Comment on: "Convective flow of granular masses under vertical vibrations" (C. Laroche, S. Douady and S. Fauve, J. Phys. France 50 (1989) 699-706)

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Comment on: ”Convective flow of granular masses

under vertical vibrations” (C. Laroche, S. Douady and

S. Fauve, J. Phys. France 50 (1989) 699-706)

P. Evesque

To cite this version:

697

Short Communication

Comment

on:

"Convective

flow of

_granular

masses

under vertical vibrations"

(C.

Laroche,

S.

_Douady

and S.

_{Fauve, J.}

_Phys.

France 50

_{(1989) 699-706)}

R

_Evesque

Laboratoire

_d’Optique

de la Matière

_Condensée,

Tour 13-5ème

_étage,

Université P. et M.

_Curie,

4

place

Jussieu,

75252 Paris Cedex

_05,

France.

(Reçu

le 23 novembre _1989,

_accepté

le

_{15 février}

₁₉₉₀₎

Résumé. 2014 Nous montrons _que le rôle de l’air doit être

_négligeable

dans les

_expériences

de Laroche et al.. Nous nous _appuyons essentiellement sur les

_expériences

de

_Faraday

_{qui expliquent}

les

_figures

de Chladni et sur les

_{interprétations qu’il}

en donne. Nous

_invoquons

aussi d’autres résultats

_plus

récents. Abstract. 2014 It is demonstrated

using Faraday exprimental

results and

_{interpretations}

that air should not

_{play a major}

cast in the

_experimental

data

_published

_by

Laroche et al.. This is also

_supported

_by

other more recent studies.

J.

_Phys.

France 51

₍₁₉₉₀₎

697-700 15 AVRIL

_1990,

Classification

Physics

Abstracts 46.10-47.20F-05.60

The

_experimental

results

_reported

in this

_paper

are

_really

beautiful and no doubt

_they

will

help understanding

the convective flow

_regim

and the _very

_peculiar

_shapes

and

_geometries

that

a sand

_pile

can take when it is

_vertically

shaken.

However,

it seems to us that the

interprota-tion

_given

in this

_paper

_emphasizes

the effect of air too

_much,

so that these

_phenomena

are still misunderstood from our

_point

of view.

Furthermore,

one can test

_{qualitatively}

and

_{quantitatively}

a correct

_{interprétation}

of these

results,

when it will be

_achieved,

_by

_comparing

_directly

its theoretical

_predictions

to the other data

already published

[1-6].

Such a

_global

_{interpretation}

is not

_yet

_possible:

the

_published

experi-mental behaviors are

_quite

différent from one

_another,

_although

_they

have been obtained

_using

slightly

different

_{expérimental}

_set-ups

_[1-6];

this tends to

_prove

that a vibrated sand

_pile

is

sen-sitive to small

_{perturbations,}

such as a

_change

in the

_boundary

conditions

_[7]

or a small transverse vibration

_[7].

In

_[7],

we have not

_only

tried to discuss such

_{possibilities}

in a

_general

_fashion,

but also to check the relevance of

_already

_existing

theories

_{[2 - 3]}

to

_interpret

these

_phenomena

_{[1 - 6].}

We want to discuss here

_only

the relevance of an

_existing

air

_flow,

which is claimed

_by

Laroche et al. to create the convective

_pattern.

We do not

_deny

the existence of this air

_flow,

but

_only

contest that it is the motor of the

_pattern

under these

_{expérimental}

conditions,

_(which

are not too

698

large

accelerations and

_{large grains):}

for us, the air flow is

_only

a result and not a cause of what is

occurring.

In order to

_prove

this

_point,

let us first recall a few conclusions of

_Faraday’s

_paper:

when

spreading

a

_{light powder}

_(lycopodium,

for

_instance)

on a

_{vibrating plate,}

he has obtained

_heaps

located at anti-nodes of vibrations

_(places

of

_largest

vibrations,

i.e. nodes of

_pressure);

but when

spreading

sand on the same

_plate,

he has

_got

_heaps

at nodes of vibrations and has concluded to the lack of air effect in this case; its

_{interpretation}

was that the

_speed

of the Brownian motion of

_grains

was smaller at the nodes so that there were accumulations of

_grains

at these

_points

and formation

of

_heaps.

On the

_contrary,

for

_{light powders,}

the effect of air was

_important

and

_especially

of

an air flow induced

_by

the

_plate

vibration and located near the

_plate;

in order to

_strengthen

this

point,

he has stuck small

_pieces

of

_paper

on the

_plate

and used them as air

deflectors,

so that he

has

_changed

the

_geometries

and locations of

_{light-powder heaps, (point}

27-32 of

_Faraday’s

_paper

[2]);

(but

he does not mention _any

_change

in the

_geometry

of sand

_{heaps using}

this

_procedure).

So he has concluded to the existence of two different motors of

_heap

_creation,

one is induced

_by

a direct action of the mechanical vibrations of the

_plate

on the

_grains

and the other one is related to the air flow

_{generated by}

the

_plate

vibration,

(which

can _carry

_{grains only}

when

_they

are

_light

enough

of

_course);

the latter

_process

is thus

_only

_important

when the

_powder

is

_{light (i.e.}

made

up

of very

small

_grains).

He has confirmed this

_{analysis by exhausting}

the air from the container

surrounding

the

_{vibrating plate, (point}

33-36 of his

_paper):

below a 5 cm _mercury

_pressure,

he has

got

light-powder heaps

located at nodes of

_vibrations,

as if it were a

_{large-grain powder;}

but above 10 cm _mercury

_pressure,

_{light-powder heaps}

are

_recovering

their classical

_locations,

at anti-nodes of

_vibration,

so that the

_{atmospheric-pressure}

_patterns

are recovered.

Futhermore,

other

_papers

_support

this

_point

of view of

_Faraday:

_they

claim

_[3,

_8]

that air has

only

little influence on the

_dynamics

of a vibrated bed when the size of its

_grains

is

_{large enough,}

which is the case for

_grains

in the

_experiments

of Laroche et al.

_(0.63

to 0.80 mm

_diameter).

Concerning

our own

_experience

of

_granular

_materials,

we do _agree with this

_{approximation}

and we think that air effect

_might

be

_{neglected: during}

our

_{experimental investigation}

of the

properties

of a

_{vertically-shaken}

sand

_pile

_[5-7],

_{(using glass}

_spheres

of diameters 0.2 mm or

0.4 mm or 1

_mm),

we have checked the

_posssible

existence of an air effect in two different _ways and

_proved

that air was

_{negligible. Firstly,}

we have

_repeated

our

_experiments

at différent air

pressures,

from 4 mm of

_mercury

to

_atmospheric

_pressure,

and we have not detected

_any

_change

of the

_{heap shape}

or of the convective-flow

_pattern

_(we

want to

_emphasize

that 4 mm of _mercury is 10 times lower than the lowest

_pressure

studied

_by

_Faraday

and at which he had

_changed

the

locations of

_lycopodium

_{heaps). Secondly,}

we have

_investigated

the

_shape

taken

_by

the

_heap

when the

_boundary

conditions are

_changed;

for

instance,

we have covered the walls of our closed

_cell,

which

_contains

the

_granular

_medium,

with a metallic

_grid

located at a

_given

distance from the wall so that the air could have flown

_freely

from the bottom to the

_top

of the

_pile

without

_passing

through

this

_{pile; (grids}

were

_permeable

to air but not to the

_beads);

we have detected no

_change

of the

_pile

characteristics when it was

_vertically

shaken under these circumstances.

However,

we have

_already

mentioned the

_great

_sensitivity

of the

_experimental

behaviors ob-tained with vibrated sand

_pile

on the

_experimental

conditions such as boundaries.

So,

as Laroche

et aL have not used the same

_set-up

as _ours, a small doubt

_might

_persist

and it would be better to test

_directly

the influence of the air in their case

_by

_using

a

_grid

instead of a

_plate

in their

ex-perimental

set-up.

(Such

an

_experiment

has also been used

_by

_Savage

_[3]

to test the

_negligible

importance

of

_air).

The

_{strongest argument}

of Laroche et al. which

_supports

the air influence is the absence of

convective

_pattern

when vacuum

(10-5’Ibrr)

is

_performed

in their

cell; however,

it

_might

occur that

spheres

get

spontaneously charged

at such a low

_pressure

so that the medium becomes

_strongly

699

As a last

remark,

we have restricted the discussion to the influence of an air flow on the

_pattern

obtained

_by

Laroche et

_aL,

and said that it is of little

_importance.

We have not

_yet

discussed the effect of a

_{quasistatic surrounding compressible}

and viscous fluid on this

_pile;

this _may be

more

_important

than it can be

_thought

at first

_sight,

since this

_surrounding

medium ensures sound

propagation

even in a non-cohesive and

_unpressed

_granular

medium,

i.e. when it is

_levitating.

It also ensures a time

_dependent

resistance to deformation under the same conditions

_{(levitation).}

References

[1]

WALKER

J.,

Sci. Am. 247

₍₁₉₈₂₎

167.

[2]

FARADAY

_M.,

_Phyl.

Trans. R. Soc. London 52

₍₁₈₃₁₎

299.

[3]

SAVAGE

S.B.,

J. Fluid Mech. 194

₍₁₉₈₈₎

457.

[4]

TAKAHASHI

_H.,

SUZUIU _A., TANAKA

T., Powder

Technol. 2

_(1968/69)

65-77.

[5]

RAJCHENBACH

J.,

EVESQUE

P.,

C.R.Acad. Sci. Paris Sér.II 307

₍₁₉₈₈₎

1-4.

[6]

EVESQUE

P.,

RAJCHENBACH

J.,

Phys.

Rev. Lett. 62

₍₁₉₈₉₎

44.