(~

being

the

_viscosity

of the

_liquid)

and

0 the

_dynamic

contact

_angle

that verifies

_equation

(7) (we

assume _{that pressures}

_{equilibrate quickly) ;}

this meniscus is established in a _{very short time}

( = b 2v*

(a b)-2/3).

An adiabatic film

(precur-sor-film

_[7])

is

_pushed

_up

_by

the meniscus until the latter reaches

_equilibrium.

Let us write the two basic

_{equations determining}

the

_creeping

of the

_microscopic

film :

(i)

assuming

that _{the film creeps with} a Poiseuille

flow,

the

_{hydrodynamic equation}

can be written :

U is the mean

_velocity

of the

_liquid

front and

P _{is the pressure} inside the film :

(ii)

the mass conservation

_equation

is :

By combining

(10)

and

_(11),

we obtain for a vertical

fiber :

Following [8],

we look for a self-similar solution for the

_profile

_{e(h, t ) : e (h, t )}

=

z~(t)

f(h/h~(t)).

1026

where u =

h/h~(t).

Two

regimes

_can be

dis-tinguished according

to the value of u :

u 1

(small heights).

The static film is

already

established and viscous terms have to be

_neglected.

Then

_equation

₍₁₃₎

becomes :

The solution of

₍₁₄₎

is

_{f(u) = (u}

+

u0)-1/3

with

Uo = K- 2/b . ht (t).

We thus

_get

back the static

profile

(8).

u > 1.e(h,t) ec

and the

_disjoining

_pressure

now is

_larger

than the

_hydrostatic

_pressure.

Equation

(13)

becomes :

The solution of

₍₁₅₎

is

_f(u)

=

2/u2

that we can

rewrite :

The

_{tip height}

_hd

of this

_dynamic

_tongue

is

_given

_by

with

_{D (eo )}

= 2 v *

a2/e0.

For v*=2500cm/s, a = 3 Â

and

_{eo = 30 A,}

D (eo )

=

10- 5

cm/s : _one centimeter of fiber is wetted

in one

_day.

The static

_profile

ends _up at

_{height hs}

determined

by matching

the solutions of

_{equations (14)}

and

(15) :

2 u2 =

(u

+

uO)-1/3

and u - 1.

Let us

_{call t3}

the time defined

_by

_{uo = 1.}

v

This time defines the moment when

_gravity

acts. For v * =

2 500 cm/s,

K-1=

1 mm,

a = 3 Å

and b =

30 03BCm,

t3 = 1

year.

As UO 1

_(t

_{t3), hs}

is

_given

_{by :}

with

_D(ec)

= 2 v *

a2/ec.

As _{u0 >} 1

_(t

>

t3),

the diffusion law

(19)

changes

to :

The creep rises

faster,

and the final

_height

H

(Eq.

(9))

is reached for

_hs

=

hd

= fi

_at

time t4 :

For

_typical

values of the

_parameters

_{(see above),}

one

_might

as well say never

_{since t4}

= 200 years.

These

_profiles

are drawn in

_figure

2b.

4.

_Experiments.

4.1 PROOFS FOR THE EXISTENCE OF A WETTING

FILM. - We have first looked for the

existence of the above described

_wetting

film.

_Figure

3. is a

microphotography

of two

_polyester

fibers

_(of

diame-ter 20

_{micrometers).}

We have

_spreaded

on one of

the fibers a silicone

_oil,

in which a fluorescent

_dye

(NBD)

had been introduced _up to saturation and we

, have looked at the fibers

using

a UV

light

source.

We can see on

thé

_picture

that there is some

fluorescence between the

_unspreaded

_droplets,

thus

revealing

a

_liquid

film. The second fiber on the

picture

is

_dry

and is shown as a référence. This

simple experiment

proves that in

spite

of the

pres-ence of

_unspreaded

_drops,

the fiber is

_actually

wetted.

We have also noticed that when a small

_drop

is close to a

_large

one, the former

empties

in the

latter ;

this

_phenomenon

in

_analogous

to the one of

two

_unequal

_{soap bubbles connected}

_by

a straw.

From the

_study

of the

_dynamics

_{of this process,} we were able

[9]

to calculate an estimated

_wetting

film

thickness for a 19 micrometers

_Nylon

fiber covered

by

a

_spin

finish

oil ;

this thickness of order 200

A

is in

_qualitative

_agreement

with our theoretical

predic-tions,

although

involving

too

_large

Hamaker

con-stants.

4.2 CREEPING OF A LIQUID ON A FIBER: FIRST OBSERVATIONS.

4.2.1

_{Experimentals.}

- We have studied the

upward

creep of

liquid

a-methyl naphtalene :

(03B3lab

= 36

dyn/cm

and _q = 1.5 x

10-2

_P,

v* =

03B3/~ = 2 400 cm/s)

on

polypropylene

fibers of

diameter 45 03BC. We have

investigated

the

profile

of

the

_creeping

_liquid

_by

an

_analysis

of the electron

spin

resonance

_{signal 03A3(h,t)}

of a nitroxide label of

formula

dissolved in the

_{a-methyl naphtalene}

at a

concen-tration of 4.7 M. The

_experimental

_set-up

is shown in

_figure

4.

_{By using}

this

method,

we benefit from

the very

high sensitivity

of ESR

_(it

should be

possible

to detect a

_wetting

film of 20

Â

on a

_single

fiber).

We have checked that the

_Young

contact

angle

fibers is zero

_by

observation

_through

Fig.

3. -

Photography

under

_microscope

of two

_polyester

fibers

_(diameter

= 20

microns).

One fiber has been covered

by

fluorescent

_dyed

silicone

_(see

text for

_{explanation).}

Fig.

4. - Schematical

représentation

of the

_experimental

set-up used for the

_profile

determination. h is the

_height

above the reservoir and L the size of the

_cavity

(L

= 2.3

cm ).

revealing

that the surface is not

_chemically

homo-geneous. Seven fibers are set in the same

_glass

test

tube in order to increase the

_signal/noise

ratio

_(the

noise comes

_mostly

of the electronic

_part

of the

spectrometer).

We call

_e(h,t)

the thickness of the film as a function of the

_height

h above the reservoir and the time t. The ESR

_signal

_{X(h, t )}

_rigorously

is the convolution of

_e(h,t)

with the

_apparatus

func-tion

_depending

on the

_cavity

size

_(height

L,

L = 23

mm)

and _on the

gain

of the

amplifier.

The

ESR

_spectrum

of the reservoir solution is reduced to

a

_single

_peak

because of the

_high

label concentration

leading

to

_{spin exchange.}

On the other hand the

spectrum

of the labelled

_liquid

on the fiber consists of three

_{peaks :}

we think that it is due to a slower

diffusion of labels molecules

_leading

to less

_exchange

1028

adsorption

on the fiber or a

_possible

diffusion of the

label inside the fiber. This

_problem

is _{still open. In} a

first

_{approximation,}

the thickness e of the film can

be deduced

_{from 03A3(h,t)}

_by

a

_simple

calibration

where

_{03A3(h, t)}

is the

_height

of the central

_{peak :}

e = 127

03A3, e

in

Â

and X

in

ESR-signal

units.

4.2.2 Velocity of

the

_upward

_creep. - The labelled

liquid

is introduced into the bottom of the vessel at t = 0. We

_try

_to detect the onset of the

signal

at

different

_heights

above the reservoir : because of the small value of the

_signal/noise

ratio,

we have to

record several ESR

_spectra

_{and average}

them.

Each

spectrum

is rather

_long

to record

_{(10 min)}

since we use the

_{highest sensitivity}

of the ESR

_apparatus

involving

large

time-constants. That is

_why

we

_got

only

two data

_{points :}

_{hl -}

_L/2

= 261

_{mm, t1}

=

52

min ;

h2 - L/2

= 516

_{mm, t2}

= 160 min. If we

assume that the

_dependence

on t for the advance of this

_tongue

_{(corresponding}

to a film of 20

_Â)

is a

power law : h -

L/2 ~ t03B1

we

_{get a}

=

0.60 ±

0.05.

We _{remain very} careful as

_regards

that result because of the little

data,

but we have been

_{quite surprised}

not to have

_got

a diffusion law

(a

=

0.5 ) :

both

capillary

rise and

_creeping

of a

_microscopic

_dynamic

film

_{(Eq. (17))}

lead to such a law. Another feature is

that

_experimental

_{upward creeping}

times are much

too small to be

_interpreted

as a

wetting

_phenomenon.

The diffusion law which ruled the advance of the

dynamic

tongue

has been

_proposed

above

(Eq. (17)) :

h2 = D(e0)t

with

_{D (eo )}

=

2v*a2/e0.

The diffusion coefficient

_D(e0)

associated with our

system

can be

_{theoretically}

estimated :

_{D(eo) =}

10- 5

_{cm/s (one}

centimeter of fiber is wetted in one

day).

That is

_why

we

_suspected

a

_capillary

phenome-non : electron

_{microscope pictures}

which have been

recently

taken in the research center of Atochem in Levallois

_(we

thank for their kindness C.

_Taupin

and M.

_Allain)

show that the surface of our

polyp-ropylene

fibers is

_{actually rough}

_{(Fig. 5).}

Axisym-metric _{grooves may be} observed and it is reasonable

to assume that the

_liquid

has been

_conveyed

_through

a

_capillary

_process.

Lucas-Washburn’s

_{equation [11, 12]}

describes the

simple

situation of a

_capillary

tube

_{(radius r)}

_partially

dipped

in an infinite

_{reservoir ;}

_assuming

a Poiseuille flow it reads as

That can be

_roughly

_{integrated :}

From our

_experimental

data

_(h

=

hl, t

=

tl,

v * = 2 400

_cm/s)

we

_get

r = 1 micrometer. This is in

a

_quite

_good

_agreement

with what could be observed

on the

_microscope

_pictures,

even if the grooves seem

to be a little smaller than this value of one

mi-crometer.

_Maybe

we have an unusual

_capillary

rise as observed

_by

Moldover and Gammon

_{[13] :}

when the

_capillary

tube has a diameter of the order of the

range of intermolecular

forces,

the

macroscopic

capillary

rise is modified : the

_liquid

_creeps

_higher

than

_K-2/r.

_Legait

and De Gennes

_[14]

have

analysed

such a situation between two vertical

_plates

distant from r. Because of the

_disjoining

_{pressure in} this confined _space,

_they

_propose to

_{replace r by}

r * =

r - 1.5 a2/3r1/3

_so that the

liquid

rises _up to

Fig.

5. -

K-2/r*.

In the Lucas-Washburn

_equation,

the gra-dient term is altered

_(we

have to

_replace

r

_by

r*)

while the

_hydrodynamic

radius remains

un-changed.

The

_creeping

still is

_diffusive,

but the coefficient of diffusion is now :

For a

_given

r, the rise time is reduced. Of course this correction on r is very small for r - 1 micrometer

(0394r r ~

1

_{% ) ;}

but it could be _very

_interesting

to

study

anomalous

_capillary

rise

_{by working}

on fibers with _{very small grooves}

_(r

1 000

_Â).

We

_currently

work on this

_problem

which is an

_{original expression}

of

_long-range

interactions. 4.2.3

_Profiles.

- Let

us recall that for non-adsorbed

spin

labels the thickness of the film

_e(h,t)

is

proportionnal

to the

_{ESR-signal :}

_{e(h,t) =}

127 03A3(h,t);

we

_present

for our data

either 03A3

or e : in a

_regime

where

adsorption

is

suspected

to be

predominant e

does not mean

_anything

more.

Our results are drawn in

_figures

6 to 9 : e versus t

for h constant in

_figure

6, 03A3

versus h for t constant in

figure

7,

Log 03A3

versus

_Log

_(h

+

_h0),

in

_figure

8

(ho

=

K- 2/b).

The first remark is that two

regimes,

more and more

_{distinguishable}

as time goes

by,

can

be seen in

_figures

7 or 8. We call

hK

the

height

of the

kink between the two

_regimes.

Fig.

6. -

Thickness e of the

_liquid

film versus time for h = 272 _mm.

For h

_hK

the

_intensity

of the

_{signal 03A3}

is much

too

_large

to be relevant of

_wetting

or

_capillarity

and

may be due to the

_strong

_adsorption

of the labelled molecules onto the bottom of the fiber. We cannot

explain

the

_strange

_{behavior : 03A3(h) ~ (h + h0)-03B1}

with a = 6.0 ± 0.2.

A very striking

feature is that

_hK

is

_equal

to

ho (ho =

K-2/b),

the error bar for this measure

being

1 _cm,

_half-length

on the ESR

_cavity.

This may

be a curious

coincidence,

and we are

_working

on this

problem by using

fibers of different diameters.

Fig.

7. - ESR

signal -Y

versus

_height

h above the reservoir for : D

(t

= 375

min);

₊

(t

= 1 437

min);

0

(t

=

3 308

_min.)

Fig.

8. -

Log 1:

versus

_Log

_(h

+

_h0)

with

_{ho =}

_{K-2/b : 0}

(t

= 117

_{min) ;}

+

_(t

= 375

min) ; 0

(t

= 1 437

_min);

A

_(t

= 3 308

min ) ;

_x

(t

= 10 049

min ).

Fig.

9. - Short time behavior :

(a) e (t )

with t around 117

min ;

h -

_L/2

= 272 _{mm ;}

(b) logarithmic profile

of

1030

For h >

_hK

we first

_get

_{profiles verifying : e - t}

and e - h - a with a = 2.1 ± 0.6

(Fig. 9).

That could

be

_compatible

with the

_creeping

of a

_dynamic

_tongue

(Eq. (16))

but this rise is too

_rapid

to be

_interpreted

as a

_{wetting phenomenon}

(Sect. 4.2.2).

Then

(Fig. 8)

« decreases down to the value a =

0.30 ± 0.10. This

_exponent

is

_compatible

with the

asymptotic

value 0.33 of

_equation

_{(8) (static}

_profile

of a

_microscopic

film on a vertical

_{fiber) :}

that is

_why

we

_interprete

this film as a

_wetting

film. Because of the grooves,

liquid

is first carried _up

_by

_{capillarity ;}

then each _groove acts as a reservoir from which a

wetting

film can be

_laterally

_{emitted. This process is}

quasi-instantaneously :

time to diffuse on

_length

b

_{(Eq. (19))}

is for our

_system

about five seconds. One can

_roughly

estimate the contribution of the grooves to the ESR

_signal,

substract it from

X,

and

_{using equation (8)}

we

_get

from the measured

profile a

= 2.5

A

_{or a} reasonable effective Hamaker

constant A =

ASL - ALL

= 4.1 _x

10-13

_ergs.

5. Conclusion.

We have shown that thin textile fibers can be covered

_by

a

_liquid

film when

_they

are in contact

with a reservoir

_containing

a

_{wetting liquid.}

Com-pared

with the

_theory

_{(Sect. 2),}

the

_dynamics

of the

creeping

is too

_{rapid :}

this

_express-rise

can be

explained by

the surface

_roughness,

and it can be

industrially

interesting

to

_provoke

the

existence

of such axial _{grooves. A}

_microscopic

_wetting

film can

then

_develop

from thèse

_striations,

the measured

profile

e(h)

obeys

power law in

agreement

with the theoretical

_prediction.

_Systematic

_experiments

with fibers of different diameters and

_polarities

are

cur-rently

under _progress.

Acknowledgment.

One of us

_(D.Q.)

thanks ATOCHEM for financial

support.

References

[1]

CHOU, T. _{W., MCCULLOUGH,} R. and PIPES, B., in Pour la Science, French issue of Sci. Am.

(Décembre 1986).

[2]

DE

GENNES,

P. G., Rev. Mod.

_Phys.

57

₍₁₉₈₅₎

827.

[3]

BROCHARD-WYART,

F., J. Chem.

_Phys.

84

₍₁₉₈₆₎

4664.

[4]

BROCHARD-WYART,

F., DI MEGLIO, J. M. and

QUERE,

D., submitted to

_Langmuir.

[5]

CARROLL,

B. _J., J. Colloid

_Interface

Sci. 57

₍₁₉₇₆₎

488.

[6]

TANNER,

L., J.

_Phys.

D 12

₍₁₉₇₉₎

1473.

[7]

DE

_GENNES,

P.

_G.,

C. R. Hebd. Séan. Acad. Sci. Paris Sér. II 298

₍₁₉₈₆₎

111.

[8]

JOANNY, J. F.,

Thesis,

Paris

_(1985).

[9]

DI _MEGLIO, J. _M., C. R. Hebd. Séan. Acad. Sci. Paris Sér. II, 303

₍₁₉₈₆₎

437.

[10]

SACKMAN, E. and TRAUBLE, H., J.A.C.S. 94

₍₁₉₇₂₎

4482.

[11]

LUCAS, R., Kolloid Z., 23

₍₁₉₁₈₎

15.

[12]

WASHBURN, E. W.,

Phys.

Rev. 17

₍₁₉₂₁₎

273.

[13]

MOLDOVER, M. R. and

_GAMMON,

R. W., J. Chem.

Phys.

80

₍₁₉₈₄₎

528.

[14]

LEGAIT, B. and DE

GENNES,

P. _G., J.

_Phys.

Lett. 45