GEOLOGIJA 30, 207-217 (1987), Ljubljana
UDK 548.5:552.12.13(450.82)=20
The importance of clustering phenomena in magmas
Giuseppe Lucido
Istituto di Mineralogia, Petrografia e Geochimica, Università di Palermo, via Archirafi n. 36
90123 Palermo, Italy
Abstract
Currently, clustering phenomena receive considerable attention in stellar
systems and in fluid-dynamics problems. Although the whirling motions are
regarded as a problem of basic significance for geology, the mechanisms for
forming clustering processes in magmas are still poorly understood. Luckily, the
discovery of felsic clusters in some basaltic rocks of Western Sicily throws light on
this subject. The main aspects of cluster evolution occurring in the magma are
described, and a three-stage process is proposed. The coalescing mechanism and
the interparticle interactions due to the surface forces are emphasized.
In the author's opinion the conditions now existing in the Earth's upper
mantle favour clustering phenomena of this kind.
Introduction
Vortices consist of matter in motion around a common axis. The clustering
concept is very important because the whirling motions are observable, for instance,
in the galaxies of the Universe, in the spiral arms of the galaxies, in the planetary
system, in the Earth's atmosphere and in magmas. In this latter case, clustering
processes are of interest in the study of the movement and solidification of magma
and lava as well as in evaluating processes of energy extraction.
In the simplest approximation, known as the Boussinesq approximation, a fluid is
assumed to be incompressible (except for thermal expansion, which provides the
buoyancy) and convective onset in a non-rotating fluid is governed entirely by the
Rayleigh number. For a fluid layer of depth H, with constant kinematic viscosity
V = [A/e and thermal diffusivity k, the Rayleigh number is: Ra = ^^^, where g is
the gravitational acceleration, a is the coefficient of thermal expansion, and ß is the
difference between the actual temperature gradient and the adiabatic temperature
gradient. The essential idea is that convection in magmas does not begin until the
Rayleigh number exceeds some critical value, which depends on the imposed boun-
dary conditions, but is usually in the neighborhood of 1,500 (Spera, 1980). It may be
thought of as the ratio of buoyancy forces favoring convection to the viscous forces
retarding flow. Normally natural convection will become turbulent when the Rayle-
igh number exceeds 103(Rohsenow & Choi, 1961). The high Prandtl number ^ in
208	Giuseppe Lucido
this case, however, tends to raise this critical Rayleigh number turbulent transition
point. Hieber and Gebhart (1971) studied this problem and their result for the
critical Rayleigh number for the onset of turbulence can be put in this form:
The critical Rayleigh number determined from this equation for the heat exchan-
ger in basaltic magma is 4,5 X 10^2 (Hardee, 1981). So, according to Hardee (1981),
since the actual Rayleigh number (9,9 x 10^®) is much larger than the critical Rayleigh
number (4,5 x 10^^), the convections is turbulent.
In this paper, on the basis of the remarkable textural characteristics of the
Sicilian igneous rocks and taking into account the present state of experimental
knowledge concerning the interparticle forces, a three-stage transport mechanism is
proposed. It is suggested that this mechanism may play a very important role in
upper mantle convection.
Geological setting
The igneous rocks in which felsic clusters occur, are situated near S. Stefano di
Quisquina (Sicily). They are located in the Sicano basin that lies along the western
Sicily bridge between the Neogene-Pleistocene basins of Caltanissetta on the east
and Castelvetrano on the west (C a t a 1 a n o & D'Argenio, 1978). Detailed geologic
mapping of the igneous outcrop has been by Broquet (1968). From the Upper Trias
to the Miocene the Sicano basin was involved in tensional tectonic activity verifiable
in the tectono-sedimentary evolution of the facies and in the characteristics of the
fissurai magmatism. The E-W fault system and its conjugates allows for the identifi-
cation of the tectonic directrices which fed this magmatism. Beginning from the
Tortonian, in connection with the anticlockwise rotation of the African plate, the
Maghrebian compression front affected this area building the chain of the Sicani
Mts.
The Sicilian igneous rock was first reported on by Baldacci (1886) who conside-
red it a basaltic dyke. The outcropping rock consists of three small hillocks that crop
out upon a probable erosion surface of Palaeocene, Eocene and Oligocene sediments.
It generally shows porphyritic texture, but panidiomorphic and ocellar structure are
also observed. The fresh basic samples are black, whereas the weathered ones have
a greenish colour due to the presence of chlorite and other alteration products. The
light clusters fundamentally are subspheroidal or ellipsoidal and form a strong
centrast to the basaltic matrix. Lacking geochronological data and because of the
poor field-relationships the actual age of the outcrop is uncertain.
Coalescence and clustering in the magma
During research carried out on the Sicilian rocks of the Sicano basin, a mecha-
nism forming silicic segregations from basaltic magma was discovered (see Lucido,
1983). This mechanism suggests that the formation of silicic segregations is a conse-
quence of liquid immiscibility phenomena. In particular, the author found that at the
moment of immiscibility much of the magmatic melt was in a state of intensive
motion. For instance, Figure 1 shows a vortex of felsic composition in the surrouding
basic host-rock. Minerals occurring in the basic host-rock are the same as those in the
The importance of clustering phenomena in magmas_209
Fig. 1. Hand-specimen showing a whirling
felsic portion in the surrounding basaltic
magma. Scale in cm
Fig. 2. Felsic clusters, scattered in the basaltis matrix, point that under
certain circumstances a phase seration occurred in the Sicilian magma.
Magnification, x6
14 - Geologija 30
210	Giuseppe Lucido
whirling felsic portions, but they occur in differing proportions, with light and
hydrous phases concentrated in the felsic fractions. These felsic aggregates are
characterized by the following mineralogical assemblage: K-feldspar, plagioclase,
kaersutite, titanaugite, analcite and zeolites. Among the accessory minerals are:
ilmenite, titanomagnetite, anorthoclase, biotite, aegirine-augite and apatite (see
Lucido, 1981).
During immiscibility, due to liquid phase separation of the basaltic magma, an
enormous number of barely visible clusters (having diameter up to 1mm in size)
appear throughout the Sicilian magmatic melt (Fig. 2). This new liquid phase differs
sharply in composition from the original magma; at the same time, the matrix also
changes its composition. The diffusion from one phase into the other (and vice-versa)
is promoted by the fact that the liquid-liquid interface is always mobile (D e 1 i t s y n
et al., 1974). From the equation of motion of a liquid drop in liquid we know at the
liquid-liquid interface, the normal velocity component vanishes, whereas the tangen-
tial component is finite (Levich, 1959). Because translational and rotational moti-
ons at the instant of immiscibility originate simultaneously, everywhere and point in
the most diverse directions, the motion becomes chaotic or turbulent. The turbulence
of magmatic liquid produces zones of lower component concentrations in the space
between two converging and independently rotating clusters, which then begin to
coalesce via a neck (Fig. 3), and become larger. In the emulsion generated in the
magma, the clusters tend to become larger so as to decrease the surface energy of the
system, while at the same time turbulence tends to deform and shatter the enlarged
clusters, and prevents them from growing beyond a certain size. So, such a magma is
an unstable system, in which there are constant changes in surface tension, viscosity
Fig. 3. Photograph showing light clusters coalescing via a neck to form
larger clusters. Some clusters clearly show cups point towards the basaltic
liquid. Magnification, x3
The importance of clustering phenomena in magmas	211
Fig. 4. This Fig. exhibits three different-textured layers. The lower
layer (A) shows a phaneritic texture, with common subvariolitic
crystallization between inosilicates and feldspars. The middle layer
(B) is characterized by subophitic texture with equigranular and
elongated feldspar crystals. The upper part (C) is the basaltic portion.
Undoubtedly density gradients between the liquid phases must have
played an important role. Scale in mm
Fig. 5. A single spheroidal whirl forming an independent flow in the
Sicilian magma. The view of Figure 5 is three-dimensional: the upper part
of it shows half a whirl such as in occurs in outcrop; the lower part of the
photograph represents the whirl vertically dissectioned along its diameter.
Width of Figure 5 is 25 cm
212	Giuseppe Lucido
and density until the melt is stabilized and the motion ceases. Upon separation into
immiscible liquids, layering of liquid phases chiefly occurs during the period of
turbulence in the melt. After the period of intensive turbulence, there is a further
change in the volumes of liquid layers. This process occurs under comparatively
quiescent conditions (Fig. 4) and is controlled by the rate of settling (or floating up) of
the band of clusters in the corresponding matrices (Delitsyn et al., 1974). Upon
separation, the individual whirl forms independent flow in the magma (Fig. 5). In
whirls formed in the turbulent liquid, there are zones of denser and less dense
emulsion. In emulsion zones that have thickened to a certain density, motion ceases
(i. e. viscosity increases), so relative to zones of less dense emulsion these zones
behave as solid boundary surfaces, along which the friction is higher than elsewhere
in the magmatic liquid. Within the remaining less dense zones, the motion of
emulsion will continue to create new zones of denser and less dense emulsion until
motion ceases completely. Field and microscopic observations show that clusters
with a diameter more than a certain critical value are deformed (markedly elongated)
and behave like liquis under gravity. Vice-versa, clusters having a subcriticai diame-
ter are not deformed and retain their spherical shape.
Discussion and conclusions
Theoretical considerations
Various magmatic processes (for instance, differentiation, crystallization, poly-
merization and degasification) occur at the expense of a certain energy reserve
(Zavaritskii & Sobolev, 1964) and lead to the formation of colloid systems.
Colloids dispersed in the magma can be either magmaphilic or magmaphobic,
depending on whether the energy obtained by their solvation by the magma liquid is
higher or lower, respectively, than the sum of their aggregation energy and the
dissociation energy of the liquid silicate (Yariv & Cross, 1979). It is therefore not
surprising that various mineral species are recorded to have been derived through the
colloidal state and show spheroidal forms, e.g. the so called colloform structures
(Augustithis, 1982).
The present state of experimental knowledge concerning the forces that govern
the properties of colloidal dispersions has been recently reviewed (Israelachvili,
1981). According to the Hellman-Feymman theorem all intermolecular forces are
strictly electrostatic in origin. Nevertheless, it has been found convenient to classify
the major forces between particle surfaces into van der Waals' forces, electrostatic
and double-layer forces, polymer and steric forces, structural forces (hydrogen
bonding, hydration and hydrophobic interactions), and adhesive forces. These inter-
particle forces are not as stong as covalent or metallic binding forces and their
weakness and very short range (« 1 цт) makes them difficult to measure directly.
The behaviour of a colloidal system is far more complex than any gas-fluid
system. Ageing and time-dependent effects often occur for dispersions in electrolyte
solutions when equilibrium is attained slowly or not at all. More complex behaviour,
such as hysteresis effects, occurs in polymer dispersions. Thus, at present not even an
empirical equation of state, similar to the van der Waals' equation, exists for any
colloidal system. It is worth reflecting what a force between two particles implies.
For large particles with large forces it is realtively simple: if the force is attractive
The importance of clustering phenomena in magmas	213
they will stick, if repulsive they will repel. But when the forces are weak and the
particles small, entropy effects may not be ignored and only a complete thermodyna-
mic or statistical mechanical treatment can expose all the subtle concentration - and
temperature - dependent phase transitions, phase changes, polydispersity, and other
diverse properties of a colloidal dispersion (see Israelachvili, 1981). Surface
forces that lead to aggregation are primarily van der Waals. Recently, experimental
techniques have been developed to measure the van der Waals' forces in liquids,
either indirectly (Sab i sky & Anderson, 1973; Requena et al., 1975) or directly
(Blake, 1975; Israelachvili & Adams, 1978; Derjaguin et al., 1978).
The above surface forces may therefore be responsible for the attraction between
particles. In a magma, for example, the coalescence fundamentally depends on these
interparticle forces existing in the melt. According to Delitsyn and others. (1974),
in fact, these forces cause considerble turbulence during the coalescence, hastening
equilibration. An excellent two-dimensional display of this turbulence is observable
on the surface of a hot thin soup between fat globules. H a 11 e r (1965) has develepoed
the mathematical theory of coalescence, based on kinetic studies of the liquid-liquid
immiscible microphases in alkali borosilicate melts. As a matter of fact, most
researchers (e.g. Philpotts & Hodgson, 1958; Ferguson & Currie, 1971,
1972; Gélinas et al., 1976; Cawthorn et al., 1979; Philpotts, 1979; Fumes et
al., 1981) agree that coalescence is involved in the silicate liquid immiscibility origin.
Comparison with theory
The spinodal decomposition is important or potentially important in every system
in which we observe a clustering phenomenon. The theory of spinodal decomposition
is based on the diffusion equation modified by thermodynamic requirements, which
relates a spontaneous flux of matter to a gradient in composition (see, for example,
C a h n, 1968). This theory is phenomenological, and each parameter can be measured
by independent thermodynamic or diffusion experiments. Consider for instance the
dynamics of the various clustering phenomena in a model system composed of two
species of mobile individuals in which individuals of the same species have a short-
range preferential attraction to each other.
Take first the case that is almost random: preference for like members is small.
The individuals execute a nearly random walk, but have a tendency to join favoura-
ble clusters and linger there a little longer. Clusters have no permanence, they form
and disappear. If we perform a diffusion experiment by setting up a concentration
gradient, the gradient would tend to disappear. The attraction to high concentration
is not sufficient to prevent normal diffusion down the concentration gradient.
Now consider the other extreme-preference for the like species is so large that in
a gradient the flux of the individuals is in the direction in which they are attracted,
i.e., up the concentration gradient. This kind of model leads to spontaneous separa-
tion into two »phases«. This system is within the spinodal. The individuals in the
gradient move toward the cluster of their species and cause its concentration to
increase, leaving a depleted zone around it. The outer edge of this depleted zone
contains individuals that now also sense a concentration gradient, but away from the
original particle. Because of their short-range interactions they sense only the
depleted zone and move away from it, building up a new cluster a short distance
away from the original one. We thus expect rapid formation of extremely small
clusters approximately periodically arrayed in space.
214	Giuseppe Lucido
In the case intermediate between these extremes, attractions are not steong
enough to cause a flux up a concentration gradient but strong enough that a large
cluster will attract and hold the individual. This situation is the case for nucleation
and growth. Let's now see what the processes are, and how and when they operate in
magmas.
When preference for the clusters is high, phase separations may be initiated by
statistical concentration fluctuations not far from the critical, which allow the
formation of stable nuclei at an extremely small degree of supersaturation (C a h n,
1961). In particular, if the controlling feature of the phase separation is the charge
density, then the temperature decrease brings about a decrease of the fluctuations
characterizing the critical behavior. In this manner, the fluctuations involving high
charge ions really will be more damped than the others. According to this, the
magmatic fluid will tend to separate into two immiscible liquid portions, one
enriched in elements like iron, magnesium, calcium, titanium etc., and the other
enriched in low charge density ions and elements having the tendency to form
polymaric networks.
In the case of the Sicilian rocks, the extreme-preference for light clusters is so
large that in a gradient the flux of the clusters is in the direction in which they are
attracted. Because of the short-range interactions due to the surface forces, the
clusters coalesce to form larger clusters (Fig. 3).
Comparing the foregoing results and evidence to theory, a three-stage process for
the Sicilian basaltic magma may be reconstructed.
1.	In the first stage cybotaxic zones, the nuclei of future phases, are formed in the
Sicilian magma. Indeed, it is possible to see very small light spots in the basic portion
(A) of Figure 5. This splitting phenomenon can be explained in two different ways: a)
the cybotaxic zones are formed in a homogeneous melt near the binodal point; b) the
phase separation occurred by spinodal decomposition. On the basis of the textural
characteristics of the Sicilian rocks, and on the basis of the known data on the
dynamics of fluids, the writer thinks that the clusters originated by spinodal mecha-
nism.
2.	The second stage is the stage of liquid immiscibility (see Lucido, 1981).
A well-developed example of this phenomenon occurs in the portion (B) of Figure 5.
3.	After unmixing, an agglutination process of clusters which tends to stabilize
the turbulence of the magmatic melt occurs. The light portion (C) of Figure 5 repre-
sents the result of this agglutination process, and it is a portion richer in alkalic
alumino-silicates than the surrounding basic rock.
Application to the upper mantle
Although there is still no indication of a consensus on the nature of mantle
dynamics, importance of whirling motions in the thermal evolution of the Earth is
clearly established. It may be expected that convection is the dominant heat transfer
mechanism in the Earth's upper mantle. In this regard, in fact, magmatic vortexes
under the Earth's crust were long ago hypothesized (e. g. Hopkins, 1939; Bull,
1921; Holmes, 1931; Pekeris, 1935; Hales, 1936).
Convection in magma at liquidus and subliquidus temperature has been analyzed
using Bingham plastic and power-law rheology models (see, for instance, Hardee
& Dunn, 1981). It is interesting to note that a noticeable change in the trend of the
convective heat flux data has been observed in the vicinity of the liquidus tempera-
The importance of clustering phenomena in magmas	215
ture. Above the liquidus, magma (or molten lava) behaves as a Newtonian fluid
(Shaw et al., 1968). At temperatures below the liquidus, non-Newtonian behavior
begins to appear (Shaw et al., 1968; Pinkerton & Sparks, 1978). It is generally
believed that this deviation from Newtonian behavior is due to time-dependent
structural changes in the melt.
The application of the Sicilian phase separation mechanism to the upper mantle
at first leads to the formation of very small clusters (new silicate-liquid nuclei)
having more acidic composition than the surrounding melt and of course pseudo-
plastic behavior.As the phase separation proceeds the magmatic fluid will comprise
immiscible portions in a state of dispersion. After unmixing, in the long run the
interparticle surface forces decidedly prevail and are resonsible for an attraction
process of colloidal clusters (mushes) which tends to stabilize the turbulence of the
melt. In this attraction process, finite compressibility and viscous dissipation tend, of
course, to decrease the flow speed for a given Ra, and so contribute to the melt
stabilization.
Recently, Ar z i (1978) suggested that most of the upper-mantle low velocity zone
(L V Z), if partially melted, is likely to be stabilized somewhat below a non-zero
rheological critical melt percentage (R C M P). For most rocks, the R C M P is
probably within the range of 20 ±10%. It is a drastic transition with viscosities
lowered by several decades due to breakdown of the solid and interlocked crystalline
skeleton, and onset of rapid convective heat transfer. In agreement with Ar z i (1978),
much is explained if the original suggestion by Press (1959) that the L V Z is at »a
state nar the melting point« is revised to »near the R C M P«. According to this, and
assuming that in proximity to the lithosphere-asthenosphere boundary magma tends
to occur at near the liquidus temperature, »the writer proposes that the L V Z is to be
considered as the transition zone from Newtonian to non-Newtonian behavior«.
Acknowledgements
The author is indebted to S. J. Aarseth, Cambridge University, for his interest and
helpful comments on the manuscript. This paper is the outgrowth of research
sponsored by the Ministry of Education (M. P. I.) and by the National Research
Council (C. N. R.) of Rome.
References
Arzi, A. A. 1978, Critical phenomena in the rheology of partially melted rocks. Tectonop-
hysics 44, 173-184, Amsterdam.
Augustithis, S. S. 1982, Atlas of the sphaeroidal textures and structures and their
genetic significance. Theophrastus Publications S. A., 329 p. Athens.
Baldacci, L. 1886, Descrizione geologica dell'isola di Sicilia. Carta Geol. Ital. scale
1:100.000, Roma.
B1 a k e, T. D. 1975, Investigation of equilibrium wetting films of n-alkanes on a-alumina. J.
Chem. Soc. Faraday Trans. I, 71, 192-208, London.
Broquet, P. 1968, Étude géologique de la région des Madonies (Sicily).Thèses, Doct. Sci.
Nat. I.R.E.S., Palermo.
Bull, A. J. 1921, A hypothesis of mountain building. Geol. Mag. 58, 364-367, Cambridge
(U. K.).
Cahn, J. W. 1961, On spinodal decomposition. Acta Met. 9, 795-801.
C ahn, J. W. 1968, Spinodal decomposition. Trans. Am. Inst. Min. Metall. Pet. Eng. 242,
166-180.
216	Giuseppe Lucido
Catalano, R. & D'Argenio, B. 1978, An essay of palinspastic restoration across
western Sicily. Geol. Rom. 17, 145-159, Roma.
Cawthorn, R. G., Mclver, J. R., McCarthy, T. S., Wyatt, B. A., Ferguson, J.
& Barnes, S.J. 1979, Possible liquid immiscibility textures in high magnesia basalts from the
Ventersdorp Supergroup, South Africa, J. Geol. 87, 105-113, Chicago.
Delitsyn, L. M., Melent'yev, B.N. & Delitsyna, L. V. 1974, Liquation in melts, its
origin, evolution and stabilization. Akad. Nauk. S.S.S.R., Doklady 219, 190-192, Moscow.
Derjaguin, B. V., Rabinovich, Y.I. & Churaev, N. V. 1978, Direct measurement of
molecular forces. Nature 272, 313-318, London.
Ferguson, J. & Currie, K. L. 1971, Evidence of liquid immiscibility in alkaline
ultrabasic dikes at Callender Bay, Ontario. J. Petrol. 12, 561-585, Oxford (U. K.).
Ferguson, J. & Currie, K. L. 1972, Silicate Immiscibility in the Ancient .Basalts'of the
Barberton Mountain Land, Transvaal. Nature 235, 86-89, London.
Furnes, H., Malm, O. A. & Robins, B. 1981, Evidence for liquid immiscibility in
Middle Jurassic pyroclastics from the North Sea, and alteration trends of the glass phases. N.
Jb. Miner. Abh. 141, 309-323, Stuttgart.
Gélinas, L., Brooks, C. & Trzciensk, W. E. Jr. 1976, Archean variolites-quenched
immiscible liquids. Can. J. Earth Sci. 13, 210-230.
Hales, A. L. 1936, Convection currents in the Earth. Mon. Not. R. Astronom. Soc. Geophys.
Suppl. 3, 373-379.
Hall er, W. 1965, Rearrangement kinetics of the liquid-liquid immiscible microphases in
alkali borosilicate melts. J. Chem. Phys. 42, 686-693, New York.
Hardee, H. C. 1981, Convective heat extraction from molten magma. J. Volcanol. Geo-
therm. Res. 10, 175-193, Amsterdam.
Hardee, H. C. & Dunn, J. C. 1981, Convective heat transfer in magmas near the
liquidus. J. Volcanol. Geotherm. Res. 10, 195-207, Amsterdam.
Hieber, C. A. & Gebhart, B. 1971, Stability of vertical natural convection boundary
layers: expansions at large Prandtl number. J. Fluid Mech. 49, 577-591, Cambridge (U. K.).
Holmes, A. 1931, Radioactivity and earth movements. Trans. Geol. Soc. Glasgow 18,
559-606, Glasgow.
Hopkins, W. 1839, Preliminary observations on the refrigeration of the globe. Phil. Trans.
R. Soc. 129, 381-385, London.
Israelachvili, J. N. 1981, The forces between surfaces. Phylos. Mag. 43, 753-770,
London.
Israelachvili, J.N. & Adams, G. E. 1978, Measurement of forces between two mica
surfaces in aqueous electrolyte solutions in the range 0-100 nm. J. Chem. Soc. Faraday Trans. I,
74, 975-1001, London.
Levich, V. G. 1959, Fiziko-khimicheskaya gidrodinamika (Physicochemical Hydrodyna-
mics), (English translation, Prentice-Hall), Moscow.
Lucido, G. 1981, Silicate liquid immiscibility in alkaline rocks of western Sicily. Chem.
Geol. 31, 335-346, Amsterdam.
Lucido, G. 1983, A mechanism forming silicic segregations from basaltic magma discove-
red in igneous rocks of Western Sicily. Geol. Mag. 120, 321-329, Cambridge (U. K.).
Pekeris, C. L. 1935, Thermal convection in the interior of the Earth. Mon. Not. R.
Astronom. Soc. Geophys. Suppl. 3, 346-367.
Philpotts, A. R. 1979, Silicate liquid immiscibility in tholeiitic basalts. J. Petrol. 20,
99-118, Oxford (U. K.).
Philpotts, A. R. & Hodgson, C.J. 1968, Role of liquid immiscibility in alkaline rock
genesis. Rep. Twenty-third Int. Geol. Congr. 2, 175-188, Prague.
Pinkerton, H. & Sparks R. S. J. 1978, Field measurements on the rheology of lava.
Nature 276, 383-385, London.
Press, F. 1959, Some implications on mantle and crustal structure from G waves and Love
waves. J. Geophys. Res. 64, 565-568, Washington.
Requena, J., Billet, D. F. & Haydon, D. A. 1975, Van der Waals forces in oil-
water systems from the study of thin lipid films. I. Measurement of the contact angle and the
estimation of the van der Waals free energy of thinning of a film. Proc. R. Soc.A. 347, 141-159,
London.
Rohsenow, W. M. & Choi, H. 1961, Heat, Mass and Momentum Transfer. Prentice-
Hall, 205 p. Englewood Cliffs (N. J.).
Sabisky, E. S. & Anderson, C. H. 1973, Verification of the Lifshitz theory of the van
der Waals potential using liquid-helium films. Phys. Rev. A7, 790-806, Woodbury (N. Y.).
The importance of clustering phenomena in magmas_217
Shaw, H.R., Wright, T.L., Peck, D.L. & Oka mura, R. 1968,Theviscosity of basaltic
magma, an analysis of field measurements in Makaopuhi Lava Lake, Hawaii. Am. J. Sci. 266,
225-263, New Haven (U.S.A.).
Spera, F. J. 1980, Aspects of magma transport. In »Physics of Magmatic Processes«. R. B.
Hargraves, Ed., Princeton Univ. Press, 265-323, Princeton (N. J.).
Yariv, S. & Cross H. 1979, Geochemistry of colloid systems - For Earth Scientists.
Springer-Verlag 450 p. Berlin, Heidelberg, New York.
Zavaritskii, A.N. & Sobolev, V. S. 1964, The physicochemical principles of igneous
petrology. Israel Program for Scientific Translations, 414 p. Jerusalem.