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Theory of Physical Treatment of Water
prepared
by
Under Construction
Professor Young I. Cho, Ph.D., Department of Mechanical Engineering & Mechanics
Drexel University, Philadelphia, PA 19104
URL: http://httpsrv.ocs.drexel.edu/faculty/choyi
Introduction
Scale is formed in many water-processing applications such as boilers, heat exchangers,
condensers, evaporators, cooling towers, and pipe walls. Scale often observed in industry
includes calcium carbonate, calcium sulfate, barium sulfate, silica, iron scales, and others. The
types of scale differ from industry to industry, depending on the contents of available water.
One of the most common forms of scale is calcium carbonate (CaCO3), which occurs naturally
as an ingredient of chalk, limestone, and marble. Water passing over and permeating through
rocks dissolves calcium carbonate, and when this water subsequently flows through a water
system the calcium carbonate precipitates out to form a hard scale. This clogs pipes and
encrusts heat transfer surfaces. Usually the correction of the problem of scale build-up is
accomplished by acid cleaning, scraping, and water or sand blasting, an operation which incurs
downtime and repair costs.
Various chemicals are successfully used to prevent scale by reducing water hardness and silica
as well as removing alkalinity. Acid cleaning has been effective in removing existing scale and is
a part of routine maintenance. However, the cost of chemical treatment recurs every month in
most cases. Furthermore, the loss of equipment material due to the acid cleaning is of a matter
of concern.
This paper presents a theory of physical (i.e., non-chemical) water treatment representing an
environmentally clean technology to prevent and remove scales. The physical water treatment
offers an alternative to the chemical water treatment. History shows that there were attempts
to treat water-using magnets two to three thousand years ago. In the United States, there have
been numerous efforts for the past 150 years to introduce various physical water treatments as
manifested by the long list of patents awarded by the U.S. patent office.
One of the major problems in the physical water treatment is the lack of understanding of its
operating principle (or theory). Currently there are more than 100 companies marketing
different types of physical water treatment products in the world. Each provides a paragraph
explaining how its product works. Some of the claims are correct and acceptable while many are
at fault from the perspective of fundamental physics and physical chemistry. Furthermore, most
claims are testimonial statements. For example, they state that the treatment completely
cleaned old scales from pipe in two months. Although these statements collected from field
applications are very valuable and helpful in marketing, they do not add much in understanding
the theory of the physical water treatment. The objective of this paper is to review the
fundamental theory on which all physical water treatment products are based.
Background
Scale deposition mechanism is often explained by a process that includes dissolution of
minerals, supersaturation, nucleation, precipitation, crystal growth, and, finally, scale
deposition. Many variables control the scale deposition mechanism. The three most important
variables are pH, temperature and pressure, because the solubility of scale-causing minerals are
critically dependent on these three variables. The solubility of calcium carbonate decreases with
increasing pH and temperature whereas it decreases with decreasing pressure. When conditions
such as pH, temperature, and pressure change in a flow system such that the solubility of scalecausing minerals decreases, the electrostatic Coulombic attraction between the dissolved
mineral ions and metal surfaces makes these minerals stick to the surfaces. This is why scales
are unavoidable without some active scale prevention measures.
Many billions of dollars are lost due to the equipment failure or replacement caused by scale
build-up. For example, most heat exchangers used in a hard water area need regular
maintenance every three to six months and a major overhaul every three to five years. Thus,
reduction or prevention of scale deposits would create huge economic benefits. In fact, if we
successfully demonstrate the effectiveness of any physical water treatment technology in
preventing and removing scales, then this technology will revolutionize many industries,
including power, agricultural (i.e., poultry), mining, chemical, marine (i.e., ships), food
processing, pharmaceutical industries to name a few.
The Confusion
It is well known that there are two types of calcium carbonates: calcite and aragonite as shown
in Fig. 1. In all chemistry textbooks and relevant reference books, calcite is described
consistently as the calcium carbonate which is formed at a lower temperature (i.e., below
30oC), easily removable with weak acid, less-adherent than aragonite, having a hexagonal
crystal shape and a specific gravity of 2.71. Aragonite is described as the one which is formed at
high temperature (i.e., above 30oC), difficult to remove, having an orthorhombic crystal shape
and a specific gravity of 2.94. Specifically, they describe the aragonite as a more dangerous
form of calcium carbonate in boiler and other heat transfer equipment since it forms a harder
and denser deposit than the calcite. When calcium carbonate is formed at temperature above
30oC, both aragonite (~80%) and calcite (~20%) are formed. However, at a temperature below
30oC, almost all the calcium carbonates are calcite. This is one of the important facts which
should be clarified in order to propose the present theory of water treatment in this paper. The
confusion was caused by the physical water treatment industry in their commercial brochures,
where calcite was described as the more dense and more-adherent than aragonite. It is time to
correct the mistake.
Classification of Water Treatment Methods
Most water treatment devices can be classified in three categories: permanent magnets,
induction device, and in-line electrodes. Figure 2 shows a typical example of each device. Note
that the actual arrangements in commercial devices can be quite different from the illustrations
in Fig. 2. Devices using permanent magnets critically depend on the magnetic strength of
permanent magnet, and the average strength of permanent magnet is in the range of 4,000 to
6,000 gauss as shown in the table below.
Induction devices utilize complex pulsing current to produce induced oscillating electric field
inside pipes. In most cases, the magnetic field produced from the induction is slightly larger
than the earth's magnetic field so the induction device should not be considered as a magnetic
device at all.
Type of magnets Strength (Gauss)
____________________________________________________
Induction device 0.1 - 10
refrigerator magnets that hold notes 100
bar magnet 100 - 1,000
scale removing magnets 4,000 - 6,000
large scientific magnets 20,000 - 40,000
superconducting magnets 5,000,000 - 10,000,000
_____________________________________________________
Table: Comparison of magnetic strength
Fig. 2 Examples of permanent magnet, induction device, and in-line electrode device
Devices based on in-line electrodes use a high energy electrode at the center of pipe and also
utilize complex pulsing currents between the center electrode and wall, where water makes
direct contact with the center electrode and wall section. This in-line technology requires cutting
of an existing pipe. Although cutting the existing pipe is a major challenge from the installation
and marketing point of view, this in-line technology provides very effective means of treating
water due to the direct contact between the in-line unit and water. The in-line technology uses
one of the following: electromagnetic, electrostatic, electronic, or ultrasound methods. All four
methods have positive effects on the interference of crystalline formation. The electrostatic unit
requires a relatively high voltage whereas the electronic unit does not.
Review of Prior Theories
A brief review of a few of the prior theories and research is appropriate at this point. Moody
[U.S. Patent 3,228,878] pointed out that scale-causing particles including calcium carbonate,
magnesium carbonate, silicon dioxide are diamagnetic, i.e., repelled by the magnetic. He
proposed a scale prevention method through an alteration of the energy content of the
diamagnetic substances.
It has been claimed in commercial brochures of permanent magnets that when water is treated
by a strong permanent magnet, the scale-causing ions (mostly diamagnetic) become
magnetized instantaneously, having induced magnetic dipole. Consequently, these diamagnetic
scale-causing ions repel each other, resulting in the prevention of scale build-up and removal of
existing scales. The magnetization lasts over some distance and period even after the
diamagnetic scale-causing ions leave the area under the strong magnetic field. To the best of
our knowledge, these claims can not be justified by the laws of physics. A similar claim of a
single, instantaneous jolt to break large clusters of scale-causing diamagnetic molecules has
been made. The existence of the large clusters in a saturated or even in a supersaturated
solution can not be justified based on thermodynamic principles. All scale-causing ions in
solution are in a dissolved state, and the solution becomes supersaturated when parameters
such as pH, temperature, pressure, etc. change, thus, resulting in the precipitation of
diamagnetic clusters.
The induced magnetic moments or simply magnetization M of a material is defined as the net
magnetic moment per unit volume, i.e., the vector sum of all the atomic magnetic moments in a
unit volume. Conventionally, the ratio of the induced magnetization to the applied magnetic
field, M/B, is called the magnetic susceptibility. In non-ferromagnetic materials, the induced
magnetic forces are so much smaller than the electric forces, that thermal motions can knock
out the alignment by the atomic dipole moments even at temperatures as low as a few tenths of
a degree Kelvin. So, it would be impossible to have any permanent lining up of the magnets at
room temperature [Feynman et al. Vol. II, p.34-2]. The above statement was made for solid.
Thus, the permanent lining up of diamagnetic scale-causing ions in liquid is not possible.
Therefore, the claim that the scale-causing ions become magnetized instantaneously, having
induced magnetic dipole, is not correct.
Spiegel [1] proposed a mechanism in support of his patent which focuses on what he describes
as the specific work function. This is the shift of electrons on the surface of a solid which he
claims to accomplish through the use of a rotating disc of permanent magnets. This shift in
electronic charge will affect the rate of growth and the morphology of the growing crystal. He
cites the experimental work of Donaldson and Grimes [2], who found that untreated water
would preferentially form aragonite, whereas magnetically treated water would preferentially
form calcite.
Herzog et. al [3] focused on the effect of iron, which is generally present in natural waters, and
is highly affected by magnetic fields. They have presented experimental evidence that in the
presence of iron ions, the growth of calcite is inhibited, while aragonite growth is unaffected.
Iron also inhibited the natural conversion of aragonite into calcite. It was suggested that
magnetic treatment could possibly induce the liberation of iron into the water stream, thus
inhibiting the growth of scale.
De Baat [4] has proposed in his patent that the magnetic treatment affects the orientation of
the water molecule itself. This orientation is proposed to result in the ions of impurities (calcium
and magnesium) coming out of solution. The resulting precipitate forms in the water as opposed
to nucleating at the wall surface of the pipe. These loose precipitates can then be filtered out of
solution.
Kronenberg [5] studied the effects of permanent magnets on water by preparing water samples
dried on glass slides for microscopic observation. He found microscopic evidence indicating a
change in crystal formation due to the magnetic treatment. Calcium carbonate in untreated
water was found to crystallize in massive, prismatic crystals along the solid/water interface.
Treated water formed circular crystals not at the interface but within the water phase. The
circular crystals would re-crystallize slowly over a period of days and then dissolve back into
solution. The proposed mechanism is based on the energy absorbed by the water molecules. He
states that the internal frequency of the water ‘cage’ formed from hydration of particles in
solution is in the range of 1-10 kHz, with a multiple-magnetic configuration able to supply this.
One of the common observations in the use of permanent magnets in water treatment is the
effect of flow velocity on the effectiveness of water treatment device. Moody [U.S. Patent
3,228,878] mentioned that approximately one half foot per second was sufficient for most
scale-causing substances. Kronenberg [5] reports that the relationship between the
effectiveness of permanent magnets and flow velocity has in almost all cases a maximum for
one velocity. In his tests, he reported the optimum velocity of 2.5 and 4.6 m/s for single and
double distances between magnets, respectively. Bartz [private communication] reports that the
threshold flow velocity in most cases was 23 ft/s (i.e., 7 m/s), above which permanent magnets
work the best. Mag-Well reduces the cross-sectional area by approximately 75% in order to
increase the flow velocity, where they install permanent magnets. In the use of permanent
magnets, it appears that the flow velocity plays a major role, and the reason for that has not
been clearly explained.
Past claims can be broadly categorized into two areas - magnetic or electric effects on (1) water
and (2) crystal formation. The former can be briefly described below and the latter will be
described in the subsequent sections. According to water chemistry most water molecules are
locked in aggregates in liquid water, and less than 20% exist as free water molecules [cite
Bailar]. This is because water molecules have a dipole moment - the hydrogen atom is attracted
to the oxygen atom of the adjacent water molecule. Most physical water treatment devices
produce molecular agitation whose frequency is tuned to the natural frequency of the water
molecules vibrating in the aggregates. Through the cooperative resonance of the water
molecules, free water molecules become available, dissolving existing scales. Figure 3 shows a
schematic diagram of the above-mentioned resonance process to break the hydrogen bonds in
water aggregates.
Fig. 3 Schematic diagram of proposed hypothesis: liquid water clusters are broken into free
separate water molecules.
Although there are substantial differences in the claims, there are certain areas of commonalty.
There is a time-dependent magnetic or electric field produced, either from the motion of
charged particle passing fixed magnets, or from an oscillating current in an electric coil wrapped
around a pipe. The time-dependent magnetic or electric field yields a molecular disturbance
which affects any particle with an electric charge. Most past theories were rejected by the
scientific community because the observation was presented, often with little or no
incorporation into the accepted theories of natural science. It is the intent of this paper to
present a theory consistent with commonly accepted ideologies of science.
Proposed Theory-Macro Description
Although there are three different types of physical water treatment devices, we believe that the
operating principles of the three devices are based on the same laws governing the physical and
chemical behavior of water and scale-causing dissolved ions. The origin of scale problem is in a
'localized' supersaturation, and the physical water treatment eliminates the localized
supersaturation, in which the scale-causing minerals such as calcium and magnesium ions are
unstably hydrated or 'barely hanging in', thus ready to come out of the solution.
We propose that all physical water treatment devices provides the necessary energy such that
the required overall free energy change, associated with the formation of a critical nucleus
under heterogeneous condition, is achieved. Once the nucleus has reached a critical mass, the
crystallization continues spontaneously until the precipitate is visible. This crystallization occurs
within the water phase. Therefore the scale that is formed does not grow and encrust the pipe
walls, but is suspended with the carrier fluid.
In addition to the change in nucleation site, the physical treatment also affects the crystal
structure of the scale. Under treatment, the mineral ions are driven into creation of the nonadherent crystal form of the scale. This type of scale is often described as powdery and fluffy,
and easily removed by turbulence and routine blowdowns of equipment.
As a result of the forced precipitation, the water becomes undersaturated and is then able to
dissolve the scale that it comes in contact with. This explains the removal of scale deposits
which has been formed prior to the physical treatment. Figure 4 shows a schematic diagram of
the above-mentioned precipitation process for an induction cable technology.
Fig. 4 Schematic diagram of precipitation process occurring in water treatment with induction
technology
Permanent magnets produce molecular agitation when charged molecules or water molecules
(i.e., polar molecule) enter the region under strong magnetic field. The molecular force
experienced by the dissolved ions or water molecules is proportional to the product of flow
velocity and the strength of magnetic field as
Molecular agitation in permanent magnet = V x B (1)
where V is the flow velocity and B is the strength of permanent magnet. Therefore, it is
important to have a relatively large magnitude of flow velocity in the use of permanent magnet.
The larger the flow velocity, the more efficiently the permanent magnet works. The frequency of
molecular agitation comes from both the flow velocity and the number of permanent magnets.
Hence, the optimization which should include flow velocity, pipe size, water hardness, etc. is
extremely important in the use of a permanent magnet for the purpose of water treatment.
In the induction device, a cable is wrapped around a pipe. The cable is connected to an
electronic unit that sends a complex, dynamic current to produce extremely small, time-varying
magnetic fields inside the pipe. The time-varying magnetic field produces an induced, oscillating
electric field inside the pipe, a phenomenon that is well known as the Faraday's law.
= - (2)
where E = induced electric field vector. The induced, oscillating electric field provides the
necessary molecular agitation for scale prevention and removal. The major advantage of the
induction device is in the non-invasive nature and its effectiveness does not depend on flow
velocity. It does not require the cutting of a section of the pipe so that the installation is
extremely simple. The drawback of the induction device is the fact that the treatment of water
becomes weak at the center of the pipe where flow has the maximum velocity.
The device using an in-line electrode provides the water treatment where flow becomes
maximized, which is one of the major strengths of this device. Furthermore, the effectiveness of
this device does not depend on the flow velocity in pipe. However, this device requires a cutting
of an existing pipe section.
Proposed Theory-Micro Description
To understand the mechanism of physical water treatment, we will begin with a discussion of
the energy of nucleation. In order to understand the process of nucleation, which can be either
heterogeneous or homogeneous, it is necessary to introduce the concept of Gibbs free energy of
a substance. The Gibbs free energy of the formation of a substance is defined as the heat
content for the formation of the substance minus the product of the temperature and the
entropy. This function is often used to evaluate thermodynamic equilibrium. If the Gibbs energy
is zero, the reaction is at equilibrium, while a spontaneous reaction will result in a reduction in
the change in Gibbs free energy.
The Gibbs energy of nucleation is the summation of two distinct portions, a bulk energy term
and a surface energy term.
DG(nucleation) = DG(bulk) + DG(surface) (3)
The bulk energy term can be defined as
DG(bulk) = -jKT [] = (4)
where j is the number of molecules in the nucleus, k is the Boltzmann constant, T is
temperature, V is the molecular volume and a/ao is the ratio of the actual and equilibrium
activities. This can be considered the ratio of supersaturation. Note that this term is always
negative, indicating that this term always drives the reaction forward spontaneously. This is the
energy released during crystallization from the making of bonds. The surface term can be
defined as
DG(surface) = 4prg (5)
where r is the radius of the nucleus, and g is the interfacial energy. This term is the energy
required to make the surface of the nucleus, and is positive in sign. In terms of radius, the
Gibbs free energy can be thought of in the following manner.
DG(crystallization) = [function of radius] + [function of radius] (6)
At the initiation of nucleation, the number of molecules in the nucleus is small, making the bulk
term relatively small. The surface term will dominate, making the overall Gibbs free energy
positive in sign. Thus, the reaction will not occur spontaneously without energy input from
outside the system. However, as the crystal grows, the bulk term will become more dominant
and the reaction will eventually continue spontaneously. Figure 4 shows the qualitative trend of
how DG (crystallization) varies with nucleus size for different supersaturation ratios.
Fig. 4 Profiles of Gibbs free energy at three different supersaturation ratios
(i.e., a/ao <1, 1, and 100)
This figure shows how the Gibbs free energy of crystallization is affected by the size of the
nucleus and the degree of supersaturation. Assuming the solution is supersaturated, the nucleus
must grow beyond a critical size before the bulk term dominates and the reaction proceeds
spontaneously. The energy that must be supplied into the system before this happens can be
considered the activation energy of nucleation. In the vein of conventional reaction rate theory,
the rate of nucleus formation can be expressed as
Rate of Nucleation = A exp [-G(activation)/kT] (7)
where A is similar to the frequency factor in reaction rate equation. This factor adjusts for the
number of effective collisions as related to the total number of collisions. In this manner, it can
be seen that the rate of nucleation is dependent on four basic quantities; the frequency factor,
the temperature, the interfacial energy, and the degree of saturation.
It is well accepted that the nucleation that occurs in natural waters is predominantly from
heterogeneous nucleation. Any foreign material which will reduce the interfacial energy between
the solid and liquid phase will promote nucleation. Conventionally, this refers to an agreement
in lattice types and energies, but can also occur when surface adsorption differs. This is the
basis for the effect of the physical treatment of water.
The second proposed effect from the magnetic treatment concerns the force imparted by
changing magnetic field. As the water experiences the changing magnetic field, the generated
Lorentz force imparts force on all charged ions within the field. In the same manner that heat
energy increases molecular vibration and stretches these bonds of hydration, the induced
voltage from the changing magnetic field will similarly increase the energy of the system.
The forces imparted by the magnetic treatment are clearly smaller than the bond energies of
solvation. Therefore, the magnetic treatment will not directly affect the macro-property of
solubility. Rather, it is proposed that the energy from the magnetic treatment will cause an
increase in the water-to-ion bond energy, resulting in a weaker attachment of the ions to the
surrounding cluster of water molecules. In this scenario, the solvated ions are affected more by
the large number of intermolecular collisions which occur naturally in the water flow. Referring
back to equation 5, this indicates that the frequency factor (A) increases, resulting in a larger
number of collisions successfully culminating in nucleation.
The Lorentz force imparted from the changing magnetic fields will affect the charged particles
within its field. Again, the forces under discussion are not large enough to cause a shift in macro
particles. However, it is adequate and sufficient for the Lorentz force to affect the dipole
moment of the ions. It is conceivable that the force would induce a temporary dipole moment
on a neutral molecule, but is more likely to shift the charge location on a polar molecule subtly.
It is this concept which changes the morphology of the crystal formed.
When pure calcium carbonate precipitates naturally under typical environmental conditions, the
predominant crystalline form can either be aragonite or calcite form depending on temperature
or pressure. The difference in Gibbs free energy between the formation of calcite (-269.78
Kcal/mole) and aragonite (-269.53 Kcal/mole) is only -0.25 Kcal/ mole. It should be noted that
there is no equilibrium condition for those two pure substances. The transfer or reaction is
spontaneous as long as aragonite remains at specified temperature and pressure. For example,
the pipe wall in a heat exchanger is more prone to form aragonite than calcite because of higher
pipe wall temperature. In contrast, due to the physical treatment of water (using either electric
or magnetic field) calcite will form in the liquid phase since the temperature is lower in the liquid
phase.
If the standard dipole moments of the ions are disturbed by the magnetic treatment, the
solvated ion will have a different energy with the evolving nucleus. Just as the heterogeneous
nucleation rate increases due to lowered interfacial energy, a shift in dipole moment can also
result in increased nucleation.
Discussion
Any theory of physical water treatment must be able to explain four distinct phenomena. The
first is the immediate forced precipitation of calcium carbonate from water, the second is the
predominant formation of the calcite (non-adherent) form of calcium carbonate, the third is the
dissolution of calcium carbonate which had been formed prior to treatment and the fourth is the
overall temporary nature of the treatment.
The forced precipitation is explained by heterogeneous nucleation theory. Dissolved ions are
constantly participating in collisions with the impurities in the water phase. The small
percentage of the collisions that are effective in nucleation are statistically accounted for by the
frequency factor previously described. The induced voltage provided by the magnetic treatment
changes the effectiveness of the collisions, increasing the number of collisions that result in
nucleation.
The change in the frequency factor can be explained by the weakening of the hydrogen bond
between the ion and the surrounding water molecules. The Lorentz force will orient the charges
of the ions (both positive and negative) so that the surface charges of the ions which are
colliding in the parallel direction to the electric field will be enhanced. Along with an increase in
the kinetic energy of the colliding ions, the electric field will also increase the Coulombic
attraction of the ions by increasing its dipole moment. All of these factors will improve the
efficiency of the collisions, resulting in a larger number of resulting nuclei. This is the basis for
the immediate precipitation that is observed from the physical treatment.
The explanation of how the physical treatment of water results in the formation of the nonadherent, crystalline form of calcium carbonate in the liquid phase is explained by the lattice
energies of crystals. For untreated water, after a nucleus has been created, crystals in general
will grow at the pipe wall in layers by forming the lattice structure which depends on
temperature at the pipe wall. For calcium carbonate crystals at higher pipe wall temperature,
this structure is the aragonite form, which is dendritic, dense, and adherent. In this structure,
adjacent carbonate ions in each crystal layer are oriented in opposite directions as shown in Fig.
1. The Lorentz force produced by a water treatment device changes the random orientation of
the carbonate ions in solution. As the carbonate ions come out of solution to form the next
crystal layer, they are all oriented in the same direction due to this Lorentz force. When calcium
carbonate crystallizes with this ordered and similar orientation of carbonate ions, the result is
the formation of calcite and not aragonite. Therefore the observed change in adherent scale to
non-adherent scale is explainable by a shift in crystal lattice structure.
The dissolution of scale which had been formed prior to physical treatment is explainable by the
concepts of chemical equilibrium. Most natural waters are saturated or slightly less than
saturated with calcium carbonate. What this means is that the following reaction is at
equilibrium.
Ca+ HCO
CaCO (8)
Any change in concentration will shift the reaction based on LeChatelier's principle of
equilibrium. Under physical treatment, additional calcium carbonate will be forced to precipitate
in liquid phase, as calcite but not as aragonite. There will therefore be two reactions at
equilibrium.
Ca+ HCO
CaCO (9)
Ca+ HCO
CaCO (10)
As the physical treatment increases the formation of water-born calcite, the concentration of
bicarbonate ions will fall in Eq. (10). This depletes the reactants of Eq. (9) and will force this
reaction to dissolve prior-formed aragonite to find a new level of equilibrium. The previously
formed calcium carbonate solid in the form of aragonite (mostly localized at pipe walls) will
thereby dissolve into solution, creating calcium and bicarbonate ions until a new state of
chemical equilibrium is reached.
The last phenomenon is the documented temporary effects of physical treatment, which is
strongly related to the above-mentioned removal of previous scale deposits. Once the water is
treated and the calcite solid has formed, the system is not in chemical equilibrium. Referring
again to Eq. (8), the reaction has been forced to the right, and there are not enough reactants
to support the solubility constant. Therefore, some of the calcite solid will dissolve back into the
solution until it reaches chemical equilibrium again. As the scale that is forced to precipitate and
the previously deposited scale are redissolved, the water slowly reverts back into a state of
equilibrium, explaining the temporary nature of the physical treatment. The solid that remains is
in a stable state. The re-dissolving of aragonite back into solution occurs rapidly since it is a
more stable form of calcium carbonate (?).
This paper has proved a standard scientific explanation for each of the reported phenomena
associated with physical water treatment. These effects are well documented in literature, and
the authors have directly observed the effects of physical treatment under strict controls. It is
hoped that this discussion will help dispel the 'black magic' aura that has surrounded physical
water treatment, and it can be studied and accepted as a legitimate treatment, rooted in
science.
#3
The rate of nucleation of a solution or melt can be affected considerably by the presence of
mere traces of impurities in the system. However an impurity that acts as a nucleation inhibitor
in one case may not necessarily be effective in another; indeed it may act as an accelerator. No
general rule applies and each case must be considered separately.
Many reported cases of spontaneous(homogeneous) nucleation are found on careful
examination to have been induced in some way. Indeed, it is generally accepted that true
homogeneous nucleation is not a common event.
The overall free energy change associated with the formation of a critical nucleus under
heterogeneous conditions DG'crit, must be less than the corresponding free energy change,
DGcrit, associated with homogeneous nucleation, i.e.
DG'crit = f DGcrit (1)
where the factor f is less than unity.
It has been indicated above that the interfacial tension, g, is one of the important factors
controlling the nucleation process. Figure A shows an interfacial energy diagram for three
phases in contact; in this case, however, the three phases are not the more familiar solid, liquid
and gas, but two solids and a liquid. The three interfacial tensions are denoted by gcl (between
the solid crystalline phase, c, and the liquid l). gsl (between another foreign solid surface, s, and
the liquid) and gcs (between the solid crystalline phase and the foreign solid surface). Resolving
these forces in a horizontal direction
gsl = gcs + gcl Cos q
or
Cos q = (gsl - gcs) / gcl (2)
The angle q, the angle of contrast between the crystalline deposit and the foreign solid surface,
corresponds to the angle of wetting in liquid-solid systems.
The factor f in equation 1 can be expressed (Volmer, 1939) as
f = [(2 + Cos q) (1 - Cos q)2] / 4 (3)
Thus, when q = 180o, Cos q = -1 and f = 1, equation 1 becomes
DG'crit = DGcrit (4)
When q lies between 0 and 180o, f < 1; therefore
DG'crit < DGcrit (5)
When q = 0, f = 0, and
DG'crit = 0 (6)
The three cases represented by equations 4-6 can be interpreted as follows. For the case of
complete non-affinity between the crystalline solid and the foreign solid surface (corresponding
to that of complete non-wetting in liquid-solid systems), q =180o , and equation 4 applies, i.e.
the overall free energy of nucleation is the same as that required for homogeneous or
spontaneous nucleation. For the case of partial affinity (cf. the partial wetting of a solid with a
liquid), 0<q<180o, and equation 7 applies, which indicates that nucleation is easier to achieve
because the overall excess free energy required is less than that for homogeneous nucleation.
For the case of complete affinity (cf. Complete wetting) q = 0, and the free energy of nucleation
of zero. This case corresponds to the seeding of a supersaturated solution with crystals of the
required crystalline product , i.e. no nuclei have to be formed in the solution. Figure B indicates
the relationship between f and q.
As mentioned above, the heterogeneous nucleation of a solution can occur by seeding from
embryos retained in cavities, e.g. in foreign bodies or the walls of the retaining vessel, under
conditions in which the embryo would normally be unstable on a flat surface. This problem has
been analyzed by Turnbull (1950) for different types of cavity. The maximum diameter of a
cylindrical cavity which will retain a stable embryo is given by
dmax = 4 gcl Cos q / DGv (7)
where DGv is the volume free energy for the phase transformation. If the system is heated, this
reducing the supersaturation or supercooling and eliminating all embryos in cavities larger than
dmax, and subsequently cooled, the embryos retained in the cavities smaller than dmax will
grow to the mouth of the cavity. They will then act as nuclei only if the cavity size dmax >= 2rc,
where rc is the size of a critical nucleus.