The year 2017 marks the 100th anniversary of premature death of Marian Smoluchowski, an outstanding Polish physicist, a pioneer of the kinetic theory of matter currently known as statistical physics. On this occasion, we have published the volume containing: essays on Smoluchowskis life and his contribution to science, translations into English of Marian Smoluchowskis papers originally published in German, French and Polish. Among them three extremely important articles have been prepared for the first time especially for this publication.
A Contribution to the Theory of Electric Endosmosis and a Few Related Phenomena. Smoluchowski received a remarkable result in this paper. He showed that under the thin double layer assumption, the fluid flow in such phenomena is independent of boundary shape. The paper was published in 1903 in Polish and French.
On the Kinetic Theory of the Brownian Molecular Motion and of Suspensions. The paper played a very important role in convincing scientists as to the validity of the kinetic theory of matter. This paper (published in 1906) was translated from the German original into English by Rudolf Schmitz from RWTH Aachen and Robert Jones from Queen Mary College University of London.
Molecular-Kinetic Theory of the Opalescence of Gases in the Critical State and a Few Related Phenomena. The same two physicists translated Marian Smoluchowskis paper on critical opalescence published in German in 1908 (French and Polish versions appeared in 1907). Explaining this mysterious phenomenon, discovered at the end of the 19th century, was at the time a great challenge for scientists.
Some of his [Marian Smoluchowski ed. note\ fundamental contributions concerned the role of statistical fluctuations in phenomena involving assemblies of particles, and confirmed their importance in explaining phenomena like the Brownian motion and opalescence. One might say that, before him, most studies were concerned with the thermodynamic variables representing the first means or expected values of the relevant random variables. Because it went further into an examination of the deviations and second moments, the work of Smoluchowski gave further confirmation to the reality of a kinetic picture of matter.
Stanisław Ulam, Marian Smoluchowski and the Theory of Probabilities in Physics (Los Alamos Scientific Laboratory, Los Alamos, New Mexico, US, 1956).
On the occasion of 100th anniversary of death of Marian Smoluchowski, an outstanding Polish physicist, a pioneer of the kinetic theory of matter currently known as statistical physics, we published the volume containing essays on Smoluchowskis life and his contribution to science and translations into English of his extremely important papers originally published in German, French and Polish.
W roku 2017 upłynęło 100 lat od przedwczesnej śmierci Mariana Smoluchowskiego, wybitnego polskiego fizyka, pioniera kinetycznej teorii materii obecnie znanej jako fizyka statystyczna. Z tej okazji wydaliśmy tom zawierający: eseje o życiu Smoluchowskiego i jego wkładzie w naukę, tłumaczenia na język polski artykułów Mariana Smoluchowskiego pierwotnie wydanych w języku niemieckim, francuskim i polskim. Wśród nich znalazły się trzy niezwykle ważne artykuły przetłumaczone po raz pierwszy specjalnie do niniejszej publikacji.
A Contribution to the Theory of Electric Endosmosis and a Few Related Phenomena. Smoluchowski uzyskał w tej pracy znakomite wyniki. Wykazał, że w takich zjawiskach, przy założeniu cienkiej warstwy podwójnej, przepływ cieczy jest niezależny od kształtu brzegu obszaru. Artykuł został opublikowany w 1903 w języku polskim i francuskim.
On the Kinetic Theory of the Brownian Molecular Motion and of Suspensions. Artykuł (opublikowany w 1906) odegrał bardzo ważną rolę w przekonaniu naukowców o słuszności kinetycznej teorii materii. Przekładu z języka niemieckiego na angielski dokonali Rudolf Schmitz z RWTH Aachen i Robert Jones z Queen Mary College University of London.
Molecular-Kinetic Theory of the Opalescence of Gases in the Critical State and a Few Related Phenomena. Ci sami dwaj fizycy przetłumaczyli pracę Mariana Smoluchowskiego na temat opalescencji krytycznej opublikowaną w 1908 w języku niemieckim (wersja francuska i polska pojawiły się wcześniej w 1907). Objaśnienie tego tajemniczego zjawiska, odkrytego pod koniec XIX wieku, było wówczas wielkim wyzwaniem dla naukowców.
Darmowy fragment publikacji:
On the Kinetic Theory of the Brownian Molecular
Motion and of Suspensions
Annalen der Physik, Band 21, pp. 756–780, 1906
translated from German by R. Schmitz* and R. B. Jones**
§1. The widely disputed question as to the nature of the phenomena of motion
discovered in 1827 by botanist Robert Brown, which occur when microscopically
small particles are suspended in (cid:30)(cid:31)uids, was recently re-addressed in two theoretical
papers by Einstein1. The conclusions of these papers completely agree with some
results that I had obtained a few years ago, following a completely di(cid:28)ferent line
of thought, and that I consider ever since to be a substantial argument in favour
of the kinetic nature of this phenomenon. Although I was hitherto unable to con-
duct an experimental investigation on the consequences of this point of view, which
I originally intended to do, I have decided after all to publish these ideas now, since
thereby I hope to contribute in clarifying this interesting issue, especially since my
method seems to me more direct, simpler, and perhaps also more convincing than
To remedy, at least partially, the lack of direct experimental veri(cid:29)(cid:27)cation, I shall
give an overview summarizing the hitherto known experimental results, which, in
conjunction with a critical analysis of the di(cid:28)ferent explanation attempts, seem to
give clear hints that the Brownian phenomenon is indeed identical to the molecular
motions predicted by theory. The paper is concluded by some remarks on suspen-
sions (pseudo-solutions) which are related to the present topic.
*Institute for Theoretical Solid State Physics, RWTH Aachen University, Templergraben 55, 52056
**Queen Mary University of London, The School of Physics and Astronomy, Mile End Road, London
E1 4NS, UK.
1A. Einstein, Ann. d. Phys. 17, p. 549, 1905; 19, p. 371, 1906.
§2. The hitherto existing reports of experiments2 on Brownian motion mainly
prompt negative conclusions, i.e. they exclude various kinds of explanation that are
deemed possible at the outset.
The following facts may be considered proven:
The universality of the Brownian phenomenon. – An extraordinary variety of
the most diverse substances have been suspended in pulverized form in liquids and
examined (especially by Brown, Wiener, Cantoni, Gouy), and in all cases those mo-
tions were observed, if only the particles were small enough. Quite the same holds
for microscopically small droplets and gas bubbles (e.g. in the cavities of certain min-
erals that are (cid:29)(cid:27)lled with liquid). Gouy says: “Le point le plus important est la général-
ité du phénomène; des millers de particules ont été examinées et dans aucun cas on
n’a vu une particule en suspension qui n’o(cid:28)frit pas le mouvement habituel...”*
The smaller the diameter s of the particles, the larger is the speed of motion v.
Fors 0.004mm, motion is barely noticeable, whereas close to the limit of visibility
under the microscope it is extremely vivid. Aside from a few crude data by Wiener, it
seems that absolute measurements were only performed by Felix Exner, who found
for water at 23◦ temperature:
s = 0.00013
v = 0.00027
Concerning the in(cid:30)(cid:31)uence of the composition we (cid:29)(cid:27)nd contradicting statements
from di(cid:28)ferent observers. Gouy and, similarly, also Jevons claim that particles of
(cid:29)(cid:27)xed size show little speed variation, regardless of what substance they are com-
posed and whether they are solid, liquid or gaseous. On the other hand, Cantoni
claims that chemical composition is relevant as well. (Ag is supposed to move faster
than Fe, Pt faster than Pb, and the like). Here, it may perhaps play a role that di(cid:28)fer-
2The sources used here are contained in the following list of references: R. Brown, Pogg. Ann. 14, p.
294, 1828; Cantoni, Nuovo Cimento 27, p. 156, 1867; Rendic. J. Lomb. 1, p. 56, 1868; 22, p. 152, 1889;
Dancer, Proc. Manch. Soc. 9, p. 82, 1869; Felix Exner, Ann. d. Phys. 2, p. 843, 1900; Sigmund Exner, Wiener
Sitzungsber. 56, p. 116, 1867; G. Gouy, Journ. d Phys. 7, p. 561, 1888; Comp. rend. 109, p. 102, 1889; Jevons,
Proc. Manch. Soc. 9, p. 78, 1869; F. Kolaček, Beibl. 13, p. 877, 1889; K. Maltézos, Comp. rend. 121, p. 303,
1895; Ann. de chim. et phys. 1, p. 559, 1894; Meade Bache, Proc. Amer. Phil. Soc. 33, 1894; Chem. News 71,
p. 47, 1895; G. van der Mensbrugghe, Pogg. Ann. 138, p. 323, 1869; Muncke, Pogg. Ann. 17, p. 159, 1829;
A. E. Nägeli, Münch. Sitzungsber. 1879, p. 389; G. Quincke, Naturf.-Vers. Düsseldorf 1898, p. 28; Beibl. 23,
p. 934, 1898; E. Raehlmann, Phys. Zeitschr. 4, p. 884, 1903; Regnauld, Journ. d. pharm. (3) 34, p. 141, 1857;
Fr. Schultze, Pogg. Ann. 129, p. 366, 1866; W. V. Spring, Rec. Trav. Chim. Pays-Bas 19, p. 204, 1900; O.
Wiener, Pogg. Ann. 118, p. 79, 1863.
*“The most important point is the generality of the phenomenon; thousands of particles have been
examined and in not a single case has one seen a suspended particle that did not show the usual motion...”
On the Kinetic Theory of the Brownian Molecular Motion and of Suspensions
ent substances cannot be pulverized equally well. In any case, the in(cid:30)(cid:31)uence of the
composition of the particles seems less obvious.
No doubt, however, there is a profound dependence on the nature of the (cid:30)(cid:31)uid
medium, namely on its viscosity: motions are most agile in water and liquids of
great (cid:30)(cid:31)uidity, less in viscous (cid:30)(cid:31)uids and completely absent in syrup-like (cid:30)(cid:31)uids, like
oil, glycerin, sulfuric acid. They become, however, clearly visible, when glycerin is
heated to 50◦ (S. Exner), whereupon its viscosity decreases considerably. Cantoni
states that alcohol, petrol and ether are less active than water, whereas according to
Muncke it is alcohol that is most active.
§3. Related to the universality of the phenomenon is its temporal stability.
Nearly all observers emphasize this fact: as long as the particles are suspended in
the liquid, the movement continues without alteration. Only when particles are
deposited at the bottom or at the walls of the container do they stop moving. For
this reason, it is easier to track, for some time, the motion of particles that have
nearly the same density as the ambient liquid (mastic, gamboge) than tracking heav-
ier particles which settle quickly, and, for the same reason (Maltézos, Gouy, Spring),
the motion is disrupted by adding saline solution (Jevons), which is well known to
cause sedimentation of the particles.
Cantoni observed a specimen, suspended in para(cid:28)(cid:29)(cid:27)n oil between cover slips, for
a whole year without noticing a diminishing of the movement3.
§4. Highly characteristic is the independence of these phenomena from external
conditions. The most diverse measures turned out to be without any e(cid:28)fect. One may
cover the liquid by glass to prevent evaporation (Wiener, Cantoni, Gouy, Exner et.
al.), or put it in a heat bath of uniform temperature (Gouy) or place it in a vibration-
free location (Exner, Gouy). One may store it for weeks in the dark (Meade Bache),
boil it for hours (Maltézos), one may interrupt heat radiation from the incident
light, change colour of the light or weaken its intensity by a factor 1000 (Gouy) –
all this has no impact.
Intensive illumination causes a change only in that it gradually increases the
temperature of the (cid:30)(cid:31)uid, which is associated with an enhancement of the mobility
(Exner), especially for very viscous (cid:30)(cid:31)uids in which viscosity strongly decreases with
rising temperature. F. Exner has recorded in one case (water) an enhancement from
v = 0.00032cm/sec at 20◦ to 0.00051 at 71◦.
§5. Concerning the explanation of Brownian motion, it follows mainly from
§4 that theories based on external energy sources are untenable, thus especially the
3Admixture of gelatine hampers the movements, which may be due to the viscosity of gelatine (honey-
comb structure, Bütschli). Analogue observations by Quincke may be explained similarly (in(cid:30)(cid:31)uence of
hypothesis which suggests itself in the (cid:29)(cid:27)rst place: that one is dealing here with con-
vective currents caused by temperature inhomogeneities. The untenability of the
latter explanation also follows from considerations of a di(cid:28)ferent kind. Thus, mo-
tion in water at temperature 4◦ should completely terminate, whereas, in reality,
it continues with only slightly diminished magnitude up to the ice point (Meade
Bache). Reduction of the thickness of the (cid:30)(cid:31)uid layer down to a small fraction of
a millimeter by placing a cover glass atop should largely diminish mobility, yet there
is no sign of it. A rough estimate shows that, in this case, a temperature gradient in
the range of 100000◦ per cm would be necessary to generate convective currents of
the observed velocity. Of course, in larger vessels such currents appear as well, but
the collective motions caused by them, which are common to a larger number of
particles, are very di(cid:28)ferent from the irregular, jittering Brownian motions.
It should also be noted that the maximal temperature di(cid:28)ferences near a spheri-
cal, completely black particle, which is exposed to direct sun irradiation, amount
to a fraction of the coe(cid:28)(cid:29)(cid:27)cient ca/k = 1/300◦ (assuming: radiation intensity
c = 1/30, radius a = 10−4cm, heat conductivity k = 10−3 (water)). Consistent
with what has been said above, this may su(cid:28)(cid:29)(cid:27)ce to establish the impossibility of
Regnauld’s explanation, which is based on the formation of convective currents
in the neighbourhood of each particle owing to absorption of radiation at its
The independence of the Brownian phenomenon from light intensity also
speaks against the theories of Koláček and Quincke, which respectively take it to
be either an analogue of radiometer motion or a manifestation of periodic capillary
motions, as analysed by Quincke. In any case, it seems hard to understand how con-
tinuous irradiation could cause the periodic propagation of the warmer (cid:30)(cid:31)uid layers
on top of the cooler ones at the surface of the particles, as assumed by Quincke,
and how there could possibly be a link between the exceptional phenomenon of
periodic capillary motion, which only appears in certain cases (oil in soap solution,
alcohol in saline solution etc.), and the universal Brownian motion, which is inde-
pendent of the composition of the particles. It is, after all, very probable that suf-
(cid:29)(cid:27)ciently strong irradiation can cause movements, yet these would be very di(cid:28)ferent
from the Brownian motion.
§6. There remain only those theories that assumeinternal energy sources. From
the outset, we must reject conjectures which assume the existence of mutual repul-
sion forces (Meade Bache) and related electrical forces (Jevons, Raehlmann), be-
cause these could only cause a certain arrangement of the particles, but not their
continual motion, and especially because the nature of such forces would consti-
tute a new puzzle.
On the Kinetic Theory of the Brownian Molecular Motion and of Suspensions
Also, the view that we are dealing here with manifestations of capillary energy
is untenable. Maltézos assumes that small contaminations are the primary cause for
the disruption of capillary equilibrium, while Mensbrugghe refers to the example
of pieces of camphor dancing on water. But, in this case, it would be inexplicable
that deliberate contaminations have no e(cid:28)fect, that also completely insoluble sub-
stances (diamond, graphite) move and, above all, that motions don’t cease when
conditions have settled. The microscopically small gas bubbles enclosed in miner-
als should have reached capillary equilibrium after all, and yet they move.
§7. We now turn to the kinetic theories which view the internal heat energy as
the real cause. If one observes Brownian motion under the microscope, one imme-
diately gets the impression that the motion of the (cid:30)(cid:31)uid molecules must look just
like that. This is not an oscillatory motion, nor a steady one, but a trembling or,
as Gouy puts it, a swarming motion (fourmillement); the particles perform irreg-
ular zigzag movements, as if they were driven due to random collisions with the
(cid:30)(cid:31)uid molecules, and despite their feverish motion they only progress slowly from
This phenomenon was, in fact, explained from this point of view by many re-
searchers (Wiener, Cantoni, Renard, Boussinesq, Gouy). In doing so, two types of
interpretation are still possible. Wiener and Gouy assume that, within a region of
the order of 1 µ3, the internal motions of the (cid:30)(cid:31)uid are aligned and that these are
displayed by the particles, whereas Maltézos objected that there is no reason at all
to assume parallelism of [(cid:30)(cid:31)uid] motion within regions of 1 µ3 and that this hypoth-
esis is not compatible with the independence of these motions at larger separations.
We shall come back to these considerations in the sequel, but, for the time being,
we shall investigate the simplest kind of kinetic interpretation of this phenomenon,
according to which Brownian motion is the immediate result of the momentum
transfer from the (cid:30)(cid:31)uid molecules to the particles.
Nägeli thought to disprove this kind of explanation by referring to the small-
ness of the velocities caused by such collisions. Thus, a water molecule colliding
with a particle of 10−4cm diameter (and density 1) would give it a velocity of just
3· 10−6mm/sec, which is far below the scale of Brownian motion. Truly, successive
impulses add up, but Nägeli argues that these must cancel on average, since they oc-
cur in all spatial directions, and that the (cid:29)(cid:27)nal result therefore couldn’t be markedly
larger [than that for a single collision].
§8. This is the same error in reasoning as if a gambler were to believe that he can
never lose an amount of money that is greater than the stake of a single throw. Let
us follow this analogy a bit further. Assuming equal probability for gain and loss,
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