acids, salts and various other substances, and are stable only under
certain conditions of temperature, those which exist at one temperature
being destroyed or changed to other compounds at a different
temperature.
=188. Theory of Barus.=—Brewer’s hypothesis, however, is not in harmony
with the demonstration of Barus, who proves that a given particle of
clay has the same density in ether as in water.
The physical and mathematical aspects of sedimentation have also been
carefully studied by Barus.[126] The mathematical conditions of a fine
particle suspended in a liquid and free from the influences of
flocculation are described by Barus in the following equations.
If P be the resistance encountered by a solid spherule of radius r,
moving through a viscous liquid at the rate x, and if k be the
frictional coefficient, then P = 6πkrx. Again, the effective part of the
weight of the particle is P´ = ⁴⁄₃πr³ (ρ-ρ´)g, where g is the
acceleration of gravity and ρ and ρ´ the density of solid particle and
liquid, respectively. In case of uniform motion P = P´. Hence x = 2/9kr²
(ρ-ρ´)g ... (1).
In any given case of thoroughly triturated material the particles vary
in size from a very small to a relatively large value; but by far the
greater number approach a certain mean figure and dimension. An example
of this condition of things may be formulated. To avoid mathematical
entanglement let y = Ax^{³⁄₂}e^{-x²} ... (2) where y is the probable
occurrence of the rate of subsidence x. If now the turbidity of the
liquid (avoiding optical considerations) be defined as proportional to
the mass of solid material particles suspended in unit of volume of
liquid, then the degree of turbidity which the given ydx particles add
to the liquid is, _caeteris paribus_, proportional to r³ydx, where r is
the mean radius. Hence the turbidity, T, at the outset of the experiment
(immediately after shaking), is T = T₀∫₀^∞r³ydx = T₀, where equations
(1) and (2) have been incorporated.
If the plane at a depth d below the surface of the liquid be regarded,
then at a time after shaking the residual turbidity is
(3) ... T_{d} = T₀∫^{d/t}₀r³ydx = T₀(1 − (1 + (d²/t² × e^{-d²/t²}))
The equation describes the observed occurrences fairly well.
The phenomena of stratification observed by Brewer are explained by
Barus from the above formula: In proportion as the time of subsidence is
greater, the tube shows opacity at the bottom, shading off gradually
upward, through translucency, into clearness at the top. If, instead of
equation (2), there be introduced the condition of a more abrupt
maximum, if, in other words, the particles be very nearly of the same
size, then subsidence must take place in unbroken column capped by a
plane surface which at the time zero coincided with the free surface of
the liquid. Again, suppose one-half of the particles of this column
differ in some way uniformly from the other half. Then at the outset
there are two continuous columns coinciding, or, as it were,
interpenetrating throughout their extent. But the rate of subsidence of
these two columns is necessarily different, since the particles, each
for each, differ in density, radius and frictional qualities, by given
fixed amounts. Hence the two surfaces of demarcation at the time zero
coincided with the free surface. In general, if there be n groups of
particles uniformly distributed, then at the time zero n continuous
columns interpenetrate and coincide throughout their extent. At the time
t, the free surface will be represented by n consecutive surfaces of
demarcation below it, each of which caps a column, the particles of
which form a distinct group.
From a further discussion of the mathematical condition under which the
subsidence of the particles takes place, Barus is of the opinion that
Durham’s theory of suspension being only a lower limit of solution is
rapidly gaining ground, yet without being attended with concise
experimental evidence which will account for the differences in the rate
of subsidence. On the contrary, Brewer’s hypothesis of colloidal
hydrates is more easily subjected to experimental proof. The test shows
that the particles retain their normal density, no matter how they are
suspended or circumstanced.
Further, in the explanation of the phenomenon of sedimentation, the
following principle may be regarded as determined; namely, if particles
of a comminuted solid are shaken up in a liquid, the distribution of
parts after shaking will tend to take place in such a way that the
potential energy of the system of solid particles and liquid, at every
stage of subsidence, is the minimum compatible with the given
conditions.
According to Barus it is necessary, in order to pass judgment on the
validity of any of the given hypotheses, to have in hand better
statistics of the size of the particles relatively to the water
molecule, than are now available. Inasmuch as the particles in pure
water are individualized and granular, it is apparently at once
permissible to infer the size of the particles from the observed rates
of subsidence. His observations show that the said rate decreases in
marked degree with the turbidity of the mixture. Hence the known formulæ
for single particles are not rigorously applicable, though it cannot be
asserted whether the cause of discrepancy is physical or mathematical in
kind. It follows that special deductions must be made for the subsidence
of stated groups of particles before an estimate of their mean size can
fairly be obtained.
Rowland[127] reaches a closer approximation for the fall of a single
particle by showing that the liquid, even at a large distance from the
particle, is not at rest.
In the case of water, however, it is noticed that despite the large
surface energy of the liquid, subsidence takes place in such a way that
for a given mass of suspended sediment the surfaces of separation are a
maximum. On the other hand, in case of subsidence in ether or in salt
solutions, the solid particles behave much like the capillary spherules
of a heavy liquid shaken up in a lighter liquid with which it does not
mix. In other words, the tendency here is to reduce surfaces of
separation to the least possible value, large particles growing in mass
and bulk mechanically at the expense of smaller particles; in other
words, exhibiting the phenomenon of flocculation.
=189. Physical Explanation of Subsidence.=—Whitney[128] thinks that the
phenomena of the suspension of clay in water may be explained on purely
physical principles, and that neither the partial solution nor hydration
hypotheses are necessary, or will explain the suspension of clay in
water, for the solution, or hydrated substance, would still have a
higher specific gravity than the surrounding liquid. He calls attention
in the first place to the fact, that in a turbid liquid, which has been
standing for weeks and which is only faintly opalescent, the grains in
suspension are still of measurable size, if properly stained as in
bacteriological examinations and viewed through an oil emersion
objective. He gives a value of 0.0001 millimeter, as the lower limit of
the diameters of these particles of “clay,” which are usually met with
in agricultural soils. He refers to the fact that fine dust and ashes,
and even filings of metals, may remain in suspension in the air for days
and even months in very apparent clouds, or haze, although they may be a
thousand times heavier than the surrounding air. Particles of clay, no
smaller than the limits which have been assigned, should remain in
suspension in the much heavier fluid, water, for an indefinite time, for
the volume or weight of the particles (⁴⁄₃)(πr³) decreases so much more
rapidly in proportion than the surface (4πr²), that there is,
relatively, a larger amount of surface area in these fine clay
particles, and a great deal of surface friction in their movement
through a medium, and they would settle very slowly. Under ordinary
conditions, however, the mean daily range of temperature is about twenty
degrees, the mean monthly range is fifty degrees, and the yearly range
100° F., and the ordinary convection currents, induced by the normal
change of temperature, would be sufficient of itself to keep these fine
particles in suspension in the liquid for an indefinite time, as it is
known that currents of air keep fine particles of dust and ashes in
suspension. If the volume or weight of a fine gravel, having a diameter
of one and five-tenth millimeters, be taken as unity, then for a
particle, having a diameter of 0.00255 millimeter, which is the mean
diameter for Whitney’s clay group, the volume decreases in the ratio
1:0.000000004853, and the surface decreases only in the ratio
1:0.000286.
=190. Practical Applications.=—The action of mineral substances in
promoting flocculence has been taken advantage of in later times in the
construction of filters for purifying waters holding silt in solution.
In these filters the introduction of a small quantity of alum, or some
similar substance, into the water usually precedes the mechanical
separation of the flocculent material. In the same way the action of
iron and other salts on sewage waters has been made use of in their
purification and in the collection of the sewage material for
fertilizing purposes.
=191. Separation of the Soil Into Particles of Standard Size.=—The
agronomic value of a soil depends largely on the relative size of the
particles composing it. The finer the particles, within a certain limit,
the better the soil. The size of the particles may be estimated in three
ways: (1) by passing through sieves of different degrees of fineness;
(2) by allowing them to subside for a given time in water at rest; (3)
by separating them in water moving at a given rate of speed. The first
method is a crude one and is used to prepare in a rough way, the
material for the second and third processes.
=192. Separation in a Sieve.=—The soil should be dry enough to avoid
sticking to the fingers or to prevent agglutination into masses when
subjected to pressure. It should not, however, be too dry to prevent the
easy separation of any agglutinated particles under the pressure of the
thumb or of a rubber pestle.
The sieve should have circular holes punched in a sheet of metal of
convenient thickness to give it the requisite degree of strength. Sieves
made of wire gauze are not so desirable but it is difficult to get the
finer meshes as circular perforations. Such sieves cannot give a uniform
product on account of the greater diagonal diameter of the meshes and
the ease with which the separating wires can be displaced. It is
convenient to have the sieves arranged _en batterie_; say in sets of
three. Such a set should have the holes in the three sieves of the
following dimensions; _viz._,
1st sieve 2 millimeters diameter.
2nd „ 1 millimeter „
3rd „ 0.5 „ „
Coarser single sieves may be used to separate the fragments above two
millimeters diameter if such a further classification be desired. Each
sieve fits into the next finer one and the separation of a sample into
three classes of particles may be effected by a single operation. In
most cases, however, it is better to conduct each operation separately
in order to promote the passage of agglutinated particles by gentle
pressure with the thumb or with a rubber pestle. In no case should a
hard pestle be used and the pressure should never be violent enough to
disintegrate mineral particles.
There is much difference of opinion concerning the smallest size of
particles which should be obtained by the sieve.
Most analytical processes prescribe particles passing a sieve of one
millimeter mesh (¹⁄₂₅ inch). There is little doubt, however, of the fact
that a finer particle would be better fitted for subsequent analysis by
the hydraulic method.
For this purpose a sieve of 0.5 millimeter circular mesh is preferred.
=193. Sifting with Water.=—In soils where the particles adhere firmly
the sifting should be done with the help of water. In such cases the
soil is gently rubbed with a soft steple or the finger in water. It is
then transferred to the sieve or battery of sieves which are held in the
water, and rubbed through each of the sieves successively until the
separation is complete. After the filtrate has stood for a few minutes
the supernatant muddy liquor is poured off, the part remaining on the
sieve is added to it and the process repeated until only clean particles
larger than 0.5 millimeter are left on the sieve. These particles can be
dried and weighed and entered on the note book as sand. The filtrate
should be evaporated to dryness at a gentle temperature and when
sufficiently dry be rubbed up into a homogeneous mass by a rubber
pestle.
The sieve recommended by the Association of Official Agricultural
Chemists[129] for the preparation of fine earth for chemical analysis
has circular openings ¹⁄₂₅ inch (one millimeter) in diameter.
Wahnschaffe[130] directs that a sieve of two millimeters mesh be used in
preparing the sample for silt analysis and that the residue after the
silt analysis is finished, which has not been carried over by a velocity
of twenty-five millimeters per second, be separated in sieves of one
millimeter and 0.5 millimeter meshes respectively.
Hilgard objects to leaving this coarse material in the sample during the
process of churn elutriation on account of the attrition which it exerts
and therefore directs that it be separated by sieve analysis before the
elutriation begins.
=194. Method of the German Experiment Stations.=[131]—In the method
recommended for the German Agricultural Stations an attempt is made to
secure even a finer sieve separation than that already mentioned.
Sieves having the following dimensions are employed; sieve No. 1, square
meshes 0.09 millimeter in size, diagonal measure 0.11 millimeter; sieve
No. 2, square meshes 0.14 to 0.17 millimeter in diameter, diagonal
measure 0.22 to 0.24 millimeter; sieve No. 3, square meshes 0.35 to 0.39
millimeter in diameter, diagonal measure 0.45 to 0.50 millimeter;
finally a series of sieves one, two and three millimeters circular
perforations.
Five hundred grams of the soil (in the Halle Station only 250) are
placed in a porcelain dish with about one liter of water and allowed to
stand for some time with frequent stirring, on a water bath. After about
two hours, when the soil is sufficiently softened so that with the help
of a pestle it can be washed through the sieves, the process of sifting
is undertaken in the following manner: Sieve No. 3 is placed over a dish
containing water, the moistened soil placed therein and the sieve
depressed a few centimeters under the water and the soil stirred by
means of a pestle until particles no longer pass through. After the
operation is ended the residue in the sieve is washed with pure water
and dried. The part passing the sieve is thoroughly stirred and then
washed with water into sieve No. 2 and treated as before. The product
obtained in this way is brought into sieve No. 1 and carefully washed.
All the products remaining on each of the sieves are dried at 100° and
weighed. The portion passing sieve No. 1 is either dried with its wash
water or estimated by loss by deducting from the total weight taken, the
sum of the other weights obtained. If a more perfect separation of the
first sieve residue be desired it can be obtained by passing it through
sieves of the last series which may have meshes varying in size, _viz._:
one, two, or three millimeters in diameter. Each sieve of the same class
should have holes uniformly of the same size.
The sieve products are characterized as follows: The part passing a
three millimeter sieve is called fine earth, while the part remaining is
called gravel. The fine earth is separated into the following products:
The part that passes through the three millimeters opening and is left
by the two millimeters opening is called _steinkies_. The product from
the two millimeters opening and the residue from the one millimeter
opening is called _grobkies_. The product from the one millimeter
opening and the residue on the sieve No. 3 is called _feinkies_. The
product from the sieve No. 3 and the residue from the sieve No. 2 is
called coarse sand. The product from sieve No. 2 and the residue from
sieve No. 1 is called fine sand. The product from sieve No. 1 is called
dust. The dust can be further separated into sand, dust, and clay. For
the examination of the clay the Kühn silt cylinder as modified by
Wagner, is recommended. The cylinder has a diameter of eight centimeters
and a height of thirty centimeters, and is furnished with a movable exit
tube reaching to its bottom.
=195. General Classification of the Soil by Sieve Analysis.=—The
classification recommended by the German chemists is satisfactory but
the following one is more simple. All pebbles, pieces of rock, etc.,
should first be separated by a two millimeters circular mesh sieve,
dried at 105° and weighed. The result should be entered as pebbles and
coarse sand.
The finer sand may be separated with a sieve of one millimeter circular
openings.
The still finer sand is next separated with the sieve of 0.5 millimeter
circular openings as indicated above.
The sample may now be classified as follows:
1. Coarse pebbles, sticks, roots, etc., separated by hand.
2. Pebbles and coarse sand not passing a two millimeters sieve.
3. Sand not passing a one millimeter sieve.
4. Fine sand not passing a 0.5 millimeter sieve.
5. Fine earth passing a 0.5 millimeter sieve.
=196. Classification of Orth.=[132]—As fine silt are reckoned those
particles which range from 0.02 to 0.05 millimeter; as fine sand the
groups from 0.05 to 0.2 millimeter; as medium sized sand those ranging
from 0.2 to 0.5 millimeter and for large grained sand those particles
ranging from 0.5 to 2 millimeters in diameter. Particles over two
millimeters form the last classification.
SEPARATION OF THE EARTH PARTICLES BY A LIQUID.
=197. Methods of Silt Analysis.=—The further classification of the
particles of a soil passing a fine sieve can best be effected by
separation in water. The velocity with which the current moves or with
which the particles subside will cause a separation of the particles
into varying sizes. The slower the velocity the smaller the particles
which are separated. There is, however, a large and important
constituent of a soil which remains suspended in water, or in a state of
seeming solution. This suspended matter would still be carried over by a
current of water moving at a rate so slow as to make a subclassification
of it impossible. This suspended matter passing off at a given velocity
may be classed as clay, and it consists in fact chiefly of the hydrated
silicate of alumina, or other particles of equal fineness. The laws
which govern its deposit have already been discussed.
The apparatus which have been used for silt analysis may be grouped into
four classes.
(1) Apparatus depending on the rate of descent of the particles of a
soil through water at rest. The apparatus for decanting from a cylinder
or a beaker belong to this class.
(2) Apparatus which determine the rate of flow by passing the liquid
through a vessel of conical shape. The system of Nöbel is a good
illustration of this kind of apparatus.
(3) Apparatus in which the elutriating vessel is cylindrical and the
rate of flow determined by a stop-cock or pressure feed apparatus. The
system of Schöne represents this type.
(4) Apparatus in which the above system is combined with a device for
mechanically separating the particles and bringing them in a free state
into the elutriating current. The system of Hilgard is the type of this
kind of apparatus.
In practice the use of cylindrical apparatus with or without mechanical
stirring and the method by decantation have proved to be the most
reliable and satisfactory procedures. Between the beaker and churn
methods, of separation there is little choice in regard to accuracy.
Which is the superior method, is a question on which the opinions of
experienced analysts are divided. The various processes will be
described in the order already mentioned.
=198. Methods Depending on Subsidence of Soil Particles.=—The simplest
method of effecting the further separation of the soil particles is
without doubt that process which permits them to fall freely in a liquid
sensibly at rest. The practical difficulties of this method consist in
the trouble of securing a perfect separation of the particles, in
preventing flocculation after division and in avoiding currents in the
liquid of separation.
For the separation of the soil particles for this method boiling and wet
pestling are the only means employed. The flocculation of the separated
particles may be partially prevented by adding a little ammonia to the
water employed. The author has also tried dilute alcohol as the
separating liquid but the results of this method are not yet
sufficiently definite to find a place in this manual. Evidently the
practical impossibility of avoiding convection currents prevents the use
of water at a high temperature for this separation, although the
tendency to flocculation almost disappears as the temperature approaches
100°. The general method of avoiding the errors due to flocculation in
the subsidence method consists in repestling the deposited particles and
thus subjecting them as often as may be necessary to resedimentation.
These principles are well set forth by Osborne,[133] who states that
when a soil is completely suspended in water by vigorous agitation,
particles of all the sizes present are to be found throughout the entire
mass of liquid. When subsidence takes place, the larger particles will
go down more rapidly than the smaller ones, but some of the small
particles that are near the bottom will be deposited sooner than some of
the larger ones which have a much greater distance to travel. Thus,
independently of the fact that the larger particles in their descent are
somewhat impeded by the smaller, the smaller being at the same time
somewhat hastened by the larger, the sediment that reaches the bottom at
any moment is a more or less complex mixture of all the mechanical
elements of the soil. The liquid, however, above this sediment at the
same moment will have completely deposited all particles exceeding
certain dimensions of hydraulic value, determined mainly by the time of
subsidence.
If now the aforesaid first sediment be suspended in pure water, and
allowed to subside for the same time as before, the larger part of it
will be again deposited, but some will remain in suspension, consisting
of a considerable part of the finer matter of the first sediment. By
pouring off these suspended particles with the water and agitating the
sediment again with clear water as before, another portion of fine
particles will be suspended and may be decanted from it. On continuing
this process of repeated decantations it will soon be found that the
soil has been separated into two grades.
It is evident that in this way a separation can be made, but it is
perhaps not so clear that such a separation would be sharp enough for
the purposes of a mechanical soil analysis. If, for instance, the
separation is to be made at 0.05 millimeter diameter, it is evident that
by repeated decantations all below 0.01 millimeter can be washed out of
that above 0.05 millimeter, but it may not appear so probable that all
below 0.045 millimeter can be removed without removing some above 0.055
millimeter.
Such a result may be easily attained, however, if the following
principle be adhered to: