Note : Les descriptions sont présentées dans la langue officielle dans laquelle elles ont été soumises.
CA 02437948 2003-08-21
APPARATUS AND METHOD FOR PRODUCING
SMALL GAS BUBBLES IN LIQUIDS
Field of the Invention
The present invention relates to an apparatus and method for aeration and
purification of
liquids, and more particularly to an apparatus and method for producing small
gas bubbles in
liquids for purification and aeration of said liquids.
Background of the Invention
Entrainment of a gas in a liquid is required in numerous industrial processes,
typically for
the purposes of reacting the gas with such liquid or materials in such liquid,
such as dissolved
ions or finely dispersed solids, to cause reaction of such gas with materials
therein to cause same
t~ be neutralized by, react with, or precipitate or be filtered out of such
liquid..
For example, it is known to bubble ozone through water, to allow the ozone to
react and
combine with dissolved minerals and/or finely dispersed solids within the
water, so as to form
solid products which may either precipitate out of the liquid or be filtered
from the water, so as
to thereby purify the water. The ozone may further react with harmful bacteria
or the like in the
water so as to render them harmless or odourless.
Where a gas is desired to react with a liquid or finely dispersed solids in
such liquids, it is
widely known that small bubbles of gas immersed in such liquid will have, for
the same volume
of gas, a greater surface area and thus a greater liquid/gas interface, than
the same volume of gas
when such gas exists in larger bubbles.
A large gas/liquid interface is a desirable characteristic in instances where
the gas is
introduced into a liquid for the purposes of reacting the gas with the liquid
or dispersed solids in
such liquid, since greater surface area of the gas exposed to such liquid
and/or finely dispersed
solids in such liquid decreases the time it takes for the gas to react with
the liquid or finely
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dispersed solids within such liquids, thus allowing quicker processing. As
well, a lesser amount
of gas, and smaller containment vessels, can thus be used, resulting in cost
savings.
The benefits, therefore, of introducing or entraining very small bubbles of
gas, typically
in the range of 50 to 100 microns in diameter, into a liquid for the purposes
of increasing the
surface area of the gas relative to the liquid and/or finely dispersed solids
in such liquid) are
known. Small bubbles of this size are generally referred to in the art as
microbubbles. For the
purposes hereinafter of this disclosure, microbubbles will be referred to and
will be understood
as meaning gas bubbles of a diameter in the range of 50 to 100 microns, and
preferable 5 to 50
microns.
A number of devices and methods for aerating liquids, typically water, with
gas bubbles,
are known.
For example, US 2,890,838 teaches a device for filter-separating iron from
water. Water
is delivered via a pipe 13 to an air aspirator 14, and thereafter such water
having air entrained
therein is delivered via pipe 16 to the upper portion of a tank I0, where it
passes vertically
downwardly in the tank 10 to a spray valve 19. At the spray valve 19 the water-
air mixture flows
outwardly through openings 21 into chamber 22 formed in a cylindrical hollow
body 23 mounted
on valve 19. The upper end of the body 23 is cone shaped, and contacts the
mating lower cone-
shaped end 25 of valve body 26. The water-air mixture flows upwardly and
outwardly through
the cone-shaped opening formed between cone-shaped surfaces 24,25 in the form
of a vaporized
spray S, as shown in Figures 2 & 4 thereof, and mixes with the air in the tank
10 as it strikes the
underside 27 of the top 28 of the tank 10, thereby introducing air into the
liquid which in turn
oxidizes metabolic iron present in the water. Iron precipitates then settles
out of solution and
down through the water contained in tank 10e
US 5,601,724 and US 5,460,731 teach an apparatus and method, respectively of
aerating
liquids. Figs. 1 & 2 of each of '724 and '731 show a venturi air injector 10
used to inject air into
water in a conduit 12. Such air-water mixture enters the bottom portion of a
tower-like pressure
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vessel 14, where it is directed upwardly via conduit 30, where it is directed
through a cylindrical
restriction gap 19 formed between the second end 34 of conduit 30 and the top
18 of vessel 14.
The gas, being of lesser density, passes more quickly through ~ he
restriction, thereby accelerating
the liquid. As the liquid exits the restriction gap 19 it pneumatically
hammers against the top 18
of pressure vessel 14. Thereafter the liquid stream, by force of gravity,
cascades through the gas
in pressure vessel 14 downwardly to further impact plate 35. Thereafter the
liquid stream then
passes through openings 37 in plate 35 and by force of gravity cascades
through the gas in
pressure vessel 14 to further impact on liquid at the bottom of the vessel.
Thereafter such liquid,
having small bubbles of air entrained therein, is removed via a conduit from
the bottom of vessel
14.
US 5,096,596 to a "Process and Apparatus fro Removal of Mineral Contaminants
from Water'° teaches a pressurized aeration tank 24 having a tube 26
located within said tank 24
which supplies the tank 24 with raw water, which is introduced to the tank 24
via the tube 26 via
a plurality of holes 28 in the tube (ref. col. 2, lines 49-54 and Figs. 1-7).
The tube 24 only
supplies "raw water°' and not wa°ter having air bubbles
entrained therein, and is not for the
purpose of providing gas microbubbles of a range of 5-50 microns. Most
importantly, no
relationship regarding the size of the holes 28 in the tube 24 is specified to
attempt to attain
microbubbles, even if the patent further provided for the raw water to first
have bubbles
introduced therein.
US 4,556,523 teaches a microbubble injector usable to separate material of
different
density by flotation, wherein microbubbles of gas are introduced into a
chamber 14 containing a
liquid mass 16. As may be seen from Figure 1 of US ' 523, a gas admixture
device 4 receives air
through an inlet 6 and ordinary water through an inlet 8. The resulting air-
water mixture is
supplied by a conduit to the bottom of chamber 14, where it passes through an
injector wall 10
via an injector hole 12 to procure a high velocity jet of air water. A
deflector wall 18 is disposed
over such injector hole, so as to create a narrow gap around the injector
hole, which the water/air
mixture must pass through. The injector hole is preferably substantially
circular, and the height
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of the passage between the injector and deflector wall at the edge of the
injector hole is less than
one quarter of the diameter of the injector hole in the injector wall.
Disadvantageously, none of the aforementioned patents teach or disclose any
specific
design interrelation between the dimensions of the injector holes/parts/or
gaps and the conduit
outer dimensions which will best produce microbubbles in the liquid.
For example, US '838 simply provides a nut 23 on the end of the valve 24 to
adjust the
size of the aperture between cone surfaces 24,25 through which the water must
pass. No gap
dimension is ever specified which best provides bubbles of a desired small
size.
Similarly, each of US °724 and '731 simply disclose that the size of
the restriction gap 19
required is dependent upon the size of the bubbles that are produced, with no
direction as to what
gap size will produce microbubbles in the range of less than 100 microns.
These two patents
each go on to note that (at col. 6, lines 44 to 47) that the greater the
diameter of the cylindrical
edge, the closer the end of conduit 30 had to be positioned to the top 18 of
the pressure vessel 14
(i.e. the smaller the restriction gap had to be) in order to form bubbles of
the desired size. No
desired size of bubbles was ever identified, nor was there ever any
relationship specified between
the gap size and the diameter of the pipe, which would produce the smallest
bubbles, namely
microbubbles of diameter in the 5-100 micron range.
US 4,556,523 perhaps comes closest to specifying an interrelation between the
components in order to achieve desired small microbubble size in the range of
50 to 100
microns, specifying as noted above that the passage between the injector and
deflector wall at the
edge of the injector hole is less than one quarter of the diameter of the
injector hole in the
injector wall. No specific optimum size was specified. Moreover, the
particular manner by
which the microbubbles are created, namely requiring an injector wall 10 and
deflector wall 14,
requires substantial quantity of material, and is thus a particularly material-
intensive design and
thus relatively costly.
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Accordingly, a clear and real need exists for an aeration apparatus of simple
and
relatively inexpensive design having a configuration wherein the size of the
flow apertures)
through which a gas/liquid mixture flows can be accurately designed so as to
give microbubbles
of the desired small size.
Summary of the Invention
In order to meet the above need for a device able to introduce gas
microbubbles into a
liquid of simple and relatively inexpensive design, in a broad aspect of the
present invention such
invention comprises an apparatus having means for creating microbubbles in a
liquid to permit a
selected gas to better react with impurities entrained in said liquid,
comprising:
means for introducing gas bubbles, the majority of which are of a size greater
than 100
microns, into a liquid to from a liquid-gas mixture;
elongate, hollow pipe means, substantially symmetrical in cross-section of
interior
cross-sectional area, positioned substantially vertically, adapted to receive
said liquid-gas
mixture under pressure and supply said liquid-gas mixture to aperture means,
said pipe member
having plug means situate at a lowermost distal end thereof for preventing
egress of liquid
vertically downward from said distal end;
said aperture means situate on said pipe means and disposed in one or more
planes each
substantially perpendicular to a longitudinal axis of said pipe means and
extending from an
interior of said pipe means to an exterior of said pipe means, each acdapted
to direct said liquid
substantially horizontally outwardly from said pipe means; and
a containment vessel to capture said liquid-gas mixture having microbubbles of
gas
entrained therein and to permit said microbubbles to react with said entrained
impurities.
Importantly, however, and quite surprisingly, it has heen further discovered
that for an
apparatus of the above design, that in the case of a pipe member that has a
symmetric cross-
sectional area and a uniform pipe wall thickness, and a maximum interior width
Di and a
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maximum exterior width Do, a specific inter-relation need exist between the
aperture exit area Ae
of the aperture(s), and the interior cross-sectional area A; of the pipe
means, in order to achieve
creation of microbubbles of the desired small size, namely in the range of 50-
100 microns and
preferably in the range of 5-50 microns.
Accordingly, in a highly preferred embodiment, where the aperture means
consists of at
least two apertures, the pipe means is symmetric and has substantially
identical moments of
intertia about two axis in a plane of cross-section through said pipe, wherein
the combined
aperture exit area Ae of the apertures is a function of widths D; and Do ,
namely Ae is no
greater than A; x D; / Do.
Where only a single aperture is used, it has been found that Ae must not be
any greater
than Ai x Di/Do.
While the above interrelation, namely for a plurality of aperi:ures Ae <_ Ai x
Di/Do and
for a single aperture Ae < Ai x Di/2Do, means it is possible to utilize
apertures whose total
combined cross-sectional area Ae is less than Ai x Di/Do or Ai x Di/2Do in
order to create
microbubbles when said liquid-gas mixture is expelled radially outwardly
through said
aperture(s), typically, due to the desire to utilize an apparatus which
utilizes the largest flow rate
possible, it is usually greatly preferred that the greatest possible aperture
exit area be used.
Accordingly, more than one aperture will typically be desired to be used (thus
the aperture exit
area Ae may be twice as large than if only one aperture were used), and
further that the aperture
exit area Ae equal Ai xDi/Do, as such will give the greatest "throughput" of
liquid which can be
provided with gas microbubbles over a given time.
Accordingly, in a highly preferred embodiment, the pipe means will possess
more than
one aperture, and the exit area of the apertures will be equal to .Ai x Di/Do.
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In order for the above formula of Ae _< Ai x Di/Do apply for pipe members
having more
than one aperture, it is necessary that the pipe member be not only symmetric
in cross-section,
but further it have substantially identical moments of inertia about two axis
in a plane of cross-
section through said pipe. This encompasses pipes having circular, square,
hexagonal, octagonal
and the like cross-sectional shape, but not to pipes having, for example, a
rectangular cross-
section. As more fully explained in this disclosure, for geometric cross-
sectional areas which
although symmetric but which do not have identical moments of ineri:ia about
at least two axis of
a plane of cross-section, such as for rectangular pipe, such formula does not
hold true, and other
inter-relations (not the subject matter of this patent) may apply. However, in
the case of
rectangular pipe of uniform thickness, as is more fully explained below, it
has been discovered
that the required interrelation between exit areas of the apertures Ae, the
dimension of the pipe,
and the cross-sectional area Ai of the pipe is defined as
Ae <_ A; x [ D3 + D4 ]/[Dl + DZ]
where Dl is the major exterior side length, D2 is the minor exterior side
length, D3 is the major
interior side length , and D4 is the minor interior side length. However, as
rectangular pipe is
difficult to acquire, the more common application of this invention will be to
pipe members
having circular or square profiles which have identical moments of inertia
about two or more
axis in the plane of cross-section.
Accordingly, in a highly preferred embodiment, the pipe means of the present
invention
is of uniform wall thickness and has a maximum interior width I~; and a
maximum exterior
width Do , further having identical moments of inertia about at least two
separate axis in a cross
sectional plane through said pipe rrdeans; said apertures having a combined
cross-sectional exit
area Ae defined as a function of widths D; and Do and said cross-sectional
area A; of said pipe
means, wherein Ae is substantially equal to A; x D; / Do,
It is highly preferred, although not absolutely necessary, that there be a
vertical surface
which created jets of gas/liquid mixture which exit from such apertures may
impact against, in
order to assist in the creation of microbubbles of gas within the liquid.
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Accordingly, in a further refinement of the apparatus of the present
invention, such
apparatus further consists of substantially vertical surface means adapted to
be impacted by
said liquid when said liquid is directed horizontally outwardly from said pipe
means by each of
said apertures.
It is further preferred, although not absohztely necessary, that the
collection vessel for
containing the resultant liquid having microbubbles contained therein form
part of an integral
structure with the pipe means and together form a single containment vessel in
which the pipe
means is located. While there are a number of advantages to using an integral
containment
vessel having the pipe member therewithin as explained later within this
specification, including
the ability to create microbubbles within the gas/liquid mixture under an
ambient gaseous
pressure within such containment vessel, one particular advantage is that, if
desired, and if the
gas/liquid mixture in the pipe means is expelled from the apertures under
sufficient pressure, the
sides of the containment vessel may be used as the vertical surface against
which the horizontal
streams of gas/liquid which exit the apertures may be directed.
Accordingly, in a further broad embodiment of the present invention, the
apparatus of
the present invention comprises a vessel adapted to be positioned
substantially vertically and
adapted to contain a volume of gas in an upper portion thereof; means for
introducing gas
bubbles, the majority of which are of a size greater than 100 microns, into a
liquid to forma
liquid-gas mixture; elongate, hollow pipe means within said 'vessel, of
interior cross-sectional
area A; , for conveying said liquid when in a pressurized state to an interior
of said vessel,
substantially symmetrical in cross-section, situate centrally in said vessel
and proximate said
upper portion of said vessel and extending substantially vertically downwardly
within said
vessel from said upper portion thereof, and having plug means situate at a
lowermost distal end
thereof for preventing egress of liquid vertically downward from said distal
end; and at least two
apertures situate on said pipe means and disposed in one or more planes each
substantially
perpendicular to a longitudinal axis of said pipe means, extending from an
interior of said pipe
means to an exterior of said pipe means, each adapted to direct said liquid
under pressure
substantially horizontally outwardly from said pipe means.
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Again, in a preferred embodiment, where symmetrical pipe 3neans such as a
cylindrical,
square, hexagonal, octagonal, or even a triangular (equal sided) pipe member
is used, and a
containment vessel the apparatus of the present invention comprises:
i) a vessel adapted to be positioned substantially vertically and adapted to
contain a
volume of gas in an upper portion thereof;
ii) elongate, hollow pipe means for providing said liquid to an interior of
said vessel,
having a longitudinal axis and substantially symmetrical in cross-section so
as to have
identical moments of inertia about at least two separate axis in a cross-
sectional plane
through said pipe means, of uniform wall thickness, and having a maximum
interior
width D; and a maximum exterior width Do and an interior cross-sectional area
A; ,
said pipe means situate substantially centrally in said vessel and proximate
said upper
portion of said vessel and extending substantially vertically downwardly
within said
vessel, adapted for supplying a pressurized liquid to an interior of said
vessel, and
having plug means situate at a distal end thereof for preventing egress of
liquid
vertically downward from said distal end;
iii) at least two apertures situate in said pipe means and disposed in one or
more planes
each substantially perpendicular to a longitudinal axis of said pipe means,
each
extending from an interior of said pipe means to an exterior of said pipe
means, each
adapted to direct said liquid substantially horizontally outwardly from said
pipe
means, of combined cross-sectional exit area Ae; and
iv) said combined aperture exit area Ae of said apertures, defined as a
function of widths
D; and Do and said cross-sectional area A; of said pipe means, wherein Ae is
no
greater than, and preferably equal to, A; x D;/Do
The apertures) may be of any geometric shape in cross section, such as
circular (ie
cylindrical apertures), provided the exit area of such apertures) in such pipe
member meets the
requirement for exit area Ae as discussed above in order to create
microbubbles of a size in the
range of 50 to 100 microns, and preferably 5-50 microns. In particular, the
apertures may be one
or more narrow horizontally-extending rectangular slots, or alternatively one
or more vertical
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slots in such pipe member, all of which are easy to manufacture, either by
drilling in the case of
cylindrical apertures, or cutting/milling in the case of vertical or
horizontal slots.
Importantly, it has further been discovered that apertures in the pipe member
of a
maximum dimension in excess of a certain amount may not form microbubbles of
the required
small size (5-50 microns).
In particular, the maximum gap "G", namely the maximum cross-sectional
dimension
that the aperture may possess is a function of the inner cross-sectional area
of the pipe member
divided by the outer circumference of the pipe member.
Accordingly, in such cases, where the apertures) are o:F a horizontally
extending
rectangular slot, of vertical depth G, where the pipe member has an exterior
circumference C, G
should preferably be no greater than Ai/C in order to form microbubbles when
said liquid-gas
mixture is expelled from the pipe member via such aperture(s).
Likewise, where the apertures) are of a circular cross-section (ie
cylindrical), the
diameter of such aperture should preferably be no greater than Ai/C.
Again, it is possible to utilize apertures of maximum dimension (or diameter,
as the case may be)
less than Ai/C, and still create gas microbubbles of the desired size of 5-100
microns.
Accordingly, a large number of small apertures, where the total combined
aperture area Ae adds
up to the maximum Ai x DilDo may be used, in order to introduce microbubbles
in as great a
quantity of liquid over a given time. However, having to drill large numbers
of small apertures
adds to the cost and time in the manufacture of the pipe member and thus of
the apparatus of the
present invention. It is much less expensive and less time-consuming to
drill/mill as few a
number of apertures as possible (see discussion below as to what the minimum
number of
apertures may be for a circular pipe).
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The above relationship for the aperture exit area Ae is derived from the
surprising observation
that the maximum aperture dimension (i.e. the "gap" ) through which the
gas/liquid mixture must
pass is determined from the experimentally-derived observation that the
aperture dimension,
hereinafter referred to as the "gap°', which best creates microbubbles
of the desired small size, is
determined by the relationship gap "G" = A; /(pipe outer circumference).
For example, for a circular conduitlpipe of minor diameter D;, outer diameter
Do, and
crass-sectional area Ai= ~rD;2/4 it has been found that for a rectangular
aperture cut
perpendicularly into the side of the pipe, to a depth of '/Z the pipe
diameter, so as to create an
aperture to allow egress of a gas/liquid mixture under pressure therethrough,
the maximum
permissible "gap" G , namely the maximum vertical height of such horizontal
slot, is:
A;/(pipe outer circumference) _ ~rD;2/(4 ~Da~ =D;2/4D~ (Eq'n. #1)
The surface exit area Ae of two slots each formed over %2 the inner diameter
of the pipe
D; is calculated as follows:
Ae-2xgapx%Z~rxD;
Thus the maximum exit area Ae of'such apertures for a circular pipe member is
thus equal to
Ae= 2 x D;'/4Do x '/Z ~r x D; _ ~rD;3/4Da. (Eq'n. # 2)
Accordingly, Ae stated more generally in terms of A;,, where Ai = ~rD;2/4 may
be stated
as follows:
Ae = ~Di3 = ~rDi2 x D;IDo Ai x Di/Do
4Do 4
Where only one exit aperture is utilized, maximum exit area is = ~D;3/BDo, and
stated in
terms of Ai is equal to
Ai x Di/(2Do~
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In view of the above, the minimum number of apertures in a circular pipe may
be
determined. In this regard, in a preferred embodiment of the apparatus of the
present invention,
for the reasons discussed above, namely the desire to use the greatest amount
of "throughput°°
for the apparatus with the least number of holes/apertures, and thus introduce
microbubbles into
the greatest volume of liquid in the shortest time, the largest-sized aperture
utilizable equals
Ai/C. In order to achieve as much throughput of liquid which has microbubbles
introduced
therein, the apparatus in a preferred embodiment will not only possess
apertures of maximum
size, but also the combined exit area Ae of such apertures will equal the
maximum permissible
area in order that the apparatus be able to process (ie introduce gas
microbubbles) into as much
liquid as possible for a given time.
Accordingly, in the case of cylindrical pipe, having Circular (cylindrical)
apertures, the
minimum number of holes(apertures) which can be used is determined by
reference to Eq'n. #2,
which defines the maximum exit area for a circular pipe member, namely
Ae= ~rD;3l4Do
Although the surface exit area of a circular hole in a cylindrical pipe forms
a "saddle-like"
exit area on the surface of the pipe, for small diameter apertures relative to
the diameter of the
pipe, the combined surface exit area of all apertures is approximately equal
to the number of
apertures multiplied by the exit area Aapercure of each aperture:
Ae(max)= n X Aaperture(max) ~ x ('~ X Da2/4)
As discussed, Da is preferably no greater than Ai/C. Accordingly ,
substituting Ai/C for Da
produces the following:
Ae(max) =n X (~ x Da2/4)= n x (~r x [ Ai/C]Z /4 )
= n x (~r x [(n x Di2 /4)/( ~ x Do)~Z /4
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The above equation for Ae(max) can be equated to Eq°n. # 2 for the
Ae(max) of a circular pipe,
and solved for "n" as follows:
Ae(max) = n x (~r x [(~r x Di2 /4)/( ~r x Do)]2 /4 = ~rD;3/4Do
n= l6Do (Eq'n. 6)
Di
Accordingly, since Eqn. 6 may, depending on the ratio of Do/Di, produce a
fractional value for
the number of holes "n", in a preferred embodiment , the minimum number of
circular apertures
in a circular pipe member for maximum flow of liquid is defined by the
following expression,
namely:
n = nearest whole integer to [ 16 x Do / D,] (Eq°n. 6A).
It is noted that since the maximum combined aperture exit area Ae for
cylindrical pipe is Ai x
Di/Do, for apertures of small diameter DA relative to the diameter of the
cylindrical pipe, the
following is true:
AemaX n X ?L Dp(Max) 2/4
and thus
A1 X Dl/DO = n X ?L Dp(Max) 2/4
The above allows us to solve for the maximum diameter of the apertures DA(max>
, where
for circular pipe, Ai = ~DiZ follows:
4
~ x Di2 !4 x Di/Do= = n x n X DA(MaX~ Z/4
thus DA(M~~='~Di3I[n X Do]
stated alternatively, DA(MAx~ _ ~ x Ai x Di/ [n X n x Do]
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It is usually the case for most cylindrical pipe having diameters Di and Do
that "n" must
be greater than 2 for most pipe, namely there must usually be a plurality of
apertures, since
otherwise the calculated diameter DA results in a diameter greater than both
the interior diameter
Di and the exterior diameter Do, which is a physical impossibility, as
diameter DA can only be as
large as, or smaller than, Di and Do.
The above value DA~AX) for a circular pipe having cylindrical apertures may ,
in
instances where there are relatively few number of apertures (ie n is a low
number, but greater
than one as per the above) give values of DA which are higher than Ai/(outer
circumference of
pipe) and which are too high and which will generally not praduce microbubbles
of desired size
(ie less than 50 microns). Accordingly, the two criteria which are preferably
satisfied in order to
form microbubbles of the desired size are that Ae(max) = Ai x Di/Do, and
DA~Ax~ <_
Ai/Circumference of Pipe
For a square conduit of inner dimension D; and outer dimension Do, having
inner flow
area A; = D;2 and outer circumference 4 Do, for a horizontally extending slot
of Gap "G", it has
been found that the maximum gap is likewise the flow area through the pipe Ai
divided by the
exterior circumference of the (square) pipe, being 4Do. Accordingly, the
maximum vertical slot
depth "G" for a square pipe may be stated as follows:
Gap "G..( Max) = A; _ Dya
circumference 4Do
The exit area Ae for a plurality apertures in a square pipe may thus be
calculated,
knowing such maximum Gap "G". Accordingly, where the apertures comprise a pair
of
rectangular slots of vertical depth equal to the above Gap (Max), the exit
area Ae for the
apertures may be calculated as
Ae = 2 x Gap(max) x ('/2 D; + D; +'/2 D;)
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Accordingly, expressed in terms of inlet area Ai for the square pipe, Ae may
be stated as
follows:
Ae 2 x _D;2 x (2D;) = 4Di3 = Di2 x D; = Ai x Di/Do
4Do 4D~ I7~
Again, where there is only one aperture in such square pipe, Ae is thus:
AE= Gap(max) x(%2D;+D;+%2D;)
and thus, expressed in terms of Ai, is thus
Ae=Ai x Dii(2xDo)
As in the case of circular apertures in circular pipe, where there are
circular apertures in
square pipe, the diameter DA~~~ may be solved for as follows:
Ae=Ai x Di/Do (1)
Ae= n x ~ x Da 2 /4. (2) where 'n' is the number of apertures
Equating (1) with (2) allows for the diameter DA(Max) to be solved for as
follows:
Ai x Di/Do = n x ~ x Da Z /4
DA(MAX) =~4 x Di3/[n x~c x Do] _ =~4 x Ai x Di ,~ [n x~ x Do]
Again, it is usually the case for most square pipe having interior width Di
and exterior
width Do that "n" must be greater than 2 for most pipe, namely there must
usually be a plurality
of apertures, since otherwise the calculated diameter DA of the cylindrical
aperture results in a
diameter greater than either the interior width Di or the exterior width Do,
which is a physical
impossibility, as diameter DA can only be as large as, or smaller than, Di and
Do.
Again, the above value DA~MAX) for a square pipe having cylindrical apertures
may , in
instances where there are relatively few number of apertures (ie n is a low
number, but as per the
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CA 02437948 2003-08-21
above, greater than one) give values of D~, which are higher than Ai/(outer
circumference of
pipe) and which are too high and which will generally not produce microbubbles
of desired size
(ie less than 50 microns). Accordingly, the two criteria which are preferably
satisfied in order to
form microbubbles of the desired size are that Ae(max) = Ai x Di/Do, and
DA~AX)
Ai/Circumference of Pipe
It has been discovered that the above relationshih(s) hold true for any pipe
of
symmetrical cross-sectional area and having at identical moments of inertia
about at least two
axis in a plane of cross-section through such pipe.
For example, for a triangular pipe member (of equal interior side length Di
and equal
exterior side length Do so as to be symmetrical and have identical moments of
inertia about at
least two axis in a plane of cross-section through such pipe member), the
interior cross-sectional
area Ai of such pipe member of interior side length. Di is:
Ai=,_/~3 Di2
4
For two identical horizontal slots (apertures) cut into such pipe to form a
"gap" of vertical
height "G", where such slots to a depth so as to provide access to one-half of
the interior area Ai
of such pipe member, the maximum gap (ie vertical depth of each slot) is again
determined by
the relationship
Gap (Max) =Ai/pipe outer circumference= Ai/3Do= =,I-33 Di2
l2Do
The exit area of such two apertures is accordingly determined as the product
of the gap
multiplied by the perimeter of the gap. Accordingly,
Ae(max)=2 x gap x (Di + %z Di)
=2 x ,_~3 Di2 x _3 Di
l2Do 2
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CA 02437948 2003-08-21
=,_l3 _Di3
4 Do
Expressed in terms of Ai,
Ae(max)= _,r3 Di2 x Di = Ai x 13i
Do Do
The present invention , in a further of its broad aspects, relates to a method
for creating
microbubbles of gas in a liquid and exposing them to matter entrained in said
liquid.
Accordingly, in one broad aspect of the method of the present invention, such
method comprises
the steps of:
providing gas to said liquid to form a gas/liquid mixture;
directing said gas-liquid mixture into a hollow pipe member, said pipe member
having a
maximum interior width D; and a maximum exterior width Do, said pipe member
situate
proximate an upper portion of a containment vessel and extending into an
interior of said
containment vessel, said upper portion of said Containment vessel containing
said gas being
under pressure, and a bottom portion of said containment vessel substantially
containing said
liquid;
injecting said gas-liquid mixture under pressure via said pipe member, into
said
containment vessel;
spraying substantially radially outwardly from said pipe member said gas-
liquid mixture
into said upper portion of said containment vessel via at least two apertures
in said pipe
member;
said at least two apertures in said pipe member in communication with said gas-
liquid
mixture in said pipe member and having a combined area Ae sized ~.s a function
of a maximum
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CA 02437948 2003-08-21
interior widths D; and maximum outside width Do and a cross-sectional area A;
of said pipe
member, wherein Ae is substantially equal to:
A; x D;/Da
and
removing from said bottom portion of said containment vessel said liquid which
has
been exposed to said microbubbles.
In yet another aspect of the method of the present invention, such method
comprises a
method for converting a liquid-gas mixture having bubbles of gas therein the
majority of which
are greater than 5-100 microns in size to a liquid-gas mixture having
microbubbles of gas therein
the majority of which are of a size between 5-100 microns at standard
temperature and pressure,
comprising the steps of
directing said gas-liquid mixture having bubbles of gas therein the majority
of which are
greater than 5-100 microns in size into a hollow, substantially vertical pipe
member, having a
maximum interior width D; and a maximum exterior width Do ;
spraying said gas-liquid mixture substantially radially outwardly from said
pipe member
via a plurality of apertures in said pipe member, so that said gas-liquid
mixture contacts a
vertically extending surface;
said plurality of apertures in said pipe member in communication with said gas-
liquid
mixture in said pipe member and having a combined area Ae, said apertures
sized as a function
of said maximum interior width D; and said maximum outside widi:h Do and a
cross-sectional
area A; of said pipe member, wherein Ae is no greater than, and preferably
equal to:
A; x D;/Do
collecting a resulting gas-liquid mixture having microbubbles of gas entrained
therein in
a vessel; and
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CA 02437948 2003-08-21
removing said gas-liquid mixture from said vessel.
In a further refinement of the methods of the present invention, one such
method further
comprises the step of collecting within said bottom portion of said vessel
said liquid with
microbubbles entrained therein and withdrawing said liquid from said bottom of
said vessel at a
rate approximately equal to a rate at which said liquid is introduced into
said containment
vessel.
In yet a further refinement of the aforesaid methods, the rate of withdrawing
the liquid
from the bottom of the vessel is substantially at a rate which microbubbles
entrained in said
liquid rise in the vessel, so that at a time when liquid is removed from said
bottom of said vessel
said microbubbles will have travelled upwardly a distance through said liquid
equal to a depth of
liquid in the bottom of the vessel.
In yet a further aspect of the method of the present invention, the liquid-gas
mixture
sprayed from said pipe member may be passed through a baffle plate member
positioned in the
containment vessel below said pipe member and intermediate said upper portion
and said bottom
portion of said containment vessel, and the rate of injection and removal of
gas-liquid from the
vessel adjusted so that baffle plate member is positioned above the level of
the liquid in the
vessel.
To assist in formation of microbubbles, it is preferred that the pressure of
the gas in the
upper portion of the vessel be of a pressure of at least 25 psig. 'The step of
spraying the liquid-gas
mixture substantially radially outwardly via the apertures may further in a
preferred embodiment
be adapted to spray such liquid-gas mixture against the sides of the
containment vessel.
From another perspective , the invention in a preferred embodiment comprises a
method
for continuously purifying a liquid containing impurities by exposing the
liquid and impurities
for a time in a substantially vertically containment vessel to rr.~icrobubbles
in the range of 5-100
microns in diameter, comprising the steps of:
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CA 02437948 2003-08-21
directing a gas-liquid mixture containing impurities and bubbles of gas the
majority of
which are in excess of 100 microns in diameter into a hollow pipe member, said
pipe member of
uniform thiclmess and having a maximum interior width Di and a maximum
exterior width Do
and identical moments of inertia on two axis in a plane of cross-section
through said pipe means,
said pipe means situate proximate an upper portion of said contaimnent vessel
and extending
vertically downwardly in an interior of said containment vessel, said upper
portion of said
containment vessel containing said gas, and being under pressure of at least
25 psig;
injecting said gas-liquid mixture, under a pressure of at least 5 psig higher
than said gas
in said containment vessel, into said vessel via said pipe member;
spraying said gas-liquid mixture substantially horizontally outwardly from
said pipe
member into said upper portion of said containment vessel via a plurality of
apertures in said
pipe member so that said gas-liquid mixture contacts interior sides of said
vessel;
said plurality of apertures in said pipe member in communication with said gas-
liquid
mixture in said pipe member and having a combined area Ae, said apertures
sized as a function
of said maximum interior width D; and said maximum outside width Do and a
cross-sectional
area A; of said pipe member, wherein Ae is no greater than:
A; x D;/Da
collecting said gas-liquid mixture, now having microbubbles of gas entrained
therein the
majority of which are now of a size less than 100 microns in diameter, in a
bottom portion of
said containment vessel;
removing, from said bottom portion of said vessel, said liquid with gas
microbubbles
entrained therein at a rate which said microbubbles entrained in said liquid
rise in said vessel so
as to permit said gas microbubbles time to react with impurities in said
liquid; and
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CA 02437948 2003-08-21
supplying said liquid-gas mixture to said pipe member sub stantially at a rate
at which
said liquid-gas mixture having gas microbubbles entrained therein is removed
from the bottom of
said vessel.
Advantageously, the present invention in a particular refinement of both of
one of the
method and apparatus of the present invention, makes use of a sorting
phenomenon in order to
obtain microbubbles of the desired size.
Specifically, in a particular embodiment where a gas- liquid mixture having
gas bubbles
of substantially large size (>100 microns) entrained therein is sprayed
outwardly from a pipe
member and captured in a containment vessel, liqL~id having some large (>100
microns) as well
as small (<100 micron) gas bubbles (but preferably a preponderance of small
gas bubbles) is
collected in said vessel. However, gas bubbles in said liquid which fall
vertically down in said
vessel when expelled from said aperture tend to fall to various depths in said
containment vessel,
before starting to rise in such vessel, depending on the size of the gas
bubble entrained in
surrounding liquid. Specifically, larger gas bubbles within the liquid tend to
fall a lesser
distance downwardly in liquid collecting at a bottom portion of i:he
containment/collection
vessel than smaller gas bubbles.
Accordingly, by proper vertical positioning of a liquid-withdrawal tube from
the
containment vessel this °'sorting" of bubbles within the liquid
collecting in the bottom portion of
the vessel can be taken into account in obtaining liquid having gas bubbles of
the lesser (more
desirable) smaller diameter. Specifically, positioning of such withdrawal tube
on such vessel at a
position somewhat above a lowermost portion of said vessel and immediately
below a
lowermost level in said vessel which bubbles of a size larger than 100 microns
initially fall to
before rising in said vessel, and at a level within said bottom portion of
said vessel which
bubbles of a size less than 100 microns initially fall to before rising in
said vessel, will allow the
withdrawal tube to withdraw from said vessel only a gas-liquid mixture having
smaller (ie <I00
micron ) bubbles .
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CA 02437948 2003-08-21
Accordingly, in a preferred method of the present invention taking advantage
of the
above "sorting" principle in order to obtain gas microbubbles of a size less
than 100 microns,
such method comprises a method for producing a liquid having gas microbubbles
therein the
majority of which are of a size less than 100 microns, comprising the steps
of.
providing gas to said liquid to form a gas/liquid mixture;
directing said gas-liquid mixture into a hollow pipe member, said pipe member
having a
maximum interior width D; and a maximum exterior width Do, said pipe member
situate
proximate an upper portion of a containment vessel and extending into an
interior of said
containment vessel, said upper portion of said containment vessel containing
said gas being
under pressure, and a bottom portion of said containment vessel substantially
containing said
liquid;
spraying substantially radially outwardly fiom said pipe member said gas-
liquid mixture
into said upper portion of said containment vessel via at least two apertures
in said pipe
member;
and
removing from said bottom portion of said containment vessel, at a position
somewhat
above a lowermost portion of said vessel, said gas-:liquid mixture;
said position being a position immediately below a lowermost level in said
vessel which
bubbles of a size larger than 100 microns initially fall to before rising in
said vessel, and at a
level within said bottom portion of said vessel which bubbles of a size less
than 100 microns
initially fall to before rising in said vessel.
In a further embodiment the invention consists of an apparatus for making use
of the
"sorting" phenomenon.
-22-
CA 02437948 2003-08-21
Accordingly, in such refinement of the apparatus of the present invention, the
containment vessel of the present invention comprises gas-liquid withdrawal
means, such
withdrawal means in communication with an interior of the vessel proximate a
bottom portion
thereof, vessel, adapted to withdraw a gas-liquid mixture having microbubbles
of entrained gas
therein from said interior of such vessel, such withdrawal means situate on
said vessel at a
position, said position being at a level on said vessel below a lowermost
level within said vessel
which bubbles of a size larger than 100 microns fall to before rising in
liquid in said vessel, and
at a level which bubbles of a size less than 100 microns fall to before rising
in said vessel.
Brief Description of the Drawings
The following drawings, showing selected embodiments of the invention, are non-
limiting and illustrative only. For a complete definition of the scope of the
invention, reference
is to be had to the summary of the invention and the claims.
Figure 1 shows a front view of one embodiment of the apparatus of the present
invention
for creating microbubbles of gas , said apparatus in the embodiment shown
using a cylindrical
pipe member and a plurality of horizontally-extending cylindrical apertures;
Figure 2 is an enlarged view of area "A" ofFigure 1;
Figure 3 is an enlarged vie~,v of area "B" of Figure 2, showing in detail
circular apertures
formed in the pipe member;
Figure 4 is a view of an alternative embodiment of the present invention,
similar to that
shown in Figure 1, showing utilization of an inclined but substantially
vertical baffle member;
Figure 5 is an enlarged view of a particular embodiment showing of a pipe
member of
the present invention of circular cross-section, further showing an embodiment
of the pipe
-23-
CA 02437948 2003-08-21
member having horizontally-extending rectangular slots formed in such pipe
member for acting
as apertures to permit the expulsion of a gas-liquid mixture from such pipe
member;
Figure SA is a section through the pipe member of Figure 5, taken along plane
X-X;
Figure 5B is a section through the pipe member of Figure 5, taken along plane
Y-Y;
Figure 6 is an enlarged view of a particular embodiment showing of a pipe
member of
the present invention of square cross-section, further showing an embodiment
of the pipe
member having horizontally-extending rectangular slots formed in such pipe
member for acting
as apertures to permit the expulsion of a gas-liquid mixture from such pipe
member;
Figure 6A is a section through the pipe member of Figure 6, taken along plane
X-X;
Figure 7 is an enlarged view of a particular embodiment showing of a pipe
member of
the present invention of triangular (equal sided) cross-section, further
showing an embodiment
of the pipe member having horizontally-extending rectangular slots formed in
such pipe member
for acting as apertures to permit the expulsion of a gas-liquid mixture from
such pipe member;
Figure 7A is a section through the pipe member of Figure 7, taken along plane
X-X;
Figure 8 is an enlarged view of a particular embodiment showing of a pipe
member of
the present invention of rectangular cross-section, further showing an
embodiment of the pipe
member having horizontally-extending rectangular slots formed in such pipe
member for acting
as apertures to permit the expulsion of a gas-liquid mixture from such pipe
member;
Figure 8A is a section through the pipe member of Figure ~, taken along plane
X-X
-24-
CA 02437948 2003-08-21
Figure 9 is a side view similar to Figure 1 showing another embodiment of the
apparatus
of the present invention, wherein the apertures for forming the microbubbles
are situate in a plug
member which is itself situated at the extreme lowermost distal end of the
plug member;
Figure 10 is an enlarged view of area "A" of Figure 9;
Figure 11 is yet a further side view similar to Figure l and 9, showing yet
another
embodiment of the apparatus of the present invention, in this case having
circular apertures
situate in the plug member at the extreme lowermost end of the pipe member;
Figure 12 is an enlarged view of area "A" of Figure 11;
Figure 13 is an enlarged view of the baffle plate member shown in Figs. 1,9,
and 11;
Figure 14 is a cross-sectional view of a particular embodiment of the
apparatus of the
present invention which was selected to conduct tests on;
Figure 15 is schematic view of additional test apparatus used to test the
operability of the
apparatus and method of the present invention;
Figure 16 is a table setting out test data obtained using the test apparatus
of Figure 14
and 15; and
Figure 17 is a graph showing a plot of aperture exit area Ae as a function of
bubble
diameter, such data obtained from data using the test apparatus shown in
Figure I4 and 15; and
-25-
CA 02437948 2003-08-21
Detailed Description of the Invention
Fig. 1 shows one embodiment of the apparatus 10 of the present invention for
producing
microbubbles 12 in a liquid 14.
A means 16 for introducing gas bubbles 20 into such liquid 14 flowing in pipe
9 is
provided. Means 16 may be a venturi , namely a converging-diverging nozzle, as
known in the
art, having at the converging portion an aperture 17 through which gas,
typically although not
always air, is drawn and flows in the form of bubbles 20 into the liquid, to
form a gas-liquid
mixture 22. Alternatively, and more typically, means 16 is simply an orifice
to permit the
injection of gas under pressure into said liquid 14 in pipe member 12,
resulting in formation of
gas bubbles 20 within liquid 14, which is under a resulting pressure.
The supply of gas may be from ambient air, if air is the desired gas to be
introduced, as
shown in Fig. 1, or alternatively nay be from a pressurized tank of gas (not
shown), if some
other form of gas (such as HZ or COZ) is desired to be introduced.
Gas bubbles 20 entrained in such gas-liquid mixture 22 in the above manner are
typically
of a size greater than 100 microns, or at least a majority of gas bubbles 20
entrained in such gas-
liquid mixture 22 are of a size greater than 100 microns, at typical ambient
temperature and
pressure (22° C and 1 atmosphere).
One of the purposes of the apparatus 10 of the present invention is to reduce
the bubble
size of the gas bubbles 20 within the gas-liquid mixture 22 to a size less
than 100 microns, and
preferably to a size in the range of 5-50 microns, in order to increase the
ability of the gas in the
gas-liquid mixture 22 to react with materials or substances entrained in the
gas-liquid mixture 22,
for the purposes of purifying and/or causing certain entrained substances in
such liquid 14 to
precipitate out of such gas-liquid mixture 22, thereby ridding such liquid 14
of such substances.
-26-
CA 02437948 2003-08-21
The gas-liquid mixture 22, having gas bubbles 20 therein the majority of which
are of a
size greater than 100 microns, is thereafter conveyed typically by means of a
hollow pipe or
conduit 24 to an elongate, hollow pipe member 24, typically although not
necessarily, situate
within a containment vessel 40, as shown in Fig. 1.
Pipe member 24 contains aperture means consisting of a one or more apertures
32,
extending from an interior 33 of such pipe member 24 to an exterior 37 of pipe
member 24 (see
enlarged view of one embodiment of pipe member 24 shown in Fig. 3, wherein
pipe member 24
is cylindrical in cross-section, having a plurality of cylindrical apertures
therein). Each of
apertures 32 may be of any geometric shape, but preferably are of a
cylindrical shape as shown
in Fig. 3, a cylindrical aperture being the resultant shape that results from
drilling of such
aperture 32 during manufacture using a circular drill bit, drilling being one
of the easiest means
of forming such apertures 32. Each of said apertures 32 extend horizontally
outwardly and
substantially perpendicular to a longitudinal axis of the pipe member 24. Pipe
member 24 is
positioned substantially vertically, as shown in Fig. 1, and is adapted to
receive the liquid-gas
mixture 22 and supply same un~.er pressure to apertures 32. Each of apertures
32 extend
horizontally outwardly from interior 33 of pipe member 24 to exterior 37 of
pipe member 24.
Pipe member 24 further possesses a plug member 25, situate at a lowermost
distal end thereof for
preventing egress of liquid-gas mixture 22 from said pipe member 24.
As hereinafter explained, the size (both width and cross-sectional area) of
such apertures
32 is dependent in a preferred embodiment on certain formulae which are
preferably maintained
to allow formation of microbubbles 12 of a desired size, namely less than 100
microns, and
preferably 5-50 microns, when the gas-liquid mixture 22 is expelled under
pressure from the pipe
member 24 via apertures 32 .
A containment vessel 40 is further provided. In a preferred embodiment,
containment
vessel 40 is an elongate, vertically-extending column, configured so as to
receive therewithin
pipe member 24 in an upper portion 42 thereof Specifically, in the embodiment
shown in Fig.
l, containment vessel 40 is formed of a vertical conduit 46, having threaded
flange members
-27-
CA 02437948 2003-08-21
43 affixed (in the preferred embodiment by welding for conduits of weldable
metallic material
and where such conduits are of a plastic material such as polyvinyl
chloride(PVC), by an
adhesive or a bonding agent such chloroform] at each of a bottom and top end
44,45 respectively
. Flanges 41,43 are adapted to receive plate members 47,48 at each of said top
and bottom ends
44,45 which may be bolted to flange members 43 respectively by means of bolts
57, with an
intervening gasket 59, so as to form an enclosed vessel 40.
The purpose of vessel 40 is to receive and contain for a time liquid 14
expelled from said
apertures 32 at a given level "x" within said vessel 40. The resulting
microbubbles 12 produced
in the gas-liquid mixture 22 which fall from apertures 22 into vessel 40 may
react in the bottom
portion 48 of vessel 40 with substances within the liquid 14, so as to cause
impurities to
precipitate out. The remaining (purified) liquid 15 may then be removed from
vessel 40 via a
lower liquid withdrawal pipe 51.
Alternatively, or in addition, the vertical length 50 of the bottom portion 48
of vessel 40
may act as a stratification column and take advantage of a "sorting" with
respect to gas bubbles.
In this regard, any remaining gas bubbles 14 of a relatively large size (ie in
excess of 100
microns in size) which may still be entrained in said gas-liquid mixture 22
along with smaller gas
bubbles after the expulsion of the gas-liquid mixture from apertures 32 will
tend to fall into
bottom portion 48 of vessel 40. ~Iowever, larger gas bubbles tend to fall to
or above a level
(namely above line "X" as shown in Fig. 1) before beginning to rise in the
liquid column
contained in the bottom portion of vessel 40 . On the other hand, smaller
sized gas bubbles tend
to fall to a level "Z" or below such level "Z" before beginning to rise within
such liquid, as
shown in Fig. 1.
Accordingly, by positioning withdrawal pipe 51 at a level below a level "Z" to
which
the majority of larger gas bubbles fall, only liquid 15 substantially having
gas bubbles of a size
less than 100 microns may be obtained when withdrawn from withdrawal tube 51.
Such liquid
14, having a majority of gas bubbles therein of a size less than '100 microns,
may then be
transported via withdrawal pipe 51 to a further containment vessel 52 (not
shown) where such
-28-
CA 02437948 2003-08-21
gas microbubbles entrained in the liquid 14 may then react (or further react)
with substances
within such liquid 15, such as iron bacteria or other undesirable substances,
so as to render such
substances harmless or cause them to precipitate out of solution, leaving a
purified liquid 15.
Although it is not necessary that vessel 40 be an enclosed vessel, in the
preferred
embodiment it is desirable that vessel 40 be an enclosed vessel, as shown in
Fig. 1. This allows
two advantages to be realized.
Firstly, to improve the formation of gas microbubbles upon the liquid-gas
mixture 22
being expelled from aperture means within pipe member 24., the side walls 55
of an enclosed
vessel 40 may be used, where the pressure in pipe member 24 is sufficiently
high, as a vertical
surface against which resulting jets 56 of gas-liquid may impinge against
prior to falling from
upper portion 42 of vessel 40 to bottom portion 48 of vessel 40. A, depiction
of this preferred
embodiment is shown in enlarged view in Fig. 2. The impaction of the jets 56
of gas liquid
against side walls 55 tends to cause larger gas bubbles entrained in liquid 14
to break into
microbubbles, thus aiding the formation of gas microbubbles.
Secondly, the utilization of an enclosed vessel 40 assists m maintenance of
gas
microbubbles within liquid 14 in the bottom portion 48 of vessel 40, as the
vessel 40 may be
maintained under a relative pressure. In this regard, in a preferred
embodiment, the internal
relative pressure in the upper portion 42 of vessel 40 is in the range of 25
psig or above, with the
pressure of the gas-liquid mixture 22 in pipe member 24 being in the range of
S psig or higher
than the internal relative pressure within vessel 40, to permit the gas-liquid
mixture 22 within
such pipe member 24 to be expelled into upper portion 42 of vessel 40 via
apertures 32. The
maintenance of a pressure within vessel 40 less than the supplied pressure
within pipe member
24 assists in formation of gas bubbles in liquid 14. The maintenance of a
pressure within such
vessel 40 higher than ambient assists in maintaining bubbles of a small size
within the bottom
portion of the vessel 40, which is useful if the sorting feature described
above is not desired to be
used and instead the bottom portion. of vessel 40 is used as a type of
containment vessel to allow
reaction of the gas microbubbles with substances within liquid 14 , as further
explained below.
-29-
CA 02437948 2003-08-21
The embodiment of the apparatus and the method of the present invention where
the
"sorting" of bubbles according to size is employed and the withdrawal pipe 51
is situated at a
level below level "Z" to withdraw only those gas bubbles the majority of which
have a size less
than 100 microns, is particularly suited to a continuous as opposed to a batch
process.
Specifically, because the liquid ~~hich is withdrawn from withdrawal pipe 51
is substantially
comprised of microbubbles, liquid 14 having such microbubbles entrained
therein may be
continuously withdrawn from vessel 40 for subsequent processing in a reaction
vessel (not
shown ) elsewhere.
Where the bottom portion 48 of vessel 40 is itself used as a reaction vessel
to allow the
microbubbles therein to react w~.th substances in such liquid 14., either a
"batch'° or a
"continuous" process may be employed. Specifically, where a batch process is
employed,
sufficient gas-liquid mixture 22 is discharged through apertures 32 to allow
the liquid-gas
mixture 22 to rise in vessel 40 to a level "x" approximately one-half to two-
thirds the height of
vessel 40. A period of time is allowed to pass, namely the period of time
which it takes for
microbubbles of a size less than 100 microns to rise from a level at or below
level "Z" (see Fig.
3) to level "X". Thereafter the liquid 15 may be withdrawn fiom vessel 40 by
withdrawal pipe
51 at a position on such vessel anywhere intermediate level x and the base of
the vessel 40, and
preferably at a level close to level °'Ztv.
Where a continuous process of treating liquid 14 in containment vessel 40 is
desired to be
employed, liquid 14 in the liquid-gas mixture 22 is supplied to the vessel 40
via pipe member 24
at a rate approximately equal to a rate at which the liquid 1~ is withdrawn
from vessel 40 via
withdrawal pipe 51. In addition, the rate of withdrawal of liquid 15 (and the
rate of supply of
liquid 14) is adjusted so that at a i;ime when liquid is removed from said
bottom portion 48 of
vessel 40 the microbubbles will have travelled upwardly a distance through
liquid 14
substantially equal to a majority of the depth of liquid 14 in said bottom
portion of said vessel,
namely from approximately level "z" to approximately level "x". In order to
facilitate the
removal of liquid 1S which has been exposed to microbubbles for such period of
time, a vertical
-30-
CA 02437948 2003-08-21
baffle plate member 60 may be employed as shown in Fig. 4 to direct the flow
of liquid having
microbubbles entrained therein as shown in Fig. 4. In such embodiment
withdrawal tube 51 is
preferably situate close to, but below level "X'°, and withdraws liquid
15 which has been exposed
to gas microbubbles for the time :hat it takes such microbubbles after having
fallen from level
"x" to level "z" on a first side 70 of such baffle member 60 to rise on the
other side 71 of baffle
member 60 from level "Z" to level "X".
In a further embodiment, the apparatus 10 of the present invention further
includes a
horizontal baffle plate member 80 (ref. Fig. 1 and Fig. 4), positioned
intermediate upper portion
42 and bottom portion 48 of vessel 40, and above level "x" of liquid 14 in the
vessel 40, so that
gas-liquid mixture sprayed from pipe member 24 is permitted to pass through
such baffle
member 80 when falling to bottom portion 48 of vessel 40. Baffle plate member
80 is provided
with a series of orifices 82 (see Fig. 13 showing enlarged view of horizontal
baffle member 80)
to permit gas-liquid mixture 22 to further fall to bottom portion 48 of vessel
40. Baffle plate
member 80 further assists in converting gas bubbles 20 in gas-liquid mixture
22 to microbubbles.
Pipe member 24 having one or more apertures 32 therein may be any hollow
elongate
tubular member, substantially symmetrical in cross-section. Figures 5, 6, 7,
and 8 show four
separate embodiments, where such pipe member 24 is alternatively of, but not
limited to, having
a circular, square, triangular, and rectangular cross-sectional area
respectively
In order for the apertures to best form microbubbles, in a preferred
embodiment a specific
mathematical relationship exists between the interior area of the pipe member
24, and the
combined exit area Ae of apertures 32, where such pipe member 24 has a maximum
exterior
width Do and maximum interior width Di. Such relationship between the combined
exit area Ae
of the apertures 32 and the inlet area Ai of the pipe member 24 is essentially
a function of the
thickness of the pipe member (namely the ratio of Di to Do) , and is a
definite relationship for
symmetrical pipe members 24 of uniform wall thickness.
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CA 02437948 2003-08-21
Specifically, it has been found experimentally (see examples 1 and 2, below)
and
confirmed by derivation (see summary of invention, above) that for pipe
members 24 of uniform
wall thickness and having a maximum interior width Di and a maximum exterior
width Do,
where the pipe member 24 has identical moments of inertia about at least two
separate axis in a
plane of cross-section through such pipe member 24, that for formation of
microbubbles of gas
in a liquid 14 (ie bubbles of less than 100 microns) under conditions of
standard temperature and
pressure, Ae can be less than or equal t~, but no greater than Ai x Di/Do
where there exist a
plurality of apertures 32 in pipe member 24. Where only one aperture 32 exists
in pipe member
24, such aperture may only have a cross-sectional area no greater than Ai x
Di/2Do.
Figure 5 shows a detail view of a pipe member 24 of the present invention,
having a
circular cross-section, of maximum internal width Di, and maximum exterior
width Do, and
internal area Ai= ~ x Di 2 /4. Figure S also shows the configuration of pipe
member 24 and
apertures 32 used to determine the relationship between inlet area Ai and
combined aperture exit
area Ae. Two rectangular slots 90 were formed in pipe member 24, on opposite
sides thereof,
each to a depth of %z Do. Each rectangular slot 90 forms an exit area equal to
°°gap" x r~ x Di (see
Fig. 5B) , so as, in the case of two rectangular slots 90, to form a combined
exit area Ae= 2 x
"gap'°x~txDi.
It was experimentally found (see example 1, below) that the maximum combined
exit
area for at least two or more apertures was Ae can be no greater than Ai x
Di/Do where bubbles
of a size less than 100 microns are desired.
Having a maximum combined exit area Ae means that the aperture "gap'°
shown in
Figure 5 will be a maximum. Accordingly, where maximum throughput of gas-
Iiquid mixture 22
is required through apparatus 10 of the present invention, the maximum
combined aperture exit
area Ae is used. Where Ae =Ai x Di/Do, setting this equal to 2 x gap x ~c x Di
and solving for
the gap, this means the "gap°' can only be [Ai x Di/Do]/2 x ~ x Di
which stated more simply is
equal to Ai/~t x Do., where ~ x Do is the outer circumference of pipe member
24.
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CA 02437948 2003-08-21
Accordingly, in a further embodiment, a further restriction exist on the width
of the
'°gap" shown in Fig. 5, namely that the '°gap'° be no
greater than the quotient of Ai and the outer
circumference of pipe member 24, namely ~c x Do. Stated in other terms, to
form bubbles in the
extruded jets 56 of gas-liquid mixture 22 which is expelled from rectangular
slots 90 comprising
apertures 32, such apertures 32 may only be of a maximum vertical depth
(°°gap'°) of Ai/C,
namely [~t x Di Z /4 ]/ [ ~ x Do] (ie Di Z /4 Do ). Thus where the maximum
aperture distance (ie
the maximum "gap'°) of Di 2 /4 Do is used, sc as to be required to
drill the fewest slots or
apertures 32, the maximum "gap°' of aperture is typically used, namely
Ai/circumference of pipe
member 24, which for a cylindrical pipe member 24 is simply Di 2 /4 Do.
As may be seen from Figure 5, pipe member 24 possesses uniform wall thickness
(ie Do
less Di is always a constant). Moreover, as may be seen from Fig. 5A, such
pipe member 24
possesses at least two identical moments of inertia in a plane of cross-
section, namely the
moments of inertia about axis II and IZ are identical, namely ~c164 [Do4 - Di
4 ]
The same relationship applies in the case of pipe member 24 of square cross-
sectional
area Ai, as shown in Figs 6 and 6A, of uniform thickness °'t'°.
Thus for two rectangular slots 90
within square pipe member 24, as may be seen from Fig. 6A, the combined
aperture exit area Ae
may be calculated as 2 x "gap'° x [1/2 Di + Di + %z Di ]. Where the
maximum "gap'° is
determined by the surprisingly- found relationship of Ai/(circumference of
pipe), namely Ai/4
Do , then Ae thus becomes 2 x Ai/4Do x [ 2Di]= Ai x Di/Do. Again, a square
pipe member 24
has identical moments of inertia about two identical axis h and IZ in a plane
of~ cross-section,
namely h = I2 = [Do4 - Di 4 ]/12
The same relationship applies in the case of pipe member 24 of triangular
(equal sided)
cross-sectional area Ai, as may be seen from Fig. 7 and 7A. Thus for two
rectangular slots 90
within equilateral triangular pipe member 24 of depth equal to %Z Do on one
side as shown in
Fig. 7A, as may be seen from Fig. 7A, the combined aperture exit area may be
calculated as 2 x
"gap" x [1/2 Di + Di]. Where the maximum "gap" is determined by the surprising
relationship of
Ai/C, which in the case of an equilateral triangle of interior maximum width
Di equals Ai/3Do,
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CA 02437948 2003-08-21
then Ae= 2 x gap x 3/2 Di= 2 x Ai/3Do x 3/2 Di , which reduces again to Ae=Ai
x Di/Do. Again,
as may be seen from Figure 7A, an equilateral sided triangular pipe member 24
has identical
moments of inertia about two axis II and IZ in a plane of cross-section,
namely Il = IZ .
For a symmetrical pipe member 24 which does not have identical moments of
inertia
about two axis in a plane of cross-section, such as a rectangular pipe member
24 as shown in Fig.
8 and 8A (namely h BIZ ), the derived relationship of Ae=Ai x Di/Do does not
apply.
However, in the case of a rectangular pipe member 24 having maximum exterior
dimension D1 , minimum exterior dimension DZ , maximum interior dimension D3 ,
and
minimum interior dimension D4 , as shown in Fig. 8 and 8A, the combined exit
area Ae for two
rectangular slots 90 as seen in Fig. 8A is determined as 2 x °'gap" x [
%Z D4+ D3 + %z D4 ]. Again,
using the surprising result that the maximum '° gap" equals Ai/C,
namely Ail[2x (D2+ D1)], then
Ae = 2 x gap X [D4+ D3 ] = A1 X [D4+ D3 ]/ [D2 + D1 ]~
With respect to the location of the apertures 32 of the present invention,
from which gas-
liquid mixture 22 is expelled, apertures 32 may be formed within pipe member
24, as shown in
Fig. I and particularly in enlarged view shown in Figs. 3 and Figs. 4 through
8 inclusive.
Alternatively, apertures 32 may be formed in plug member 25. Fig. 9, and Fig.
10 showing
enlarged detail, illustrate formation of a pair of rectangular slots 90 which
serve as apertures 32
in plug means 25. Fig. I I, and Fig. 12 showing enlarged detail , illustrate
the employment of a
plurality of cylindrical apertures 32 in plug member 25. Of' course, as in the
case where the
apertures 32 are situate within tile pipe member 24 itself, such apertures may
be of any
geometrical cross-sectional area, with circular cross-sectional area being
preferred due to the
ease in creating cylindrical apertures 32 having circular cross-sectional
area, such as by drilling
with circular drill bits.
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XalT9p'e °~
A series of seventeen various-sized apparatus 10 were constructed in
accordance with one
of the embodiments of the invention as contemplated herein, namely that
embodiment shown in
Fig. 1, having a pair of apertures 32 in the form of horizontally-extending
rectangular slots 90,
as shown in Fig. 5.
Each of the aforesaid seventeen test units comprised a shell (referred to
above and below
as a vessel 40), having in an upper portion 42 thereof a downwardly extending,
substantially
vertical cylindrical pipe member 24 of various Di and Do, ranging from nominal
pipe nominal
diameters of 0.50 inches to 10.0 inches.
Each of pipe members 24 for the various test units had a pair of rectangular
opposed
slots 90 therein, as shown in Fig. 5. The exit area Ae for the pair of slots
was set as the
maximum, in accordance with the requirement Ae (max) = Ai x Di/Do. Because the
width of
each of the slots 90 was the width Di of each pipe member 24 as shown in Fig.
5, the vertical
depth (ie °'gap°') of each of the slots 90 was accordingly
thereby pre-determined due to the
requirement that Ae=Ai x Di/Do, and was gap~",aX> = Ai/(outer circumference of
pipe member
24).
Vessels 40 of various nominal diameter sizes were used and matched with
corresponding
pipe members 24, with the vessel 40 having a nominal diameter of approximately
six times the
pipe member 24 nominal diameter . This resulted in a matching of vessels 40
with pipe members
24, wherein the vessel 40 nominal diameter ranged from a nominal 3.0 inch
diameter to a 10.0
inch nominal diameter.
Various lengths of vessel 40 were used, ranging from 34.2 inches for a
vessel/shell 40 of
3.0 inch nominal diameter, to 260 inches for a vessel 40 of 10.0 inch nominal
diameter.
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CA 02437948 2003-08-21
Various lengths of pipe member 24 were used, ranging from approximately 7.30
inches
for a pipe member 24 of 3.0 inches nominal diameter, to 12.0 inches for all
pipe member
diameters of approximately 1.0 inches nominal diameter and greater.
Water at 15° C and air at 21°C was used as the liquid and gas,
respectively. Water,
having bubbles of air of a size greater than 100 microns therein, was provided
to pipe member
24, and sprayed into an upper portion of vessel 40 via rectangular slots 90.
Four inlet flow rates of water were used, namely 6ft/sec, 7 ft./sec, 8
ft./sec., and 9 ft./sec
into the vessel 40 via pipe member 24. A lower withdrawal pipe was used to
withdraw water
having microbubbles entrained therein from vessel 40. This resulted in
pressure in the pipe
member about 5 psig greater than ambient gas pressure which existed in vessel
40.
Tables I and II show dimensions for the seventeen apparati 10 of the present
invention
which were constructed, and the various resultant volumetric flow rates of
each of the test
apparati.
In all seventeen instances, microbubbles were formed in vessel 40 over each of
the four
volumetric flow rates, of dimensions less than 100 microns.
Table III shows retention time of microbubbles in vessel 40, for a selected 13
of the 17
test apparati. The retention time was conducted using an inlet flow velocity
of 7 ft./sec. into pipe
member 24. In such case, the retention time was rather brief, with the
intention to withdraw
water having microbubbles therein to a subsequent location (vessel), where the
retention time
could be longer.
Example 2
3 0 Purpose
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CA 02437948 2003-08-21
The purpose of this experiment was to confirm various formula for optimum
creation of microbubbles using the apparati of the present invention.
This was done by evaluating the effect of aperture size and apertures exit
area on the
size of the bubbles produced.
Apparatus
Apparatus of the type shown in Fig. 14 was selected, and in particular an
apparatus of Fig. 14 having the dimensions far inlet pipe member OD and ID and
(upper)
impaction pipe length, as well as shell (vessel) height and diameter, as per
test unit number 2 in
Tables I and II.
Figure 15 shows associated equipment used with the selected model of apparatus
10 of
the present invention in conducting the above tests. A Plexiglas receiving
tank 100 was utilized
for receiving water having microbubbles entrained therein from apparatus 10
and to permit
observation of bubble rise to permit calculation of bubble velocity (used to
determine bubble
size). A ruler 102 was attached to the outside of the tank to allow form
measuring distance
travelled by bubbles per a given time interval, to calculate (in the manner
described below) the
bubble size. A separate tank 104 was provided as a reservoir to permit supply
of water to pump
106. Additional piping 108 pez-mitted supply , via a globe valve 110 and
venturi nozzle 112 to
pipe member 24 of apparatus 10. Water exiting vessel 40 of apparatus 10 passed
through a flow
meter 115 and pressure gauge 117, and then through a globe valve 118 to
Plexiglas tank 100.
Procedure
Pipe members 24 were created, having horizontally-extending cylindrical
apertures 32,
of diameter, number, and combined exit area Ae as recorded in Figure 16.
Each combination of hole (aperture) size and exit area was tested with the
same standard
procedure set out below. Each test was run under the same conditions of back
pressure, flow
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CA 02437948 2003-08-21
rate, water volume, water temperature, and pressure drop across the Venturi
nozzle. The same
apparatus 10 was used for all the tests, and pipe member 24 ~~as changed
between runs.
Measuring the rise of the bubbles against time permitted dete~°mination
the size of the
average bubble in the tank.
~ The apparatus 10 was connected to the Plexiglas pump 100 and pump 106.;
~ Valve 118 from tank 100 was opened to allow equilibrium level between tank
100
and vessel 40 of apparatus 10;
~ Pump 106 was started and allowed to run until constant level was achieved in
vessel
40 of apparatus 10 ;
~ Valve 110 controlling flow through venturi nozzle 112 was adjusted to create
a 20
psi drop across the nozzle 112 ;
~ The back pressure on vessel 40 was then adjusted to 20 psi;
~ The apparati 10 and test equipment was left to run for 3.5 minutes;
~ Pump 106 was turned off and valve 118 between vessel 40 and tank 100 was
closed;
~ Once a clear view at the bottom to the rear of the tank 100 was established
bubble rise
was monitored and recorded at the given time intervals;
~ Once tank 100 became clear of bubbles the top of vessel 40 was removed and
pipe
member 24 was changed to a pipe member having differing number and /or
diameter
of apertures;
The above procedure was repeated for pipe members 24 having apertures 32 of
various
number and/or diameter, to determine the effect of- area and hole size on the
vessel's
performance.
The results of the measurements, and resulting calculations, are compiled in
Table 16.
Calculations
The design uses the formula
Eqn.l
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CA 02437948 2003-08-21
_ TG XDi 2
where: A;=inlet area
D; = inside diameter of pipe
S This formula defines the inlet area of pipe on the vessel 40. The inlet area
Ai is used to
determine the gap size or maximum hole dimension.
Eqn.2
Gap _ ~ ~Do
where: Gap = hole dimension or Gap size
A;= inlet area
Do = outside diameter of :pipe
This formula defines the maximum length of one of the holes' dimensions. The
maximum combined aperture exit area Ae is determined using the pipes'
dimensions in the
following formula
Eqn.3
~ ~ D; 3
C x Gad ~ ~4 - D
0
where: Ae=maximum exit area
Di = inside diameter of pipe
Dp = outside diameter of pipe
This formula defines the maximum area that will produce the desired
microbubbles. Exit
areas less than this value are capable of producing the microbubbles whereas
any area greater
than this does not produce bubbles that are sufficiently small. T3oth the hole
size and exit area are
parameters that effect the size of the bubbles that are produced by the
vessel.
Using Stokes Law the size of the bubbles produced is determined by the rise
velocity of these bubbles. Stokes Law states
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CA 02437948 2003-08-21
Eqn.4
.V,= g ( 1- na )D2
where: v = velocity of bubble rise
g = gravitational constant
pW, pa = density of wafer and air
~, = viscosity of fluid
D = diameter of gas bubble in fluid
Each of the experimental runs produced data which appear in Figure 16. Each
experimental run is also accompanied by a corresponding hole diameter, number
of holes and
exit area.
Time and distance traveled were used to calculate the rise velocity.
Eqn.S
da ° d~.
v= --
t2 ' t1
with the following units v - mm/s
d-mm
t - sec.
The rise velocity from each interval was used to calculate the corresponding
bubble
diameter using a form of Stokes Law:
Eqn.6
D~ ~8v x w
g (~tv -pa >
where D = diameter (cm)
v = velocity (cm/s)
~. = viscosity of water (Poise) = 0.0112 P
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CA 02437948 2003-08-21
g = gravitational constant = 981 cm/s2
pW = density of water = 0.99913 g/cm3 @ I S°C
pa = density of air = 1.239 mg/crn3 @ 15°C
The number of holes, the hole diameter and the resulting exit area were
determined using
the following equation.
Eqn.7
~= NH' DAZ4
where: Ae = exit area
NH = number of holes ~rDi2
DA = hole diameter
Sample Calculations
The first calculation needed was to determine the maximum exit area
D; = 0 . 824 Da =1. 05 ~_ ~XD' 3
4 x Do
~=0.4184872
The following calculations are those used to determine the exit area at a
given hole size
and number.
~=2~ ~lc~=5/32 " ~=NHXD,e,Z X 7I~
4
~_ ~ . 4026 in2
The following are a set of sample calculations for one interval. The
calculations
find the rise velocity of the bubbles and their corresponding diameters.
d2=4; dl=3; t1=5; t2=10; v= d2 d~ s
t2 ' t1
v-_ 0 . 2~,m/ s
-4i-
CA 02437948 2003-08-21
D= 0.00202948 can
Results
Results of the above tests are found in Figure 16. Fig. 16 lists the drill
sizes used for
creating the apertures, the number of holes(apertures), and the corresponding
combined exit
area Ae for each pipe member (nozzle) 24, as well as the resulting bubble
size.
As may be seen from Fig. 16, where the combined exit area Ae of the apertures
exceeded
the pre-determined exit area of Ai x Di/Do, namely exceeded 0.418487 in2 , the
bubble size was
greater than 50 microns. (ref. those tests which are highlighted).
As may also be seen from Figure i 6, where the aperture diameter was greater
than
Ai/(outer circumference of pipe member 24), namely greater than 0.161 inches,
the average
bubble size was greater than 50 microns.
Where the combined aperture exit area Ae was less than or approximately equal
to Ai x
Di/Do, namely less than or equal to 0,.418487 in2 and the aperture diameter
less than or equal to
Ai/(outer circumference of pipe member 24), bubble size was less than 50
microns.
Figure 17 is a graph prepared from that illustrates a relationship between
combined exit
area Ae and bubble diameter. The average diameter from the first 30 seconds
(in most cases)
was plotted against the exit area. Figure 17 demonstrates a defined
relationship between the two
variables that occurs while the hole diameter is held constant. This gives
evidence of the
influence of exit area on bubble size. The larger the exit area the larger the
size of the bubbles
produced.
-42-
CA 02437948 2003-08-21
Figure 17 has an area that is below and to the right of the dotted line. Such
represents a
design configuration of the apparatus 10 of the present invention which
produces
microbubbles in the desired range of less than 50 microns.
* * *
Although the disclosure describes and illustrates selected embodiments of the
invention,
it is to be understood that the invention is not limited to these particular
selected embodiments.
Many variations and modifications will now occur to those skilled in the art .
For a complete
definition of the scope of the invention, reference is to further be had to
the summary of the
invention and in particular the appended claims.
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