- Email: [email protected]
The mechanism of boundary lubrication and the properties of the lubricating film
VOL.
1 bv/s8)
277
WEAR
THE MECHANISM OF BOUNDARY LUBRICATION AND THE PROPERTIES OF THE LUBRICATING FILM SHORT-
AND
LONG-RANGE BOUNDARY
ACTION
IN THE THEORY
OF
LUBRICATION
B. V. DERYAGUIN Corresponding Member of the Academy of Sciences of U.S.S.R. in collaboration with V. V. KARASSEV, Laboratory
of
N. N. ZAKHAVAEVA
AND
SwfacePhenomena, I?asfitute of Physical Chemistry,
V. P. LAZAREV Academy of Sciences of U.S.S.R.,
Moscow (U.S.S.R.)
Two versions of the blow-off method are described, by means of which the dependence of the viscosity of oils and other non-volatile fluids on the distance from the solid wall can be measured, and the viscosity localized with an accuracy of IO A. In the case of non-polar specially purified vaseline oil the viscosity remains strictly constant to a distance of the order of IO-’ cm from the wall. The addition of polar additives causes changes in the viscosity near the wall, In a number of cases the viscosity changes discontinuously at some distances of the order of IO-~ to 10-5 cm from the wall. In the case of polar liquids the viscosity may rise or fall on approaching the wall, depending on the molecular structure. The results obtained prove that the solid wall is capable of altering the orientation of the molecules in adjacent layers of the liquid up to 10-5 cm thick, and even up to IO-~ cm thick in the case of polymeric liquids. This effect plays a substantial part in the mechanism of boundary lubrication, since oiliness always disappears if it is absent. In conclusion, an examination is made of the mechanical properties of the boundary lubrication layer which explain both the existence of static friction and the observation of the two-term friction law derived by DERYAGUIN from the molecular theory of friction. The general conclusion is the impossibility of accounting for the phenomenon of boundary lubrication without taking into consideration the specific properties of the polymolecular boundary layers of liquids.
2 USA MMEN
FASSUNG
Zwei verschiedene Varianten der sog~nannten i~bblas-methode werden beschrieben. Diese erlauben es die Abhangigkeit der Zahigkeit van &en und anderen nicht-fi~chtigen Fliissigkeiten als Funktion des Abstandes van der festen Wand zu messen und die Zahigkeit mit einer Genauigkeit bis auf ro A zu lokalisieren. Fur ein nichtpolares speziell gereinigtes Vaselinijl bleibt die Zlhigkeit streng stabil bis zu einem Abstand you der Wand van der Grossenordnung TO-~ cm. Zufiigung polarer Substanzen zu dem 01 hat eine Veranderung der Zahigkeit in der N&he der Wand zur Folge. In einer Reihe van Fallen vergndert sich die Zghigkeit sprungweise und zwar beieinem Abstand van der Wand van der GrBssenordnung r~-~-ro-s cm. Ftir polare Fliissigkeiten kann die Zahigkeit abhangig van der Struktur van Molekiilen, entweder zunehmen oder abnehmen. Versuchsergebnisse zeigen, dass eine feste Wand die Orientierung der Molekiile van Fhissigkeitsschichten bis auf einen Abstand van 10-s cm und fur polymere Fltissigkeitensogar bis auf IO-~ cm beeinflussen kann. Diese Erscheinung spielt eine bedeutende Rolle in dem Mechanismus der Grenzschmierung denn, wenn sie nicht auftritt verschwindet such regelmgssig die Schliipfrigkeit. References p. 289-290
B. V. DERYAGUIN et al.
278
VOL. 1 (Iq57/58)
Zum Schluss wird die Frage der mechanischen Eigenschaften der Grenzschichten van Fliissigkeiten besprochen, mit deren Hilfe sowohl die Existenz der statischen Reibung als such die Giiltigkeit des binomialen Reibungsgesetzes, das DERYAGUIN aus der molekullren Theorie der Reibung ableitete, erkllrt wurden. Als allgemeines Ergebnis der Untersuchungen wird festgestellt: Die Erscheinung der Grenzschmierung sind nicht zu erkllren ohne die spezifische Eigenschaften der polymolekularen Grenzschichten van Fliissigkeiten in Betracht zu ziehen.
INTRODUCTION The far greater fluid friction interaction
complexity
between
the solid
with them, an interaction factor
in the case of friction determines
velocities film
studied
at which
boundary
difficult,
ary friction
the properties
friction,
film
film is thin, whereas
in contact
viscosity
is of lesser importance
of boundary
with
by the molecular
lubricating
static
of the properties
the mechanism
as compared
of the film. This is the dominant
and especially,
investigation
out in detail
which
at the small
friction,
usually
of the boundary
lubrication
is noticeably
substance they
cation,
beyond cannot
affected
takes
lubricating
has been insufficiently
point
and by a number According
by new and original
methods,
molecular
layers
of a liquid
properties
(as compared
with
surface
OVERBEEK~, directly
related
as regards
GLAZMAN
are not important
the influence containing
themstate
of boundary
lubri-
in this respect.
by the authors
of the present
of experiments
of the solid
polar
carried
wall extends
molecules,
those of the bulk phase)
of views
producing
that have
the experimental preference
A comprehensive liquids. out by
AND DYKMAN~
such behaviour
survey
paper”,
out mostl!
through changes
many in their
a considerable
action
which
be given
effect
conception
(oiliness).
boundary
of
to the theory
ourselves oil
of
been publish-
as by VERWEY
we shall confine of
in the
investigations
have already
of an analogous
properties
show that
to the conception
should include
the author6J7 as well
and others, and
data,
must
As such surveys
the application
worked
to their lubricating
p. 289-290
on the phenomena
based on a number
for different
of colloids,
concerning
References
action.
effects
edPIb, particularly of the stability
surfaces
of the lubricating
of lubrication. divergence
the most varied
The layers
scientist9.
time is now ripe to summarize
above-mentioned
lubrication. that bound-
are in a state so close to the volume
has been expressed
Soviet
of the friction
on them.
influence
their properties of view
of other
on the mechanism
layer
any specific
to their conception,
long-distance
adsorbed
of boundary
from the assumption
only by the properties layers
the first molecular exercise
and therefore
A different
views on the mechanism
by BOWUEN~, proceeds
selves or of the monomolecular
closely
and the boundary
of fluid friction
there are two opposing
The first, worked
The
friction
up to now.
At present
that
of boundary
is in the main affected
when the lubricating
the phenomena
Since experimental is very
surfaces
which modifies
alone place.
of the phenomena
is due to the fact that the former
films
AND
to data as
are
MECHANISM OF BOUNDARY
VOL. 1 (1957/58)
A STUDY OF VISCOSITY IN THIN BOUNDARY
LUBRICATION
279
FILMS OF LUBRICATING
OILS AND OTHER
ORGANIC LIQUIDS One of the methods to measure
of establishing
their viscosity,
ties involved,
However,
the majority
the specific
properties
owing to the considerable
of the previous
not reached clear and comprehensive
comparison
slit between
of direct (optical)
the value obtained
less than that obtained of the width concluded
parallel
to flow of the liquid in the slit and
by light interference.
As the average
error in the determination
contradict
BASTOW
the measurements
BOWDEN
AND
that point to changes
of the same liquids at a distance of over 0.2 p from a solid wall.
One could agree with the authors if they had confined themselves clusion. However,
they assumed
without
sufficient grounds
also do not take place in thinner liquid layers adjacent allow of an opposite obtained,
on a
the plane with
width proved to be on an average 0.1-0.2 p
of the slit was of the same order of ma~itude,
in the viscosity
by the
studied the
based their conclusion between
is
or have
is deserved
the viscosity,
of the gap-width
resistance
The computed
that their experiments
difficul-
Special attention
planes. They
determination
from the measured
the value of its bulk viscosity.
films
experimental
studies either have been erroneous
conclusions.
work of BASTOW AND BOWDEN~~, who, in order to determine radial flow in a narrow
of boundary
BOWDEN
interpretation. based
denial of the existence
Despite
his further
of peculiar
properties
in viscosity
to walls. Yet their experiments
the arbitrary
investigations
to the above con-
that changes
extrapolation
of boundary
of the results
lubrication
in the wall-adjacent
liquid
on the
layers
at a
distance of less than 0.1 p. Returning vapours
to the same subject
on smooth
surfaces,
this paper11 too, BOWDEN’S experimental
conclusions
data, which in themselves
of surface action, inasmuch only up to the relative gations of vapour formed
in his work
BOWDEN
adsorption
of
tried to confirm his point of view. However,
on the polymolecular
in
constitute
an ungrounded
are not suitable for an estimation
as the investigation
of vapour
adsorption
pressure of 0.95. It is not surprising,
adsorption
in the immediate
by ZORIN AND DERYAGUIN~~,
extrapolation
proximity
using an optical
therefore,
of the
of the range
was carried out that the investi-
of the saturation
point per-
method, led to opposite
results
and conclusions. We shall now consider the results of direct measurements layers of organic
liquids,
original
These
method.
oils and polymers, results
performed
point disputably
of viscosity
in boundary
by a precise and completely
to the fact that in the boundary
layers of up to 0.1 p (and more, in some cases) the viscosity
has a value differing
from
that in the bulk.
MEASUREMENT
OF VISCOSITY
The shortcoming
IN BOUNDARY
LAYERS
BY THE “BLOW-OFF”
of all the methods hitherto employed
ity in thin films lies in the circumstance
in the ~ves~gation
of viscos-
that these methods, even if we disregard
other defects and sources of error, yield only average
effective
in the slit or in a layer of given thickness la. Some methods, References p_ 289-290
METHOD
their
values of the viscosity
as for instance those based
280
rt al.
IS. V. 1)ERYAGUIN
‘.‘OL. 1 (1957/58)
on the flow of a liquid through porous medial”, yield results that are even less definite, since the liquid passes through irregularly layers is completely The
“blow-off”
tion of viscosity
shaped pores for which the thickness
of the
indeterminable. method
deLised by the authors1”G6 permits
as a function
an exact
determina-
of the distance from the solid wall, the latter being deter-
mined to within & 5 A. EXl’ERIhIl
One of the sides of a plane-parallel of the liquid under investigation the slit produced
a laminar
METHOI)
slit 0.2 mm wide (Fig.
over IO /Lthick. A constant
I)
was covered with a film
stream of air blown through
flow in the film, giving it a gently sloping wedge-shaped
form. Owing to the fact that the flow of the film was caused solely by the shearing stress of the air stream,
which was uniformly
film, the flow was one-dimensional the liquid particles
depended
not on any other coordinates. a sheared deck of ordinary
distributed
as well as laminar.
exclusively
over the whole surface of the In other words, the velocity
on the distance
from the solid wall (z) but
Thus the flow in the liquid layer was similar to that in
playing cards. An elementary
layer of the liquid, parallel
to the slit wall, moved as a whole parallel to the wall with a velocity creasing according
to a definite function
This result is caused by the fact that, state of stress in the film is homogeneous, all points. If the viscosity
of the distance
owing to the absence and thcreforc
I( = u (z), in-
to the wall. of volume forces, the
the shear stress is the same at
w(‘rc the samcl at all distances
from the solid wall too, then
it would follow that the velocity gradirnt d~/c)zwould also be cverywherc II would be proportional
the same, and
to 2. In this case the film would assume the shape of the exact
wedge bounded on top by an inclined plane ; and vice versa, any variation of the viscosity strictly
on approaching
wedge-shaped
the wall would bring
after blowing-off.
a definite scale the velocity
As proof of this, it is sufficient and the axis OZ perpendicular Refe~wcrs/I, 289-290
from
thts
film profile represents
on
profile of the liquid near the solid wall.
“5
”
/////////
to point out that if we place the origin of the coordi-
nates (0) on the wetting perimeter at a distance
in the value
a deviation
near the solid wall from the profilr
In fact, the resulting
2’ ‘; /
situated
about
form of the film.
Thus we can judge the \-ariations of viscosity of the film obtained
of
(Fig.
I)
with the axis OX directed
along the wall,
to it, then the abscissa x of a point of the film profile,
h from the wall, expresses
the distance
travelled
by the corrtx-
MECHANISM
VOL. 1 (1957/58) sponding elementary travelled
LUBRICATION
layer of the liquid during the blowing-off
is proportional
of the film represents Applying
OF BOUNDARY
to the velocity:
the velocity
Newton’s
time t. But the distance
x = UZ; from which follows that the profile
profile in the liquid layers near the solid wall.
law of viscosity,
of the liquid at a distance
281
we find the following formula for the viscosity
h from the wall: II
=
Tr
d!
(1)
dx’
The right-hand
part of the formula contains the steepness dJz/dx of the film profile at
the spot where the thickness
is equal to h. T denotes
liquid, caused by the air flow. By determining off, we can establish
the law of variation
the shear stress in the layer of
the film profile obtained
of viscosity
as a function
the solid wall. Thus our main problem is to determine film in the interval the influence Depending thickness
of thickness
on the nature
of viscosity
substances
in which the variation
takes place under
chosen
oils the layer is much thinner:
greatly
to measure
depending on the object under investigation.
estimate
of the velocity
obtained
by photographing
A far more sensitive
the thickness
the interference
parameters
of the elliptical
polarization
for determining
made it impossible requiring
obtained
by
in measuring
the film thickness
the thickness
of the
from various regions of
in various regions of a film of
to apply the usual polarization
and beam
of the reflected light, which made the accurate
deter-
impossible.
This difficult problem has been successfully of the reflected
The narrowing
goniometers
of the incident
of its state of polarization
solved by means of a special modulation
polarized light, using a photoelectronic
As a detailed description
shall confine ourselves
the
near the wall may be
based on the determination
of the light reflected
wide beams.
leads to a lowering in the intensity
method of analysis
cm. Hence,
In the first case a fairly accurate of viscosity
and precise method is necessary
of observation
IO-~
of the film will vary
fringes of equal thickness,
liquids and oils. We chose a method
the film. The necessity
about
light17 (see below).
in common
and an oscillograph.
layer
liquids and solutions,
and profile
profile and the distribution
viewing the film in monochromatic
unequal thickness
In polymer
may extend to distances up to 7-8 p from the wall. For monomer
and common
methods
mination
in viscosity
of the liquid and the solid wall, the corresponding in order of magnitude.
optical
methods
of the distance from
the profile of a very thin
of the solid wall.
may vary greatly
variations
exactly
after blowing-
to describing
multiplier
can be found in the original paperls, we
the scheme of the set-up (Fig. 2) and the method
of measurement. The slit (A), illuminated isolating
by means of an object-lens on the measuring
limb;
axis with a frequency electronic
by a Hg lamp, under
the line il = 5769-5790
multiplier,
References p. 289-290
A, was projected
(L) ; a, aperture
PZ, Polaroid of about
I
V a.c. with a light filter
(F,)
into the film under investigation,
diaphragm;
set in rotation rev/set.
120
P1, iodine-quinine
around the reflected
The modulated
the voltage on which was increased
Polaroid, beam as an
light fell on the
photo-
by an amplifier with an RC
282
I:. T’. L)ERYAGLUN
Fig. 2. Optical
filter and transmitted
axmgcment
to the cathode
presence or absence of the modulation K, and K, are two quarter-wave
et (Ilk
VOL.
fnr determining
oscillograph
velocity
1
(1957’58)
profllr.
0 serving
as an indicator
of the
in the photocurrent. plates;
the principal
axes of K, are directed at
an angle of 45” to the plane of incidence, the plate K, can be rotated and is on the measuring limb. D, an D, are two thick calcite plates cut not quite parallel axis;
DP serves
sensitivity
to depolarize
of the photocathode
serves to eliminate
the beam in order to eliminate to the direction of polarization
the coherence
With the decoherenter
of
and .L components
; D,, the “decoherenter”,
D, in the “in” position to prevent modulation,
prevent
beam become
a renewed modulation
equal. With the decoherenter of the photocurrent
and i
an angle of 45” with the plane of polarization
it is necessary
The technique
of measuring
components to
and sufficient
to
so that they make,
of the light transmitted
are made in the usual manner with the azimuths
it is necessaq-
in the “out” position
orient the optical axes or the plate K,, which serves as an analyzer, Calculations
of the
of the beam.
and sufficient to rotate the polarizer P, to such a position that the of the reflected
to the optical
the influence
by plate K,.
obtained16.
was as follows.
When the film on the surface of the steel plate had been blown off by an air current during time t, the apparatus micrometer measured.
was demounted,
the plate with the film was set on a
slide, and by moving the latter the film thickness After that, a graph was plotted representing
in various regions was
the film profile.
As the films of some liquids and solution were not very stable and evinced a tendenc! to disintegrate
into drops, a different procedure was applied in this case. The thickness
was measured not after but during blowing-off line. For that purpose the chamber urements
the following modification
at a definite distance x0 from the wetting
lid was made transparent. of the technique
For rapid optical meas-
was particularly
convenient.
The oil film was smeared on the underside of a glass prism that served as a lid for thca blowing-off
chamber,
internal
reflection
parallel
and normal
appeared.
the angle of incidence
of the polarized light being 45” ; complete
was thus observed ; the amplitudes to the plane of incidence
of the component
remained
constant,
In the presence of the film this shift varied, depending
oscillations
but a phase shift on the thickness
of
the film. The advantage
of the abo\c-mentioned
azimuth needs to be measured, By plotting measurement lteferences
the thickness
technique
lies in the fact that
only one
instead of two.
of the film h against the value C
x,/t the results of the
made according to the second variant were brought to a form representing
9.289-290
voL. 1 (r957/58)
MECHANISM OF BOUNDARY LUBRICATION
283
the film velocity profile in the proximity of the solid wall, as was done in the first variant (t is the period of time from the beginning of blowing-off to the moment of measuring; h is the thickness measured at that moment). Obviously the abscissa expresses the velocity of the layers at a distance /%from the wall. Thus the graph gives the velocity profile. Its x,, was difficult to determine; we usually plotted r/t on the axis of the abscissa, which resulted in the same velocity profile but on an arbitrary scale. Figs. 3, 4, 5, 6 and 7 show the results obtained by V. V. KARASSEV; Figs. 3 and 5 were obtained
by the first method,
the rest by the second.
RESULTS OF THE MEASUREMENTS Fig. 3 refers to non-polar procedure
Vaseline oil; the polar impurities
worked out by Professor
ELOVICH, involving
were removed by a special
the use of a platinum
catalyst
at high temperature.
Fig. 3. Velocity profile for specially purified vaseline oil on a steel surface, obtained by analysis of film profile after blowing; t=zo%.
Fig. 4. Velocity profiles of 0.01% solutions of chlorine derivatives of tetracosane in vaseline oil, on a steel surface, obtained in the process of blowing. (I) Monochlorotetracosane solution, t = 23°C; (2) Trichlorotetracosane solution, t = 18.6’C; (3) Hexachlorotetracosane solution, 1 = 25%
We see that the viscosity of non-polar Vaseline oil remains a constant value equal to its value in the bulk up to a distance of about IO-~ cm from the wall. Similar results have been obtained dozens of times, which proves them to be correct beyond any reasonable doubt. Nevertheless, the addition of fatty acids or ethers in minute concentrations can disturb the linearity of the velocity profiles. With an increase in concentration the film profile becomes irregular and jagged, while a still greater increase of the concentration makes the film unstable: it no longer wets the surface, which is covered with an adsorbed film of a surface-active substance. Fig. 4 represents the velocity profile when a monochloroparaffin, trichloroparaffin or hexachloroparaffin are added to the Vaseline oil in a concentration of 0.01%. In this case the form of the profile changes and assumes a characteristic break of about 0.025 ,uin thickness. Similar results are obtained in the case of some polar substances in the pure form (see Fig. 5). In some cases, as for instance for incompletely hydrated benzanthrone (Fig. 6), the profile obtained reveals lower viscosity near the wall, which is presumably connected References
p. 289-290
B. v. DERYAGUIN et al.
284 with the ring structure orientated
of the molecules. This structure
horizontally
VOL. 1 (1()57/58) enables the molecules to become
near the wall, and this leads to a lowering of viscosity,
Fig. =j. Velocity profiles of esters on the surface of steel, obtained by analysis of film profiles after blowing. (I) Amy1 sebacate; (2) Uibutylphthalate.
Fig. 6. Velocity profiles of incompletely hydrogenated benzanthrone on a glass surface, obtained during blowing.
DISCUSSION
Inasmuch
as viscosity
that structural molecules
is a structure-sensitive
peculiarities
are present
property
occur in the boundary
in the minutest
affected by minute concentration
concentration.
of surface-active
of a definite monolayer.
cosity, and hence also in the structure monolayer
substances
molecular
solvent,
solutions
at distances up too. I 1’1,proves that the orientated the orientation
this influence
extends
is particularly
of chloroparaffins
supported
by the results
in vaseline
oil. The
the velocity profile point to the fact that the structure can change abruptly
at a certain
clusion made previously The results obtained rather complicated of surface-active points
for fatty
of adjacent
molecules
of
throughout
hundreds
of
(Fig.4)
jagged
of the experiment curves
of the boundary
representing
layers of liquids
from the solid wall; this confirms of the adsorption
the con-
of vapours of
point. acid and ether
(Fig. 7) solutions
and deserve special consideration.
in vaseline
oil are
In the case of weak concentration
molecules the velocity profile assumes a rather irregular shape, which to the structural
solvent. This heterogeneity References ~3.289-290
distance
in the case of measurement
volatile liquids near the saturation
evidently
with
of sudden changes in the vis-
layers.
This conclusion with
and that
is
indicates that the action
the film, but is connected
The appearance
is in some way able to affect
the non-polar
reveal
The fact that the structure
of the latter cannot be due to their presence throughout the formation
the results obtained
layers of a liquid in which polar
heterogeneity
can be explained
of the corresponding
by the circumstance
layers of the
that different
struc-
VOL. 1 P957/58)
Fig. 7. Velocity blowing.
MECHANISM OF BOUNDARY
LUBRICATION
285
profiles of solutions of stearic acid and amyl sebacate on a glass surface during
O/b stoaric acid; t = 18°C. (2) 0.00054 o/, stearic acid; t = 14%
(I) o.oooo~~
(3) O.OOZ~%, amyl sebacate; f = 18°C. (4) 0.0060 o:, amyl sebacate ; t = r VC.
tures of the wall-adjacent layer of the solution are possible, depending on the orientation of the adsorbed molecules, which in turn may vary over the surface. In a number of cases, if the layer is left undisturbed, we failed to observe any further appearance of irregularities in the profile, and in fact the existing ones were smoothed out. It follows that the film profile obtained after blowing-off assumes its jagged shape as a result of deformation during laminar flow and not because of its the~odynamic instability. The effect is similar to that of the formation of slip bands in plastic deformatiorP and points also to the heterogeneous structure of the boundary layer. At the same time the fluidity preserved by the boundary layer even under the small shear stress caused by the air stream shows that the mechanical properties of a liquid layer differ greatly from those of a plastic solid body, although there are apparently some exceptions to this rule; moreover, the resistance of the boundary layer to thinning points to the difference between its properties and those of the bulk liquid. It may be supposed that the boundary lubrication layer is in a state similar to that of liquid crystals with a structure in which the main part is played by the orientation of rod-shaped molecules.
Fig. 8. Photograph of the interference pattern formed on a steel surface when blowing-off a polymer of vinyl butyl ether. M = 600; z c 48 min; n.P = so mm Hg; t = 20%; C = IOO o& (M is molecular weight, z is blowing-off time, AP is pressure drop, t is temperature, C is concentration). The direction of the air jet: 4. References
p. 289.zgo
286
R. V. DERYAGUIN
et al.
VOL. 1 (r957158)
The chief difference from liquid crystals is that in the latter the solid wall causes an orientation spreading at an indefinite distance, while with liquids the distance is quite definite and small. The intermediate case may include some liquids and solutions containing polymers. As we have already shown, in this case, one can get an idea of the viscosity distribution in the proximity of the solid wall from the position of the interference fringes of equal thickness. Fig. K is a photograph of poly (vinyl butyl ether) with a molecular weight 600, which was kindly supplied by Professor M. F. SHESTAKOVSKY. The greater density of the fringes An
analysis
in the thin part of the layer of the
wall, represented The stable
photograph
graphically
complex
phenomena
thickness
are observed
yields
changes
upon the addition in detail in original
showing photographs (Figs. IO and
II)
profile
of the viscosity
of the
film
and the appearance of various
there.
on the solid
of zones of un-
polymers
two typical
to mineral ourselves
to
cases.
Fig. II. Photograph of interference pattern formed on a steel surface when blowing-off a polymer solution of vinyl butyl ether in turbine oil. M = 3,850: z = 3 min; @.P = 70 mm Hg; t = 2oT; c = o,op(,.
01: STATIC FRICTION THE TWO-TERM
vinyl
papers 1’ we shall confine
representing
Fig. IO. l’hotttgraph of interference pattern formed on a steel surface when blowing-off a polymer solution of vinyl batyl ether in turbine oil. M = 2,100; z = 12 min; hP = 20 mmHg; t = xl”(‘: I: = oq~;,.
THE NATURE
to an increase
in Fig. 9. of viscosity
oils. Sinct: they are described
points
the velocity
IN BOUNDARY
LUBRICATION
LAW OF FRICTION
The results obtained indicate the peculiarities in the structure and fluidity of the boundary layers of lubricating liquids and hence lead us to conclude that these pecuReferences p. zS9-290
VOL.
1 (ImM)
MECHANISM OF BOUNDARYLUBRICATJON
287
liarities must be taken into consideration in interpreting the phenomena of boundary lub~cation and in working out their theory. Owing to lack of space we shall not dwell on these questions, especially since the results of the investigations -in particular those concerning static and kinetic disjoining pressure in thin liquid film+‘, the kinetics of the thinning of boundary layers between two solid bodies in contact with one anotherm, the interrelation of kinetic friction and molecular orientatio#, etc. - are discussed in a number of other papers. We shall limit ourselves to a consideration of the following impo~ant problem. If the boundary lubrication layer does not possess a yield value, as is indicated by the results of application of the blowing-off method, then how can one explain static friction between solid surfaces, separated by a polymolecular layer? Yet, the existence of static friction in such cases has been convincingly proven in a number of experimental studies22. We believe that the correct auswer to the question can be found only in the two-term friction law previously formulated by ~$3 and experimentally provedsa. The validity of this law for the interpretation of the mechanical properties of liquid and solid lubricating films has been proved in the work of DERYAGUINANDLAZAREV~~. According to the two-term law of friction, the force of static friction F equaIs:
F=p(N-+-SpJ=,xNfSO
where p is the “true” coefficient of friction, N the load, S the area of real or molecular contact, and e0 the adhesion force per unit area of real or molecular contact. This formula, which in form but not in physical content is to some extent analogous to the two-term Coulomb Law (deduced empirically), expresses the idea of the double origin of the force of friction. One part of this force is caused by external pressure N, the other part by the molecular interaction of the surfaces. The law also reflects the divergence between the views of the present authors and BOWDEN,who interprets the friction phenomenal by means of the second term of the formula alone, which amounts to the assumption that the “true” coefficient of friction p equals zero. Thus, according to BOWDENand his school, friction depends on the load N only insofar as the latter increases the area S of true or molecular contact between the bodies. This point of view, first formulated by TERZAGHP, is in contradiction with experiments in which the force of friction increases with the load in strict accordance with the linear law, despite the fact that either the area of molecular contact cannot undergo essential changesz5 or that this increase in the area is slower than that of the loadz’. To this end we investigated the friction of a plane paraffin block on glass. In order to obtain a large area of contact that was not changed throughout the experiment, the paraffin was preliminarily melted while in contact with the glass surface and then allowed to solidify. In order to be certain that sliding took place not between the layers of paraffin, but on the paraffin-glass interface, the latter was covered with a multih%ferences p. 289-290
2633
et al.
l3.v. DEKYAGUIX
molecular
layer of the acid barium
method of BLODGETT and 1.3 represent dependence
AND
or calcium
dependence
bears out the correctness
The circumstance
of friction,
proves that the macroscopical
to the
of the straight
is independent
asperities
on the load. This
law of friction. lines, which is equal
of the number of molecular
layers n
of the glass surface have very little influence
of friction.
0
200 Kg. f1. 12riction force plottcil against load for paraffin on glass. tzubricant : multimolecular PJodgett-Langmuir layers of acid calcium soap with yt molecular layers. .,n=I;o,~2-~3;X,nIS~r;~,12=Gr.
of layers R. increases
__.M 200
400
6%~~
Fig. I 3. Friction force plotted against load for paraffin on glass. Lubricant: multimolecular Blodgett-Ismgmuir layers of barinm soap with ?z molecular layers. 0, n = j; 0,11 = 7; x, 12= II.
The second term in the linear law, according as the number
acid, according
of the force of friction
of our two-term
that the angle of inclination
to the true coefficient on the coefficient
salt of stearic
The number of layers PZvaried from I -61. Figs. 12
LANGMUIR.
the observed
VOL. 1 (1957/58)
to the above data, declines somewhat
from 7 to 9, and remains constant
with further
increase of nyl.This decrease in the value of the second term with increasing of the lubricating
layer can be easily explained,
assuming that in thicker lubricating
according
layers the molecular
thickness
to P. i\. REHBINUEK,
attraction
by
between the glass
and the paraffin ceases to have effect, while the adhesive force S depends only on the interaction
between the molecules of the lubricant
Another method of refuting the one-term tion consists in studying the areas of contact, remaining
the influence
and the paraffin.
law and proving the two-term
with the nature of the surfaces and the conditions
Hu compared
a metal surface and a glass point with radius of curvature
in one case, and between curvature
of
of measurement
the same.
This idea was tested by U. TOPOROFF in our laboratory. between
law of fric-
on friction of a variation in the deformability
a metal surface and a thin-walled
equal to several centimeters.
The coefficient
the friction
of about r/lo mm
glass ball with radius of
of friction on the unlubricated
metal was always greater in the second case than in the first. Hut when the metal surface was covered by an adsorbed monolayer This experiment
of stearic acid this difference
furnishes proof of the correctness
In the case of a thick layer of boundary
of the two-term
lubricant,
disappeared.
law of friction.
we have the reverse case, when
the second term is equal to zero. In fact, in the case of boundary
lubrication
the second
VOL. 1 (1957/58) term, if referred number
MECHANISM OF BOUNDARY LUBRICATION
to unit area, should
of cases of boundary
obtained
by the blowing-off
friction should be exactly consideration
lubrication method.
the yield
the observed essentially resistance
phenomena.
we must take into
the presence
with the experiments,
The conclusion drawn, that
deserves
to shear in a thin boundary
load on the film, and appears
lubricating
and disappears
the only explanation
with all the experimental
of static friction,
for the one-term
friction
lubrication.
than aformaldeductionfrom
though empiric in origin, contains an
further
investigation
and proof:
film is brought
viz. that
about by a normal
with the load. I,ack of space does not
allow us to present further evidence of this important furnishes
by the results
our point of view, however,
are, of course, somethingmore
new assumption
in a certain
in that case, static
law of AMONTON, which is strictly valid in cases of boundary The above considerations
which
to current views?
not only explains
a basis, in accordance
value 0,
equals zero, as is demonstrated
According
zero. From
the first term, which
but also provides
express
289
of the mechanism
principle,
of boundary
which, in our opinion, lubrication
consistent
data.
REFERENCES I;. I’. BOWDEN AND I). TABOR. The Friction and Lubrication of Solids. 2nd ed.. Oxford TJniv. Press, London, 1954. B. V. DERYAGUIN. N. N. ZAKHAVAEVA. M. M. KUSSAKOV. \‘. P. LAZAREV AND M. M. SAMYGUIN. Akad. Nauk. S.S.S.R., T%dy I Vsesoyuz. Konf. Treniyu i Iznosu Mashinakh, I (1947) 103-139;
I4
I5
I8 I7 Is
3 (1949) 101. B.V. D~~~~~~~~,ChtoTakoyeTreniye? (Whatisfriction?) Acad. Sci. U.S.S.R., 1951, (in Russian). A. S. AKHIIIATOV, Trudy 2 Vsesoyur. Konf. Tveniyu i Iznosu Mashinakh, 3 (1949) 133, 144. 1. C. HENNIKER. &US. Modern Phvs.. 21 (14491 xw. &. V. DERYAGUIN, Trudy Vsesoyu~. Konf. Kolloid. Khim., (Kiev) (1952) 26. Strojeniie i Fizicheskiie Svoistva Veschestva v Zhidkom Sostoianii, (Materialv Soveschaniia, ” Iqg?, -“I I v Kijevk), Kiev 1lnivy Press, Kiev, 1954, p, r41. B. V. DERYAGuIN, l‘?‘ans. Faraday Sot., 36 (1940) 203. B. V. DERYAGUIN, Izvest. Akad. Nazlk. S.S.S.R., Ser. Khim., 5 (1937) 1153; Acta Physicochim. U.R.S.S., 10 (‘939) 333, Kolloid. Zhur., 6 (1940) 291, 7 (1941) 285. B. V. DERYACUIN AND L. D. LANDAU, Acta Physicochim. U.R.S.S., 14 (1941) 633; J. Exptl. Theoret. Phys. (U.S.S.R.), II (1941) 802; 15 (1945) 662. E. VERWEY AND J. OVERBEEK, Theory of the Stability of Lyophobic Colloids, Elsevier Publ. Co., Amsterdam, 1948. J. M. GLAZMAN AND I. M. DYKMAN, Doklady Akad. Nauk S.S.S.R., IOO (1955) 299. S. BASTOW AND F. BOWDEN, Proc. Roy Sot. (London), r51 (1935) 220; B. V. DERYAGUIN, Nature, 135 (1935) 828. F. BOWDEN AND S. THROSSEL, Proc. Roy Sor. (London), A 209 (1951) 297. B. V. DERYAGUIN AND 2. M. ZORIN, Doklady Akad. Nauk S.S.S.R., 98 (1954) 93; Zhur. Fiz. Khim., 29 (1955) IoIo, 1755; 2nd Intern. Congr. Surface ActiviJy, London, 1957. B. V. DERYAGUIN AND M. M. SAMYGUIN, Akad. Nauk. S.S.S.R., Otdel. Tekh. Nauk., Inst. Mashinovedeniya, Soveschanie po Viazkosti Zhidkost. i Kolloid. Rastvorov. I (1941) 59. B. V. DERYAGUIN AND N. A. KRYLOV. dkad. Naztk. S.S.S.R.. Otdel. Tekh. Nauk., Inst. Mashinovedeniya, Soveschanie po Viazkosti Ziidkost. i Kolloid. Rastv’orov, 2 (1944) 52. B. V. DERYAGUIN, G. M. STRAKHOVSKI AND D. S. MALYSHEVA. Zhur. Eksbtl. i Teoret. Fiz.. 16 (1946) 171; Acta Physicochim. U.R.S.S., 19 (1944) 541. B. V. DERYAGUIN AND E. F. PICHUGUIN, Akad. Nauk. S.S.S.R., Trudy 2 Vsesoyuz. Konf. Treniju i Iznosu Mashinakh, I (1947) 103; 3 (1949) IOI. B. V. DERYAGUIN AND V. V. KARASSEV, Doklady Akad. Nauk. S.S.S.R., 62 (1948) 761; Kolloid. Zhur., 15 (1953) 365; Doklady Akad. Nauk. S.S.S.R., IOI (1955) 289. B. V. DERYAGUIN AND N. N. ZAKHAVAEVA, Trudy Konf. po Vysokomolekular. Soedineniyam, Akad. Nauk. S.S.S.R., Otdel. Khim. i Fiz. Mat.-Nauk, 6th Conf. 1949. p. 233. N. F. SJUTKIN, Doklady Akad. Nauk S.S.S.R., 96 (1954) 503.
B. V. DERYAGUIN
290 l* B. V. DERYAGWN
et at.
VW-.- f
AND E. V. OSUKHOV, Kolloid.Zhu:hur., I (1935) 385; Acta Physicwhim.
fI957/58j U.&S..%,
5 (1936) 1.
B.V.~~RYAGUINAND~.M.
Acta Physicockim. 6 (1940) 291.
U.R.S.S.,
KussAxoY,~~u~s~.AR~~. IO (1939) 25, 153; Trans.
Nattk,S.S.S.R.,Ser. Khim.,5(1937) 1x19; Faraday Soc.,36 (1940) 203; Xoltoid.Zhw.,
B. V. DERYAGUIN, M. M. KUSSAKOV AND L. S. LEBEDEVA, Doklady A kad. Nauk S.S.S.R., 23 (1939) 670. 3. V. DERYAGUIN,M. M. KUSSAKOV AND ASTITIJEVSKAJA, Kolloid.Zhur.,Is (1953)416. *O A. D. MALKINA AND B.V. DERYAGUIN, KolEoid. Zhw., 12 j1950)431. 21 V. I?. LAZAREV AND B. V. DERYAGUJN, Zhur. Tekk. Fiz., 23 (1953) 1977. 22 B.V.DERYAGUIN,N.N. ZAKHAVAEVA,M.M. Ku~sAKov,~~.~'.L~~zAREvAND~~.M.SAMYGU~~. Akad. Nauk. S.S.S.R., Tmdy 2 Vsesoyus. Xonf. Treniyu i Imoszc, 3 (1949) 144; Doklady Akad. Nauk. S.S.S.R., 30 (1941) rrg. zs B. V. DERYAGUIN,~. Physik, 88 (1934) 661; Zhur. Fiz. Khim., 5 (1934) 1165. 24 B. V. DERYAGUIN, Doklady Akad. Nauk S.S.S.R., 3 (1934) 93. B. V. DERYAGUIN AND V. P. LAZAREV, Kolloid. Zhur., I (1935) 293. ts B. V. DERYACWN AND V. P. LAZAREV, Akad. Nauk S.S.S.R., Trudy 2 Vs~soyuz.Kon~,Tre~aiyui Iznosu Maskinakh, 3 (1949) 106. ee TERZAGHI. Erdbau~echa~~k. Wien, 50 (1~251: ~ - _,J. J. BIK~RMAN AND E. K. krDeAi.,-Phil. &fag., 27 (1939) 687; F. BOWDEN AND D. TABOR, Proc. Roy. Sot. (London), A 169 (1939) 391. 27 J. V. KRAGELSKI, Zhw. Tekh. Fiz., x2 (1942) 726. aa W. HARDY, Proc. Roy Sot. (London), A ro8 (rgz5) I.
Received for review August, '957 AcceptedNovemberz5, 1957
1 bv/s8)
277
WEAR
THE MECHANISM OF BOUNDARY LUBRICATION AND THE PROPERTIES OF THE LUBRICATING FILM SHORT-
AND
LONG-RANGE BOUNDARY
ACTION
IN THE THEORY
OF
LUBRICATION
B. V. DERYAGUIN Corresponding Member of the Academy of Sciences of U.S.S.R. in collaboration with V. V. KARASSEV, Laboratory
of
N. N. ZAKHAVAEVA
AND
SwfacePhenomena, I?asfitute of Physical Chemistry,
V. P. LAZAREV Academy of Sciences of U.S.S.R.,
Moscow (U.S.S.R.)
Two versions of the blow-off method are described, by means of which the dependence of the viscosity of oils and other non-volatile fluids on the distance from the solid wall can be measured, and the viscosity localized with an accuracy of IO A. In the case of non-polar specially purified vaseline oil the viscosity remains strictly constant to a distance of the order of IO-’ cm from the wall. The addition of polar additives causes changes in the viscosity near the wall, In a number of cases the viscosity changes discontinuously at some distances of the order of IO-~ to 10-5 cm from the wall. In the case of polar liquids the viscosity may rise or fall on approaching the wall, depending on the molecular structure. The results obtained prove that the solid wall is capable of altering the orientation of the molecules in adjacent layers of the liquid up to 10-5 cm thick, and even up to IO-~ cm thick in the case of polymeric liquids. This effect plays a substantial part in the mechanism of boundary lubrication, since oiliness always disappears if it is absent. In conclusion, an examination is made of the mechanical properties of the boundary lubrication layer which explain both the existence of static friction and the observation of the two-term friction law derived by DERYAGUIN from the molecular theory of friction. The general conclusion is the impossibility of accounting for the phenomenon of boundary lubrication without taking into consideration the specific properties of the polymolecular boundary layers of liquids.
2 USA MMEN
FASSUNG
Zwei verschiedene Varianten der sog~nannten i~bblas-methode werden beschrieben. Diese erlauben es die Abhangigkeit der Zahigkeit van &en und anderen nicht-fi~chtigen Fliissigkeiten als Funktion des Abstandes van der festen Wand zu messen und die Zahigkeit mit einer Genauigkeit bis auf ro A zu lokalisieren. Fur ein nichtpolares speziell gereinigtes Vaselinijl bleibt die Zlhigkeit streng stabil bis zu einem Abstand you der Wand van der Grossenordnung TO-~ cm. Zufiigung polarer Substanzen zu dem 01 hat eine Veranderung der Zahigkeit in der N&he der Wand zur Folge. In einer Reihe van Fallen vergndert sich die Zghigkeit sprungweise und zwar beieinem Abstand van der Wand van der GrBssenordnung r~-~-ro-s cm. Ftir polare Fliissigkeiten kann die Zahigkeit abhangig van der Struktur van Molekiilen, entweder zunehmen oder abnehmen. Versuchsergebnisse zeigen, dass eine feste Wand die Orientierung der Molekiile van Fhissigkeitsschichten bis auf einen Abstand van 10-s cm und fur polymere Fltissigkeitensogar bis auf IO-~ cm beeinflussen kann. Diese Erscheinung spielt eine bedeutende Rolle in dem Mechanismus der Grenzschmierung denn, wenn sie nicht auftritt verschwindet such regelmgssig die Schliipfrigkeit. References p. 289-290
B. V. DERYAGUIN et al.
278
VOL. 1 (Iq57/58)
Zum Schluss wird die Frage der mechanischen Eigenschaften der Grenzschichten van Fliissigkeiten besprochen, mit deren Hilfe sowohl die Existenz der statischen Reibung als such die Giiltigkeit des binomialen Reibungsgesetzes, das DERYAGUIN aus der molekullren Theorie der Reibung ableitete, erkllrt wurden. Als allgemeines Ergebnis der Untersuchungen wird festgestellt: Die Erscheinung der Grenzschmierung sind nicht zu erkllren ohne die spezifische Eigenschaften der polymolekularen Grenzschichten van Fliissigkeiten in Betracht zu ziehen.
INTRODUCTION The far greater fluid friction interaction
complexity
between
the solid
with them, an interaction factor
in the case of friction determines
velocities film
studied
at which
boundary
difficult,
ary friction
the properties
friction,
film
film is thin, whereas
in contact
viscosity
is of lesser importance
of boundary
with
by the molecular
lubricating
static
of the properties
the mechanism
as compared
of the film. This is the dominant
and especially,
investigation
out in detail
which
at the small
friction,
usually
of the boundary
lubrication
is noticeably
substance they
cation,
beyond cannot
affected
takes
lubricating
has been insufficiently
point
and by a number According
by new and original
methods,
molecular
layers
of a liquid
properties
(as compared
with
surface
OVERBEEK~, directly
related
as regards
GLAZMAN
are not important
the influence containing
themstate
of boundary
lubri-
in this respect.
by the authors
of the present
of experiments
of the solid
polar
carried
wall extends
molecules,
those of the bulk phase)
of views
producing
that have
the experimental preference
A comprehensive liquids. out by
AND DYKMAN~
such behaviour
survey
paper”,
out mostl!
through changes
many in their
a considerable
action
which
be given
effect
conception
(oiliness).
boundary
of
to the theory
ourselves oil
of
been publish-
as by VERWEY
we shall confine of
in the
investigations
have already
of an analogous
properties
show that
to the conception
should include
the author6J7 as well
and others, and
data,
must
As such surveys
the application
worked
to their lubricating
p. 289-290
on the phenomena
based on a number
for different
of colloids,
concerning
References
action.
effects
edPIb, particularly of the stability
surfaces
of the lubricating
of lubrication. divergence
the most varied
The layers
scientist9.
time is now ripe to summarize
above-mentioned
lubrication. that bound-
are in a state so close to the volume
has been expressed
Soviet
of the friction
on them.
influence
their properties of view
of other
on the mechanism
layer
any specific
to their conception,
long-distance
adsorbed
of boundary
from the assumption
only by the properties layers
the first molecular exercise
and therefore
A different
views on the mechanism
by BOWUEN~, proceeds
selves or of the monomolecular
closely
and the boundary
of fluid friction
there are two opposing
The first, worked
The
friction
up to now.
At present
that
of boundary
is in the main affected
when the lubricating
the phenomena
Since experimental is very
surfaces
which modifies
alone place.
of the phenomena
is due to the fact that the former
films
AND
to data as
are
MECHANISM OF BOUNDARY
VOL. 1 (1957/58)
A STUDY OF VISCOSITY IN THIN BOUNDARY
LUBRICATION
279
FILMS OF LUBRICATING
OILS AND OTHER
ORGANIC LIQUIDS One of the methods to measure
of establishing
their viscosity,
ties involved,
However,
the majority
the specific
properties
owing to the considerable
of the previous
not reached clear and comprehensive
comparison
slit between
of direct (optical)
the value obtained
less than that obtained of the width concluded
parallel
to flow of the liquid in the slit and
by light interference.
As the average
error in the determination
contradict
BASTOW
the measurements
BOWDEN
AND
that point to changes
of the same liquids at a distance of over 0.2 p from a solid wall.
One could agree with the authors if they had confined themselves clusion. However,
they assumed
without
sufficient grounds
also do not take place in thinner liquid layers adjacent allow of an opposite obtained,
on a
the plane with
width proved to be on an average 0.1-0.2 p
of the slit was of the same order of ma~itude,
in the viscosity
by the
studied the
based their conclusion between
is
or have
is deserved
the viscosity,
of the gap-width
resistance
The computed
that their experiments
difficul-
Special attention
planes. They
determination
from the measured
the value of its bulk viscosity.
films
experimental
studies either have been erroneous
conclusions.
work of BASTOW AND BOWDEN~~, who, in order to determine radial flow in a narrow
of boundary
BOWDEN
interpretation. based
denial of the existence
Despite
his further
of peculiar
properties
in viscosity
to walls. Yet their experiments
the arbitrary
investigations
to the above con-
that changes
extrapolation
of boundary
of the results
lubrication
in the wall-adjacent
liquid
on the
layers
at a
distance of less than 0.1 p. Returning vapours
to the same subject
on smooth
surfaces,
this paper11 too, BOWDEN’S experimental
conclusions
data, which in themselves
of surface action, inasmuch only up to the relative gations of vapour formed
in his work
BOWDEN
adsorption
of
tried to confirm his point of view. However,
on the polymolecular
in
constitute
an ungrounded
are not suitable for an estimation
as the investigation
of vapour
adsorption
pressure of 0.95. It is not surprising,
adsorption
in the immediate
by ZORIN AND DERYAGUIN~~,
extrapolation
proximity
using an optical
therefore,
of the
of the range
was carried out that the investi-
of the saturation
point per-
method, led to opposite
results
and conclusions. We shall now consider the results of direct measurements layers of organic
liquids,
original
These
method.
oils and polymers, results
performed
point disputably
of viscosity
in boundary
by a precise and completely
to the fact that in the boundary
layers of up to 0.1 p (and more, in some cases) the viscosity
has a value differing
from
that in the bulk.
MEASUREMENT
OF VISCOSITY
The shortcoming
IN BOUNDARY
LAYERS
BY THE “BLOW-OFF”
of all the methods hitherto employed
ity in thin films lies in the circumstance
in the ~ves~gation
of viscos-
that these methods, even if we disregard
other defects and sources of error, yield only average
effective
in the slit or in a layer of given thickness la. Some methods, References p_ 289-290
METHOD
their
values of the viscosity
as for instance those based
280
rt al.
IS. V. 1)ERYAGUIN
‘.‘OL. 1 (1957/58)
on the flow of a liquid through porous medial”, yield results that are even less definite, since the liquid passes through irregularly layers is completely The
“blow-off”
tion of viscosity
shaped pores for which the thickness
of the
indeterminable. method
deLised by the authors1”G6 permits
as a function
an exact
determina-
of the distance from the solid wall, the latter being deter-
mined to within & 5 A. EXl’ERIhIl
One of the sides of a plane-parallel of the liquid under investigation the slit produced
a laminar
METHOI)
slit 0.2 mm wide (Fig.
over IO /Lthick. A constant
I)
was covered with a film
stream of air blown through
flow in the film, giving it a gently sloping wedge-shaped
form. Owing to the fact that the flow of the film was caused solely by the shearing stress of the air stream,
which was uniformly
film, the flow was one-dimensional the liquid particles
depended
not on any other coordinates. a sheared deck of ordinary
distributed
as well as laminar.
exclusively
over the whole surface of the In other words, the velocity
on the distance
from the solid wall (z) but
Thus the flow in the liquid layer was similar to that in
playing cards. An elementary
layer of the liquid, parallel
to the slit wall, moved as a whole parallel to the wall with a velocity creasing according
to a definite function
This result is caused by the fact that, state of stress in the film is homogeneous, all points. If the viscosity
of the distance
owing to the absence and thcreforc
I( = u (z), in-
to the wall. of volume forces, the
the shear stress is the same at
w(‘rc the samcl at all distances
from the solid wall too, then
it would follow that the velocity gradirnt d~/c)zwould also be cverywherc II would be proportional
the same, and
to 2. In this case the film would assume the shape of the exact
wedge bounded on top by an inclined plane ; and vice versa, any variation of the viscosity strictly
on approaching
wedge-shaped
the wall would bring
after blowing-off.
a definite scale the velocity
As proof of this, it is sufficient and the axis OZ perpendicular Refe~wcrs/I, 289-290
from
thts
film profile represents
on
profile of the liquid near the solid wall.
“5
”
/////////
to point out that if we place the origin of the coordi-
nates (0) on the wetting perimeter at a distance
in the value
a deviation
near the solid wall from the profilr
In fact, the resulting
2’ ‘; /
situated
about
form of the film.
Thus we can judge the \-ariations of viscosity of the film obtained
of
(Fig.
I)
with the axis OX directed
along the wall,
to it, then the abscissa x of a point of the film profile,
h from the wall, expresses
the distance
travelled
by the corrtx-
MECHANISM
VOL. 1 (1957/58) sponding elementary travelled
LUBRICATION
layer of the liquid during the blowing-off
is proportional
of the film represents Applying
OF BOUNDARY
to the velocity:
the velocity
Newton’s
time t. But the distance
x = UZ; from which follows that the profile
profile in the liquid layers near the solid wall.
law of viscosity,
of the liquid at a distance
281
we find the following formula for the viscosity
h from the wall: II
=
Tr
d!
(1)
dx’
The right-hand
part of the formula contains the steepness dJz/dx of the film profile at
the spot where the thickness
is equal to h. T denotes
liquid, caused by the air flow. By determining off, we can establish
the law of variation
the shear stress in the layer of
the film profile obtained
of viscosity
as a function
the solid wall. Thus our main problem is to determine film in the interval the influence Depending thickness
of thickness
on the nature
of viscosity
substances
in which the variation
takes place under
chosen
oils the layer is much thinner:
greatly
to measure
depending on the object under investigation.
estimate
of the velocity
obtained
by photographing
A far more sensitive
the thickness
the interference
parameters
of the elliptical
polarization
for determining
made it impossible requiring
obtained
by
in measuring
the film thickness
the thickness
of the
from various regions of
in various regions of a film of
to apply the usual polarization
and beam
of the reflected light, which made the accurate
deter-
impossible.
This difficult problem has been successfully of the reflected
The narrowing
goniometers
of the incident
of its state of polarization
solved by means of a special modulation
polarized light, using a photoelectronic
As a detailed description
shall confine ourselves
the
near the wall may be
based on the determination
of the light reflected
wide beams.
leads to a lowering in the intensity
method of analysis
cm. Hence,
In the first case a fairly accurate of viscosity
and precise method is necessary
of observation
IO-~
of the film will vary
fringes of equal thickness,
liquids and oils. We chose a method
the film. The necessity
about
light17 (see below).
in common
and an oscillograph.
layer
liquids and solutions,
and profile
profile and the distribution
viewing the film in monochromatic
unequal thickness
In polymer
may extend to distances up to 7-8 p from the wall. For monomer
and common
methods
mination
in viscosity
of the liquid and the solid wall, the corresponding in order of magnitude.
optical
methods
of the distance from
the profile of a very thin
of the solid wall.
may vary greatly
variations
exactly
after blowing-
to describing
multiplier
can be found in the original paperls, we
the scheme of the set-up (Fig. 2) and the method
of measurement. The slit (A), illuminated isolating
by means of an object-lens on the measuring
limb;
axis with a frequency electronic
by a Hg lamp, under
the line il = 5769-5790
multiplier,
References p. 289-290
A, was projected
(L) ; a, aperture
PZ, Polaroid of about
I
V a.c. with a light filter
(F,)
into the film under investigation,
diaphragm;
set in rotation rev/set.
120
P1, iodine-quinine
around the reflected
The modulated
the voltage on which was increased
Polaroid, beam as an
light fell on the
photo-
by an amplifier with an RC
282
I:. T’. L)ERYAGLUN
Fig. 2. Optical
filter and transmitted
axmgcment
to the cathode
presence or absence of the modulation K, and K, are two quarter-wave
et (Ilk
VOL.
fnr determining
oscillograph
velocity
1
(1957’58)
profllr.
0 serving
as an indicator
of the
in the photocurrent. plates;
the principal
axes of K, are directed at
an angle of 45” to the plane of incidence, the plate K, can be rotated and is on the measuring limb. D, an D, are two thick calcite plates cut not quite parallel axis;
DP serves
sensitivity
to depolarize
of the photocathode
serves to eliminate
the beam in order to eliminate to the direction of polarization
the coherence
With the decoherenter
of
and .L components
; D,, the “decoherenter”,
D, in the “in” position to prevent modulation,
prevent
beam become
a renewed modulation
equal. With the decoherenter of the photocurrent
and i
an angle of 45” with the plane of polarization
it is necessary
The technique
of measuring
components to
and sufficient
to
so that they make,
of the light transmitted
are made in the usual manner with the azimuths
it is necessaq-
in the “out” position
orient the optical axes or the plate K,, which serves as an analyzer, Calculations
of the
of the beam.
and sufficient to rotate the polarizer P, to such a position that the of the reflected
to the optical
the influence
by plate K,.
obtained16.
was as follows.
When the film on the surface of the steel plate had been blown off by an air current during time t, the apparatus micrometer measured.
was demounted,
the plate with the film was set on a
slide, and by moving the latter the film thickness After that, a graph was plotted representing
in various regions was
the film profile.
As the films of some liquids and solution were not very stable and evinced a tendenc! to disintegrate
into drops, a different procedure was applied in this case. The thickness
was measured not after but during blowing-off line. For that purpose the chamber urements
the following modification
at a definite distance x0 from the wetting
lid was made transparent. of the technique
For rapid optical meas-
was particularly
convenient.
The oil film was smeared on the underside of a glass prism that served as a lid for thca blowing-off
chamber,
internal
reflection
parallel
and normal
appeared.
the angle of incidence
of the polarized light being 45” ; complete
was thus observed ; the amplitudes to the plane of incidence
of the component
remained
constant,
In the presence of the film this shift varied, depending
oscillations
but a phase shift on the thickness
of
the film. The advantage
of the abo\c-mentioned
azimuth needs to be measured, By plotting measurement lteferences
the thickness
technique
lies in the fact that
only one
instead of two.
of the film h against the value C
x,/t the results of the
made according to the second variant were brought to a form representing
9.289-290
voL. 1 (r957/58)
MECHANISM OF BOUNDARY LUBRICATION
283
the film velocity profile in the proximity of the solid wall, as was done in the first variant (t is the period of time from the beginning of blowing-off to the moment of measuring; h is the thickness measured at that moment). Obviously the abscissa expresses the velocity of the layers at a distance /%from the wall. Thus the graph gives the velocity profile. Its x,, was difficult to determine; we usually plotted r/t on the axis of the abscissa, which resulted in the same velocity profile but on an arbitrary scale. Figs. 3, 4, 5, 6 and 7 show the results obtained by V. V. KARASSEV; Figs. 3 and 5 were obtained
by the first method,
the rest by the second.
RESULTS OF THE MEASUREMENTS Fig. 3 refers to non-polar procedure
Vaseline oil; the polar impurities
worked out by Professor
ELOVICH, involving
were removed by a special
the use of a platinum
catalyst
at high temperature.
Fig. 3. Velocity profile for specially purified vaseline oil on a steel surface, obtained by analysis of film profile after blowing; t=zo%.
Fig. 4. Velocity profiles of 0.01% solutions of chlorine derivatives of tetracosane in vaseline oil, on a steel surface, obtained in the process of blowing. (I) Monochlorotetracosane solution, t = 23°C; (2) Trichlorotetracosane solution, t = 18.6’C; (3) Hexachlorotetracosane solution, 1 = 25%
We see that the viscosity of non-polar Vaseline oil remains a constant value equal to its value in the bulk up to a distance of about IO-~ cm from the wall. Similar results have been obtained dozens of times, which proves them to be correct beyond any reasonable doubt. Nevertheless, the addition of fatty acids or ethers in minute concentrations can disturb the linearity of the velocity profiles. With an increase in concentration the film profile becomes irregular and jagged, while a still greater increase of the concentration makes the film unstable: it no longer wets the surface, which is covered with an adsorbed film of a surface-active substance. Fig. 4 represents the velocity profile when a monochloroparaffin, trichloroparaffin or hexachloroparaffin are added to the Vaseline oil in a concentration of 0.01%. In this case the form of the profile changes and assumes a characteristic break of about 0.025 ,uin thickness. Similar results are obtained in the case of some polar substances in the pure form (see Fig. 5). In some cases, as for instance for incompletely hydrated benzanthrone (Fig. 6), the profile obtained reveals lower viscosity near the wall, which is presumably connected References
p. 289-290
B. v. DERYAGUIN et al.
284 with the ring structure orientated
of the molecules. This structure
horizontally
VOL. 1 (1()57/58) enables the molecules to become
near the wall, and this leads to a lowering of viscosity,
Fig. =j. Velocity profiles of esters on the surface of steel, obtained by analysis of film profiles after blowing. (I) Amy1 sebacate; (2) Uibutylphthalate.
Fig. 6. Velocity profiles of incompletely hydrogenated benzanthrone on a glass surface, obtained during blowing.
DISCUSSION
Inasmuch
as viscosity
that structural molecules
is a structure-sensitive
peculiarities
are present
property
occur in the boundary
in the minutest
affected by minute concentration
concentration.
of surface-active
of a definite monolayer.
cosity, and hence also in the structure monolayer
substances
molecular
solvent,
solutions
at distances up too. I 1’1,proves that the orientated the orientation
this influence
extends
is particularly
of chloroparaffins
supported
by the results
in vaseline
oil. The
the velocity profile point to the fact that the structure can change abruptly
at a certain
clusion made previously The results obtained rather complicated of surface-active points
for fatty
of adjacent
molecules
of
throughout
hundreds
of
(Fig.4)
jagged
of the experiment curves
of the boundary
representing
layers of liquids
from the solid wall; this confirms of the adsorption
the con-
of vapours of
point. acid and ether
(Fig. 7) solutions
and deserve special consideration.
in vaseline
oil are
In the case of weak concentration
molecules the velocity profile assumes a rather irregular shape, which to the structural
solvent. This heterogeneity References ~3.289-290
distance
in the case of measurement
volatile liquids near the saturation
evidently
with
of sudden changes in the vis-
layers.
This conclusion with
and that
is
indicates that the action
the film, but is connected
The appearance
is in some way able to affect
the non-polar
reveal
The fact that the structure
of the latter cannot be due to their presence throughout the formation
the results obtained
layers of a liquid in which polar
heterogeneity
can be explained
of the corresponding
by the circumstance
layers of the
that different
struc-
VOL. 1 P957/58)
Fig. 7. Velocity blowing.
MECHANISM OF BOUNDARY
LUBRICATION
285
profiles of solutions of stearic acid and amyl sebacate on a glass surface during
O/b stoaric acid; t = 18°C. (2) 0.00054 o/, stearic acid; t = 14%
(I) o.oooo~~
(3) O.OOZ~%, amyl sebacate; f = 18°C. (4) 0.0060 o:, amyl sebacate ; t = r VC.
tures of the wall-adjacent layer of the solution are possible, depending on the orientation of the adsorbed molecules, which in turn may vary over the surface. In a number of cases, if the layer is left undisturbed, we failed to observe any further appearance of irregularities in the profile, and in fact the existing ones were smoothed out. It follows that the film profile obtained after blowing-off assumes its jagged shape as a result of deformation during laminar flow and not because of its the~odynamic instability. The effect is similar to that of the formation of slip bands in plastic deformatiorP and points also to the heterogeneous structure of the boundary layer. At the same time the fluidity preserved by the boundary layer even under the small shear stress caused by the air stream shows that the mechanical properties of a liquid layer differ greatly from those of a plastic solid body, although there are apparently some exceptions to this rule; moreover, the resistance of the boundary layer to thinning points to the difference between its properties and those of the bulk liquid. It may be supposed that the boundary lubrication layer is in a state similar to that of liquid crystals with a structure in which the main part is played by the orientation of rod-shaped molecules.
Fig. 8. Photograph of the interference pattern formed on a steel surface when blowing-off a polymer of vinyl butyl ether. M = 600; z c 48 min; n.P = so mm Hg; t = 20%; C = IOO o& (M is molecular weight, z is blowing-off time, AP is pressure drop, t is temperature, C is concentration). The direction of the air jet: 4. References
p. 289.zgo
286
R. V. DERYAGUIN
et al.
VOL. 1 (r957158)
The chief difference from liquid crystals is that in the latter the solid wall causes an orientation spreading at an indefinite distance, while with liquids the distance is quite definite and small. The intermediate case may include some liquids and solutions containing polymers. As we have already shown, in this case, one can get an idea of the viscosity distribution in the proximity of the solid wall from the position of the interference fringes of equal thickness. Fig. K is a photograph of poly (vinyl butyl ether) with a molecular weight 600, which was kindly supplied by Professor M. F. SHESTAKOVSKY. The greater density of the fringes An
analysis
in the thin part of the layer of the
wall, represented The stable
photograph
graphically
complex
phenomena
thickness
are observed
yields
changes
upon the addition in detail in original
showing photographs (Figs. IO and
II)
profile
of the viscosity
of the
film
and the appearance of various
there.
on the solid
of zones of un-
polymers
two typical
to mineral ourselves
to
cases.
Fig. II. Photograph of interference pattern formed on a steel surface when blowing-off a polymer solution of vinyl butyl ether in turbine oil. M = 3,850: z = 3 min; @.P = 70 mm Hg; t = 2oT; c = o,op(,.
01: STATIC FRICTION THE TWO-TERM
vinyl
papers 1’ we shall confine
representing
Fig. IO. l’hotttgraph of interference pattern formed on a steel surface when blowing-off a polymer solution of vinyl batyl ether in turbine oil. M = 2,100; z = 12 min; hP = 20 mmHg; t = xl”(‘: I: = oq~;,.
THE NATURE
to an increase
in Fig. 9. of viscosity
oils. Sinct: they are described
points
the velocity
IN BOUNDARY
LUBRICATION
LAW OF FRICTION
The results obtained indicate the peculiarities in the structure and fluidity of the boundary layers of lubricating liquids and hence lead us to conclude that these pecuReferences p. zS9-290
VOL.
1 (ImM)
MECHANISM OF BOUNDARYLUBRICATJON
287
liarities must be taken into consideration in interpreting the phenomena of boundary lub~cation and in working out their theory. Owing to lack of space we shall not dwell on these questions, especially since the results of the investigations -in particular those concerning static and kinetic disjoining pressure in thin liquid film+‘, the kinetics of the thinning of boundary layers between two solid bodies in contact with one anotherm, the interrelation of kinetic friction and molecular orientatio#, etc. - are discussed in a number of other papers. We shall limit ourselves to a consideration of the following impo~ant problem. If the boundary lubrication layer does not possess a yield value, as is indicated by the results of application of the blowing-off method, then how can one explain static friction between solid surfaces, separated by a polymolecular layer? Yet, the existence of static friction in such cases has been convincingly proven in a number of experimental studies22. We believe that the correct auswer to the question can be found only in the two-term friction law previously formulated by ~$3 and experimentally provedsa. The validity of this law for the interpretation of the mechanical properties of liquid and solid lubricating films has been proved in the work of DERYAGUINANDLAZAREV~~. According to the two-term law of friction, the force of static friction F equaIs:
F=p(N-+-SpJ=,xNfSO
where p is the “true” coefficient of friction, N the load, S the area of real or molecular contact, and e0 the adhesion force per unit area of real or molecular contact. This formula, which in form but not in physical content is to some extent analogous to the two-term Coulomb Law (deduced empirically), expresses the idea of the double origin of the force of friction. One part of this force is caused by external pressure N, the other part by the molecular interaction of the surfaces. The law also reflects the divergence between the views of the present authors and BOWDEN,who interprets the friction phenomenal by means of the second term of the formula alone, which amounts to the assumption that the “true” coefficient of friction p equals zero. Thus, according to BOWDENand his school, friction depends on the load N only insofar as the latter increases the area S of true or molecular contact between the bodies. This point of view, first formulated by TERZAGHP, is in contradiction with experiments in which the force of friction increases with the load in strict accordance with the linear law, despite the fact that either the area of molecular contact cannot undergo essential changesz5 or that this increase in the area is slower than that of the loadz’. To this end we investigated the friction of a plane paraffin block on glass. In order to obtain a large area of contact that was not changed throughout the experiment, the paraffin was preliminarily melted while in contact with the glass surface and then allowed to solidify. In order to be certain that sliding took place not between the layers of paraffin, but on the paraffin-glass interface, the latter was covered with a multih%ferences p. 289-290
2633
et al.
l3.v. DEKYAGUIX
molecular
layer of the acid barium
method of BLODGETT and 1.3 represent dependence
AND
or calcium
dependence
bears out the correctness
The circumstance
of friction,
proves that the macroscopical
to the
of the straight
is independent
asperities
on the load. This
law of friction. lines, which is equal
of the number of molecular
layers n
of the glass surface have very little influence
of friction.
0
200 Kg. f1. 12riction force plottcil against load for paraffin on glass. tzubricant : multimolecular PJodgett-Langmuir layers of acid calcium soap with yt molecular layers. .,n=I;o,~2-~3;X,nIS~r;~,12=Gr.
of layers R. increases
__.M 200
400
6%~~
Fig. I 3. Friction force plotted against load for paraffin on glass. Lubricant: multimolecular Blodgett-Ismgmuir layers of barinm soap with ?z molecular layers. 0, n = j; 0,11 = 7; x, 12= II.
The second term in the linear law, according as the number
acid, according
of the force of friction
of our two-term
that the angle of inclination
to the true coefficient on the coefficient
salt of stearic
The number of layers PZvaried from I -61. Figs. 12
LANGMUIR.
the observed
VOL. 1 (1957/58)
to the above data, declines somewhat
from 7 to 9, and remains constant
with further
increase of nyl.This decrease in the value of the second term with increasing of the lubricating
layer can be easily explained,
assuming that in thicker lubricating
according
layers the molecular
thickness
to P. i\. REHBINUEK,
attraction
by
between the glass
and the paraffin ceases to have effect, while the adhesive force S depends only on the interaction
between the molecules of the lubricant
Another method of refuting the one-term tion consists in studying the areas of contact, remaining
the influence
and the paraffin.
law and proving the two-term
with the nature of the surfaces and the conditions
Hu compared
a metal surface and a glass point with radius of curvature
in one case, and between curvature
of
of measurement
the same.
This idea was tested by U. TOPOROFF in our laboratory. between
law of fric-
on friction of a variation in the deformability
a metal surface and a thin-walled
equal to several centimeters.
The coefficient
the friction
of about r/lo mm
glass ball with radius of
of friction on the unlubricated
metal was always greater in the second case than in the first. Hut when the metal surface was covered by an adsorbed monolayer This experiment
of stearic acid this difference
furnishes proof of the correctness
In the case of a thick layer of boundary
of the two-term
lubricant,
disappeared.
law of friction.
we have the reverse case, when
the second term is equal to zero. In fact, in the case of boundary
lubrication
the second
VOL. 1 (1957/58) term, if referred number
MECHANISM OF BOUNDARY LUBRICATION
to unit area, should
of cases of boundary
obtained
by the blowing-off
friction should be exactly consideration
lubrication method.
the yield
the observed essentially resistance
phenomena.
we must take into
the presence
with the experiments,
The conclusion drawn, that
deserves
to shear in a thin boundary
load on the film, and appears
lubricating
and disappears
the only explanation
with all the experimental
of static friction,
for the one-term
friction
lubrication.
than aformaldeductionfrom
though empiric in origin, contains an
further
investigation
and proof:
film is brought
viz. that
about by a normal
with the load. I,ack of space does not
allow us to present further evidence of this important furnishes
by the results
our point of view, however,
are, of course, somethingmore
new assumption
in a certain
in that case, static
law of AMONTON, which is strictly valid in cases of boundary The above considerations
which
to current views?
not only explains
a basis, in accordance
value 0,
equals zero, as is demonstrated
According
zero. From
the first term, which
but also provides
express
289
of the mechanism
principle,
of boundary
which, in our opinion, lubrication
consistent
data.
REFERENCES I;. I’. BOWDEN AND I). TABOR. The Friction and Lubrication of Solids. 2nd ed.. Oxford TJniv. Press, London, 1954. B. V. DERYAGUIN. N. N. ZAKHAVAEVA. M. M. KUSSAKOV. \‘. P. LAZAREV AND M. M. SAMYGUIN. Akad. Nauk. S.S.S.R., T%dy I Vsesoyuz. Konf. Treniyu i Iznosu Mashinakh, I (1947) 103-139;
I4
I5
I8 I7 Is
3 (1949) 101. B.V. D~~~~~~~~,ChtoTakoyeTreniye? (Whatisfriction?) Acad. Sci. U.S.S.R., 1951, (in Russian). A. S. AKHIIIATOV, Trudy 2 Vsesoyur. Konf. Tveniyu i Iznosu Mashinakh, 3 (1949) 133, 144. 1. C. HENNIKER. &US. Modern Phvs.. 21 (14491 xw. &. V. DERYAGUIN, Trudy Vsesoyu~. Konf. Kolloid. Khim., (Kiev) (1952) 26. Strojeniie i Fizicheskiie Svoistva Veschestva v Zhidkom Sostoianii, (Materialv Soveschaniia, ” Iqg?, -“I I v Kijevk), Kiev 1lnivy Press, Kiev, 1954, p, r41. B. V. DERYAGuIN, l‘?‘ans. Faraday Sot., 36 (1940) 203. B. V. DERYAGUIN, Izvest. Akad. Nazlk. S.S.S.R., Ser. Khim., 5 (1937) 1153; Acta Physicochim. U.R.S.S., 10 (‘939) 333, Kolloid. Zhur., 6 (1940) 291, 7 (1941) 285. B. V. DERYACUIN AND L. D. LANDAU, Acta Physicochim. U.R.S.S., 14 (1941) 633; J. Exptl. Theoret. Phys. (U.S.S.R.), II (1941) 802; 15 (1945) 662. E. VERWEY AND J. OVERBEEK, Theory of the Stability of Lyophobic Colloids, Elsevier Publ. Co., Amsterdam, 1948. J. M. GLAZMAN AND I. M. DYKMAN, Doklady Akad. Nauk S.S.S.R., IOO (1955) 299. S. BASTOW AND F. BOWDEN, Proc. Roy Sot. (London), r51 (1935) 220; B. V. DERYAGUIN, Nature, 135 (1935) 828. F. BOWDEN AND S. THROSSEL, Proc. Roy Sor. (London), A 209 (1951) 297. B. V. DERYAGUIN AND 2. M. ZORIN, Doklady Akad. Nauk S.S.S.R., 98 (1954) 93; Zhur. Fiz. Khim., 29 (1955) IoIo, 1755; 2nd Intern. Congr. Surface ActiviJy, London, 1957. B. V. DERYAGUIN AND M. M. SAMYGUIN, Akad. Nauk. S.S.S.R., Otdel. Tekh. Nauk., Inst. Mashinovedeniya, Soveschanie po Viazkosti Zhidkost. i Kolloid. Rastvorov. I (1941) 59. B. V. DERYAGUIN AND N. A. KRYLOV. dkad. Naztk. S.S.S.R.. Otdel. Tekh. Nauk., Inst. Mashinovedeniya, Soveschanie po Viazkosti Ziidkost. i Kolloid. Rastv’orov, 2 (1944) 52. B. V. DERYAGUIN, G. M. STRAKHOVSKI AND D. S. MALYSHEVA. Zhur. Eksbtl. i Teoret. Fiz.. 16 (1946) 171; Acta Physicochim. U.R.S.S., 19 (1944) 541. B. V. DERYAGUIN AND E. F. PICHUGUIN, Akad. Nauk. S.S.S.R., Trudy 2 Vsesoyuz. Konf. Treniju i Iznosu Mashinakh, I (1947) 103; 3 (1949) IOI. B. V. DERYAGUIN AND V. V. KARASSEV, Doklady Akad. Nauk. S.S.S.R., 62 (1948) 761; Kolloid. Zhur., 15 (1953) 365; Doklady Akad. Nauk. S.S.S.R., IOI (1955) 289. B. V. DERYAGUIN AND N. N. ZAKHAVAEVA, Trudy Konf. po Vysokomolekular. Soedineniyam, Akad. Nauk. S.S.S.R., Otdel. Khim. i Fiz. Mat.-Nauk, 6th Conf. 1949. p. 233. N. F. SJUTKIN, Doklady Akad. Nauk S.S.S.R., 96 (1954) 503.
B. V. DERYAGUIN
290 l* B. V. DERYAGWN
et at.
VW-.- f
AND E. V. OSUKHOV, Kolloid.Zhu:hur., I (1935) 385; Acta Physicwhim.
fI957/58j U.&S..%,
5 (1936) 1.
B.V.~~RYAGUINAND~.M.
Acta Physicockim. 6 (1940) 291.
U.R.S.S.,
KussAxoY,~~u~s~.AR~~. IO (1939) 25, 153; Trans.
Nattk,S.S.S.R.,Ser. Khim.,5(1937) 1x19; Faraday Soc.,36 (1940) 203; Xoltoid.Zhw.,
B. V. DERYAGUIN, M. M. KUSSAKOV AND L. S. LEBEDEVA, Doklady A kad. Nauk S.S.S.R., 23 (1939) 670. 3. V. DERYAGUIN,M. M. KUSSAKOV AND ASTITIJEVSKAJA, Kolloid.Zhur.,Is (1953)416. *O A. D. MALKINA AND B.V. DERYAGUIN, KolEoid. Zhw., 12 j1950)431. 21 V. I?. LAZAREV AND B. V. DERYAGUJN, Zhur. Tekk. Fiz., 23 (1953) 1977. 22 B.V.DERYAGUIN,N.N. ZAKHAVAEVA,M.M. Ku~sAKov,~~.~'.L~~zAREvAND~~.M.SAMYGU~~. Akad. Nauk. S.S.S.R., Tmdy 2 Vsesoyus. Xonf. Treniyu i Imoszc, 3 (1949) 144; Doklady Akad. Nauk. S.S.S.R., 30 (1941) rrg. zs B. V. DERYAGUIN,~. Physik, 88 (1934) 661; Zhur. Fiz. Khim., 5 (1934) 1165. 24 B. V. DERYAGUIN, Doklady Akad. Nauk S.S.S.R., 3 (1934) 93. B. V. DERYAGUIN AND V. P. LAZAREV, Kolloid. Zhur., I (1935) 293. ts B. V. DERYACWN AND V. P. LAZAREV, Akad. Nauk S.S.S.R., Trudy 2 Vs~soyuz.Kon~,Tre~aiyui Iznosu Maskinakh, 3 (1949) 106. ee TERZAGHI. Erdbau~echa~~k. Wien, 50 (1~251: ~ - _,J. J. BIK~RMAN AND E. K. krDeAi.,-Phil. &fag., 27 (1939) 687; F. BOWDEN AND D. TABOR, Proc. Roy. Sot. (London), A 169 (1939) 391. 27 J. V. KRAGELSKI, Zhw. Tekh. Fiz., x2 (1942) 726. aa W. HARDY, Proc. Roy Sot. (London), A ro8 (rgz5) I.
Received for review August, '957 AcceptedNovemberz5, 1957