Note: Descriptions are shown in the official language in which they were submitted.
CA 02460123 2004-03-08
APPARA'~'l1S AZVD ME~.'I~i~If ~'Cfl~ Pt3l~UC~P'~G
~~ta~.~ ~A~ ~u~~L~s ~~ ~,~~u~.ns
Fieid of the Inventinu
S 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 litluids.
8ackgronnd of the Ixtventintt
11~ Entrainment of a gas in a liquid is required in numerous industrial
processes, typically for
the purposes of reacting tlzc gas with such liquid or materials in such
liquid, such as dissolved
ions or fir<ely dispersed solids, to cause reaction of such gas with materials
therein to cause same
to be neu~aIi~.ed by, xeact with, or precipitatE or be filtered out of such
liquid-
15 For example, it is known to bubble o;cone through water, to allow the ozone
to react and
combine with dissolved minerals andlor finely dispersed solids within the
water, so as to form
solid pxoducts which may either precipitate out of the liquid or be filtered
frarn the water, so as
to thereby purify the water. 'The ozone may further react with ~.arx~ful
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 bubt~les of gas immersed in such liquid will have, for
the same volume
of gas, a greater surface area and thus a greater liquidlgas interface, than
the same volume of gas
when such gas exists in larger bubbles.
A large gaslliquid interface is a desirable characteristic tat instances where
the gas is
introduced into a liquid for the purposes of reacting the gas with the liquid
or dispersed solids iu
such liquid, since greater surface area of the gas exposed to such liquid
andlar finely dispersed
solids izt such liquid decreases the time it takes for the gas to react with
the liquid or finely
.. 1 ..
CA 02460123 2005-02-25
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
preferably 5 to 50
microns.
A number of devices .and methods for aerating liquids, typically water, with
gas bubbles,
are known.
For example, US 2,850,838 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 10, 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 oP the tank 10, thereby introducing air into the
liquid which in turn
oxidizes metabolic iron presf;nt in the water. Iron precipitates then settles
out of solution and
down through the water contained in tank 10.
US 5,601,724 and US 5,460,731 teach an apparatus and method, respectively of
aeratiing
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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CA 02460123 2004-03-08
vessel l~, where it is directed ttpw~trdly via conduit 30; where it is
directed through a cylindrical
restriction gap 19 formed between the secand end 34 of conduit 3~D and the tap
1.8 of vessel 14.
The gas, being of lesser density, passes more quickly through the restriction,
thereby accelerating
the liquid. As the liduid exits the restriction gap 19 it pzzeutn.atically
hammers against the top 18
of pressure vessel 14. Thereafter the liquid stream, by farce of gravity,
cascades through the gas
in pressure vessel 14 downwardly to further impact plate 3~. TheTeafler the
liquid stream then
passes iluaugh openings 37 in plate 3S and by force of gravity cascades throw
the gas in
pressure vessel ~4 to further impact on liquid at the bottom of the vessel_
Thereafter such liquid,
having small bubbles of air entrained therein, is retnaved via a conduit from
the bottom of vessel
1~_
US S,fJ96,Sg6 to a "Process grad Apparatus far Removal of Mineral Contaminants
from Water" teaches a pressurized aeration tank 24 having a tube :'6 located
within said tanfc 24
which supplies the tank 2a with raw water, which is introduced to t:he tax~3c
24 via the tube ~6 via
a plurality of hales 28 in the tube (ref. cal. 2, lines 49-54 and Figs. 1-7).
The tube 24 only
supplies "raw water" and not water having air bubbles entrained therein, arid
is not for the
purpase of providing gas micrabubbles of a range of S-50 microtxs_ Most
importantly, no
relationship regarding the size ~af the boles ~8 in the tube 24 is specified
to attemtpt to attain
micrabubbles, even iF the patent further provided far the raw water to 1'xrst
have bubbles
introduced therein,
US 4,556,523 teaches a microbuhhle injector usable to .<separate material of
different
density by flotation, wherein microbubbles of gas are inuoduced unto a chamber
14 containing a
liquid mass 16. As may be seen from figure 1 of US ° 523, a gas
atitnixture 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 ~~
via aft injector hale 1.~ tv procure a high velocity jet of air water. A,
deflector wail 18 is disposed
over such injector hob so as to create a narrow gap around the injector hole,
which the waterlair
mixture must pass through. The injector hale is preferably substantially
circular, and the height
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CA 02460123 2004-03-08
of the passage between the injector and deflector wall at the ed~'e of the
injector hole is less than
one quarter of the diameter of the injector hale in the injector wall-
Disadvantageously, none of the aforetnentiaized patents teach or disclose any
specific
design interrelation betweetz the dimensions of the injector holes~rpartslor
gaps arid the conduit
outer dimensions which will best produce micrabubbles its the liquid-
For exartiple, ~JS '838 simply provides a nut 23 an the end of the valve 24 to
adjust the
size of the aperture between cone surfaces ~4,2a throw which the water must
pass. Na gap
l~ dirne~nsion is ever specif ed which best provides bubbles of a desired
small size.
Similarly, each of US '7~4 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 ga on to note that (at cal. 6, lines A~ to 47} that the greater the
diameter of the cylindrical
edge, the closer the end of conduit 30 had to be positioned to the tcap ~g of
the pressure vessel ~a
(i.e. the smaller the restriction gap had to be} in order to form bubbles of
the desired site. 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, nariiely
2Q microbubbles of diameter in the 5-attU micron range.
US 4,556,23 perhaps comes closest to specifying an ixrterrelation between the
components in order to achieve desixed small microbubble size in the range of
50 to 1~0
microns, speci#'ying as zioted above that the passage between the injector and
deflector wall at the
2S edge of the injector hole is less than one quarter of the diameter of the
injector hole in the
injector wall. No specific optimum site was specified- Moreover, the
particular manner by
which the microbubbles are created, namely requiring an injector wall lil and
deflector wall 14,
requires substantial q~taniity of material, aald is thus a particularly
material-intensive design and
thus relatively costly.
_q
CA 02460123 2005-02-25
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 aperture;(s)
through which a gas/liquid mixture flows can be accurately designed so as to
give microbubb~les
of the desired small size.
Summary of the InvE~ntion
In order to meet the above need for a device of simple and relatively
inexpensive design
able to introduce gas microbubbles into a liquid, in a broad aspect of the
present invention such
invention comprises an apparatus having means for creating microbubbles in a
liquid,
comprising:
means for introducing gas bubbles, the majority of which are of a size greater
than 1.00
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-;;as
mixture under first 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 adapted to
direct said liquid
substantially horizontally out~,vardly from said pipe means; and
a containment vessel., to capture said liquid-gas mixture having microbubbles
of ;;as
entrained therein.
Importantly, however., and quite surprisingly, it has been 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 unifornn pipe wall thickness, and a maximum interior
width Di and a
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CA 02460123 2005-12-13
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/2Do.
While the above interrelation, namely for a plurality of apertures where 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,
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 axea 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 ~i 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 cro~ss-
section through said pipe. This encompasses pipes having circular, square,
hexagonal, octagonal
and the like having uniform 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 inertia
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 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 dimensions of the
pipe, and the cross-
sectional area Ai of the pipe for microbubbles of the desired size to be
produced be defined as
Ae <_A; x [ D3 + D4 ]/[D~ + Dz]
where D~ 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
inventiion
is of uniform wall thickness and has a maximum interior width D; and a maximum
exterior
width Do , further having identical moments of inertia about at least two
separate orthogonal axis
in a cross-sectional plane through said pipe means; 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 ~~ 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.
CA 02460123 2005-02-25
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 i.s directed horizontally outwardly from said
pipe means by each. of
said apertures.
It is further preferred, although not absolutely necessary, that the
collection vessel for
containing the resultant liquid having microbubbles contained therein form
part of an rote~~al
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 forrn a
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 vessels and extending substantially vertically
downwardly within said
vessel from said upper portion thereof, and having plug means situate at a
lowermost distal c,nd
thereof for preventing egress of liquid vertically downward from said distal
end; and at least two
apertures situate on said piI>e 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.
_g_
CA 02460123 2005-02-25
Again, in a preferred embodiment, where symmetrical pipe means such as a
cylindrical,
square, hexagonal, octagonal, or even a triangular (equal sided) pipe member
is used, the
apparatus of the present invention comprises:
i) a containment 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 h<~ve
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 apertL~res situate in said pipe means and disposed in one or
more plmes
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, a:nd preferably 5-SO 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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CA 02460123 2005-02-25
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 of 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 acids
up to the maximum aperture area [Ai x Di/Do] may be used, in order to
introduce microbubb~les
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 A~ is derived from the
surprising observation
that the maximum aperture dimension (i.e. the "gap" ) through which the
gaslliquid mixture must
pass is determined from the experimentally-derived observation that the
aperture dimension,
hereinafter referred to as the "gap", which best creates microbabhles ofthe
desired small size, is
S detezmined by the relationship gap "G" = A, I(pipe outer circumfernnce~.
~'or example, for a circular conduitJpipe of minor diatnete:r 1'_7;, outer
diartteter DQ, and
crass-sectional area Ai= ~rD;z1$ it has been found that for a rectangular
aperture cut
perpendicularly into the side of the pips, to a depth of %z the pipe diameter,
so as ca create an
aperture to allow egress of a gasJliquid mixture under pressure: thererhraugh,
the maximum
pertni$sible "gap" C , ~atnely the maximum vertical height of such horizontal
$lot, is:
A,!(pipe outer circmnference) = ~rD,~l(~ a~t~a =p,2l4Do (~:q'rt. #1)
The surface exit ;area Ae of two slats each foamed over !a the inner diameter
of the pipe
D, is calculated as follows:
A~r2xgapx f~~xp,
Thus the maxirr~um exit area ,Ae of such apertures for a circular pipe member
is thus equal to
Ae= 2 x D,2/~Do x %x ~ x D; = 'RDi I4~)m. (1~q'n. # 2)
AcGOrdingly, Ae stated more generally iu teru2s of A;,, where Ai = ~i /~ ~Y be
stated
as follows:
A~ _ '~Di3 = xDi' X ~,lpo= At X DIIDO
dDo 4
Where only one exit aperture is utilized, maxitnurn exit area is = ~rD,~IBDo.
and slated in
terms of Ai is equal to
Ai x Di1~21~a}
_11_
CA 02460123 2004-03-08
~n view of the above, the minimum numher of apertures in a circular pipe tray
ire
determined. In this regard, ixt a preferred embadimeuut of the apparatus of
the present invention,
for the reasons discussed above, namely the desire to use the gr~;.atest
anxouttt of "throughput"
for the apparatus with the least number of halesJapertures, and thus inxroduce
micrabubbIes into
the greatest VOIUIII'~.' of llquiCl in the shortest time, the largest-si2:ed
aperture utiliza'hIe equals
Ail. In order to achieve as much 'Ghroutput of liquid which has xnlcmbubbles
introduced
therein, the apparatus in a preferred etnbodimertt witl not only possess
apertures pf maximum
size, but also the combined exit area Ae of such apertures will equal the
maxitnutn ~issihle
area in order that the apparatus he able to process (ie introduce gas
rnicrobubbles) into as much
liquid as possible ~cr a given time.
Accordingly, itx the case of cylindrical pipe, having circular (cylindrical)
apertures, the
minimum number 4f holes(apertutes) which c~x be used is detetm~ined by
reference to lrq'n. #2,
IS which defines the maximum exit area for a circular pipe member, namely
Ae= ~rD;3J4Ta~
Although the surface exit area of a circular hple in a cylindriicai pipe forms
a "sa~cidle-like"
exit area on the surFace of the pipe, for small diameter apertures :relative
to the diarr~eter of the
pipe, the combined surface exit area of all apertures is appmxiuZately equal
to the xtumber of
apertures tnultiplisd by the exit area Aa~"m of each aperture:
Ae(max)= n x A$P~,,,yt1 x (~ x 1~a214)
'~ 5
As discussed, Da is preferably no greater than Ai/C. AccoTdin~;ly ,
substituting AiIC far Da
pr4duces the following:
Ae(max) =n x (n x Da~l~)= n x (~rx [ Ai/C~'' J4 )
~= n x (~ x ~(x x D:i2 I~)J( ~ x ~0)]2 I4
_l~_
CA 02460123 2004-03-08
The above equation for A.e(max} cast he equated to l;q~n. # 2 for the
Ae(tnaac) of a circular pipe,
atld SQIVeCI fOr "n" as ~O~IOW~:
Ae(max} = n x (x x ~(x x DiZ i4}f( ~t x 1?0)]2 l4 ' xD; l4Do
n= 16~,a (~q'n.. ~)
T3i
Accartliztgly, since i=qra, t may, depending on the ratio of Doli~i, produce
~. fractional value for
the number of holes "t1", in a preferred embodixuent , the mixiirattm number
of circular apertures
in a circular pipe merrxber far tnaxitxtum #~olv of lic(uid is defined by the
following expression,
1d namely:
a = nearest w3~ole integer to ~x6 x I7~ l D~~ (Eq'n. 6A}.
It is noted that since the maximum comhined aperture exit area Ae for
cylindrical pipe i; Ai x
DilDo, for apertures cf small diameter D,, relative to the diarr;eter al' the
cylindrical pipe, the
fouowing is true:
Aen,,",= n x :r Ilx~Mm ~I4
and thus
Ai x Dil~lo = rt x ~r D,,~M~.,~a 2l4
The abtwe allows us to solve for the mxxixnum diameter ofthe apertures
lrl,"~n""~ , where
for circular pipe, Ai = ~i2 follows:
4
~r x pi2/4 x DiIDO--- ~ n x n x Dr~~~? 2l4
thras ~~.c~,~:W'~Di I(tt x Dog
z5 stated alternatively, l~Ac~r.xt ~ ~ x Ai x Dil err x ~ .x Do]
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It is usually the case i:or 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 diarr~eter 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(MAX) 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 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
Dp(MAx:) _
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 circmmference 4 Do, for a horizontally extending slot
of Gap "G", it lhas
been faund 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 rr~ay be stated as follows:
Gap "G"( Max) = A; _ _D;z
circumference 4Do
The exit area Ae for a plurality apertures in a square pipe may thus be
calculated,
knowing such maximum G;ap "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=2xGap(max) x(%ZD;+D;+%2D;)
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CA 02460123 2004-03-08
Accordingly, expressed in terms of inlet axea Ai far the sqraare pipe, Ae rnay
be stated as
follows:
At= 2 x ~ ~ x (2D;) ~ 4~ = lai2 x DL T ~.i x l~i!!ad
~~o ~~o Do
Again, where there is only one aperture in such square pipe, Ae is thus:
A~ = Crdp(ri~ax) x (%a ~, ~- h; + tz I~~
and thus, expressed in terns of A.i, is thus
t G Ae=Aa x Dil(2xDo)
As in the case of circular apernues in circular pipe, where there are circular
aper~ues in
square pipe, the diazrieter I~R«,xy may be solved for as follows:
Ae=Ai x Di/t~a ti)
IS
Ae; n x ~t x 1a, Z !4 (~) where 'n' is the number of aperttues
Equating (1) with (2) allows far the diameter D.,~~a to lae salved fir as
follows:
20 Ai x Di/pp = tz x ~ x Dd a !4
D"~M"p w~4 x Dial(n xn x Dog - -"~4 x Ai x Di J ~n x~t x 1_3aJ
Again, it is usually the case far most sguare pipe having interior width Di
and exterior
width lea chat ~n" must be greater than ~ fbr ~xtost pipe, tiaaAely there must
usually be a plurality
of aperttu~es, sit~ee othe~vise the calculated dianneter DA of the cylindrical
aperture results its. a
25 diameter greater than either the interior width Di or the exterior v~radth
Do, whieh is a physical
impossibility, as diarrieter DA can only be as large as, or smaller than, Di
and Do_
Again, the above value I}ALMAX~ fdr a sduare pipe having cylindrical apertures
may , in
instances where there are relatively Few number of apertures (ie n is a low
cumber, but as per the
_ig_
CA 02460123 2005-02-25
above, greater than one) give values of DA 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
Dp(M~) -
Ai/(Circumference of Pipe).
It has been discovered that the above relationships) 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=,r3 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= _ ,~3 Di2
l2Do
The exit area of such two apertures is accordingly determined as the product
of the ~;ap
multiplied by the perimeter o:f the gap. Accordingly,
Ae(max)=2 x gap x (Di + %z Di)
=2 x,_r3 Di2 x _3 Di
l2Do 2
- 16-
CA 02460123 2004-03-08
F.~cpressed. in terms of Ai,
~3 Di3
~ 1~0
Ae(tnax)= d3 Di2 ac Di = Aa x Di
Do Do
'rhe present invention , in a further of its broad aspects, relates to a
method for creating
microbubbles of gas in a liquid and exposin g them to matter eutrairted 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 gaslliqi+id mixture;
directing said ,has-liquid mixture into a hollow pipe member, said pipe
meznber having a
maximum interior width D, and a maximum exterior width ~~a, said pipe member
situate
proximate an upper portion of a containment vessel and extending into an
ixlterior of said
2D containment vessel, said upper partian of said cantaimnent vessel
containing said gas teeing
tinder pressure, and a bottom portion of said eontairiment vesseY
substantially containing said
liquid;
izt~ecting said gas-liquid mixture under pressure via said pipe member, infra
said
cc~nt~itW,lellt vessel;
spraying substantially radially outwardly from said pipe member said ,has-
liquid mixture
into said upper portipn of said containment vessel via at Least rw~ apertures
in said pipe
member;
said at least two apertures in said pipe member in communication with said gas-
liguid
mixture in said pipe tuember and having a combined area ~ nixed as a function
of a maximum
-i7-
CA 02460123 2005-02-25
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;/Do
and
removing from said bottom portion of said containment vessel said liquid which
lhas
been exposed to said microbu.bbles.
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, comprising the steps o~
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 width 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 ~;as-liquid mixture having microbubbles of gas
entrained therein in
a vessel; and
-18-
CA 02460123 2004-03-08
removing said gas-liquid mixture from said vassal.
In a Further refinement of the methods of the present invention, oste such
method further
comprises the step of cohecting within said bottom portion o~E' said vessel
said liquid with
rtaicrobubbles 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 introdueed into
said containment
vessel.
In yet a further refinement of the aforesaid methods, the rate of withdrawing
the liguid
from the bottom of the vessel is substantiadly at a rate which auicrobubbles
entrained in said
liquid rise in Ehe vessel, sv that at a time when liquid is retnoved frotn
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
positian.ed irl the
containment vessel below said pipe member and interruediate said upper
portiozx and said bottom
portiost of said caarainment vessel, and the race of injection and removal of
has-liquid from the
vessel adjusted so that baffle plate xneutber is positioned above xhe level of
the iiquid in the
~Q vessel.
In order far the apparatus arid method of the present invention fn form
microbubbles, the
pressure of the ;has in the upper portion of the vessel (back pressure) need
be of a pressure of at
least 10 prig to 15 psig, arid preferably at least 2d prig to 30 prig. The
initial-gas liqtud mixture,
2S in order to be provided to the apertures and sprayed therefiam, must
necessarily, due to a small
pressure dxop across the apertures, be supplied at a slightly higher pressure
than the pressure of
the gas within the upper portion of the vessel (i.e. back pressure), in. prder
to be effectively
sprayed into the interior of the vessel. The step af'spraying the liquid-gas
mixture substantially
radially outwardly via the apertures may further in a preferred embodiment be
adapted to spray
3a such liquid-gas mixture against the sides of the cantainmer;t vessel.
-19-
CA 02460123 2004-03-08
From another perspective , the invention in a preferred embodiment comprises a
method
for continuously purifying a liquid containing impuritie$ by exposing the
liquid and impurities
for a time in a substantially vertically containment vessel to microbut~bles
i» tlae range of 5-100
microns in diameter, cotngrising the steps of
directing a gas-liquid mixture containing impurities and xEubbles t?f gas the
majority of
which are in excess of 100 microns in diameter into a hollow pipe member, said
pipe member of
uniform thickness and having a maximum interior width Di and a maxitxxum
exterior width Do
and identical moments of inertia an two axis in a plane of crass-section
through said pipe means,
said pipe means situate proximate an upper portion of said containment vessel
and extending
vertically dawnwardly in an interior of said contaituneus vessel, said upper
portion of said
contairunent vessel containing said gas, and being under pressure of at least
10 psig and
preferably 15 psig or higher;
1 S injecting said gas-iicluid mixture, under a pressure of at least 5 prig
higher than said gas
in said containment vessel, into said vessel via said pipe member;
spraying said gas-liquid mixture substantially ltoxizontally outwardly from
said pipe
meml7er into said upper portion of said containment vessel via a plurality of
apertures iri said
pipe member so that said gas-liquid mixture contacts interior sides of said
vessel;
2o said plurality of apertures in said pipe member an epzmtxunieation with
said gas-liquid
mixture is said pipe member and having a combined area Aa, said apertures
nixed as a function
of said ma~tirnum interior width D, and skid maximum outside width Dm and a
cross-sectional
area A, of said pipe member, wherein A~ is no greater than:
2~ A, x Da/;po
-20-
CA 02460123 2004-03-08
collecting scud gas-liquid mixture, now having microbubhles 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 containm~xxt vessel;
removing, from said bat~om portion of said vessel, said liquid with gas
miero[aubbles
entrained therein at a rate which said micrabubbles enEraiued in said liquid.
rise in said vessel so
as to permit said gas microbubbles rime to react with impurities in said
liquid; and
supplying said liquid-gas mixture to said pige atternber st.ibstantially at a
rate at whiel3
said liquid-gas mixture having gas micrabubbles entrained therein is removed
from the bottom of
said vessel.
I0 Advantageously, the gresexrt ixtvention. in a particular re~neznent of both
of one pf 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 ~:-I DU znierons~ entrained therein is sprayed
outwardly from a pipe
i5 member and captured in a co~tairttrtent vessel, liquid having some: large
~~IOD microns) as well
as small (<lOD micronl gas bubt~Ies (but preferably a pxeponderance Qf small
gas bubbles) is
Collected a said vessel. However, gas bubbles in said liquid which fa-11
vertically down in said
vessel when expelled Pram said aperture tend to fall to various depths in said
containtttent vessel,
before starting to rise in such vessel, depextding on the size o~F the gas
bubble entrained in
surrounding liquid. Specifically. larger ,gas bubbles within the liquid textd
to fall a lesser
distance downwardly in liquid collecting at a bottom pariiQn crf the
containmentlcolleciis~n
vessel than smaller gas buhl~les.
Accordingly, by proper vertical positioning of a liduid-withdrawal tube from
the
containtnent vr~ssel ibis "sorting" of bubbles within the liquid colle~eting
in the bottom portion of
the vessel can be taken into account in. obtaining liquid hav~g gas bulalales
of the lesser (more
dzsirable) smaller diameter. Specifically, gositionirtg of such withdrawal
tube on such vessel at a
position somewhat above a lowermost portion of said vesset and immediately
below a
_ z1 _
CA 02460123 2004-03-08
lowerzn.ost level in said vessel which bubbles of a sire larger than 100
rziicrans initially fall to
'before rising in said vessel, and at a level within said bottom portion af'
said vessel which
bubbles of a sine less than 100 microns i.nitiaily fall to laefore rising in
said vessel, will allow the
withdrawal tube to withdraw fratn said vessel only a gas-Iiquicl mixture
having smaller (ie <140
micron ) pubblas .
Accordingly, in a preferred method of tine present invention taking advantage
of the
above "sorting" principle in order to obtain gas microbubbles of a site less
than 100 mienatis,
such method cau~.prises a method far producing a liquid having gas
microbubbles therein the
majority of wi~ich are of a size less than 10U microns, comprising ilte steps
pf-.
providing gas w said liquid to farm a gasltiquid mixture;
directing said has-litluid mixture into a hollow pipe merttber, said pipe
member baying a
maximum interior width .D, and a maximum exterior width 1.7w said pipe member
situate
proximate an upper portion of a cantaiument vessel and extending into an
interior of said
cantainmeut vessel, said upper portion of said contaituxieni vessel containing
said gas being
under pressure, arid a bottom portion of said containntiem vessel
substantially cantaixung said
liquid;
spraying substantially radially outwardly from said pipe member said
gas~liquid mixture
into said upper pdriion of said contairurient vessel via at least two
apertures in said pipe
member;
and
removing from said bottom pottis~u. c~f said containment vessel, at a position
somewhat
above a lowermost portion of said vessel, said gas-liquid mixture;
_ ?~ _
..,.........._ ._.,...,.. , -.:~.~.ipf bp. ~ ~-. . ~.. ..... ".... .._......
,.,",-"."qqm",.s,..~y~ ,..~~5ii~ Wm,w..,«.x.""",".,.__ ..,...._...,........
._...,...._._,~-,.,.~"".,..........."
CA 02460123 2004-03-08
said position being a position immediately below a loweta~aast level iii said
vessel which
bubbles of a site larger than 140 rnicrans initially fall to before rising in
said vessel, and at a
level within said bottarn portion of said vessel which hobbles of a size less
than i00 micmns
initially fall to beFare rising in said vessel.
In a further ezz~bodirr~ent the invention consists of an apparatus far making
use of the
"sorting" phenametton.
,Accordingly, in such refinement of the apparatus of the present invention,
the
1a containment vessel of the present invention comprises gas-liquid withdrawal
means, such
withd~wal means in catnmunication with an interior of the vessel proximate a
batiQm portion
thereat vessel, adapted tA withdraw a gas-liquid mixture having nticrabu6bles
of entrained gas
therein from said interior of such vessel, such withslr~xwal means situate on
said vessel at a
paslt~an, said posidan beixag at a level an said vessel below a lau~ermast
level within said vessel
I 5 which bubbles of a site larger than 100 rriicrans fall tp before rising in
liquid in said vessel, and
at a level which bula3~les of a size less than lOtl microns fall to before
rising in said vessel.
Brief l~escriptiaa of tb~e l~rawirtgs
~0 The following drawings, sltawing selected euibadiments of the invention,
are non-
limiting and illustratir°e only. ~'or a complete deftnitian. of the
sc:oge of the invertrian, reference
is to be lead to the sumrrrary of the inver~tian and the claims.
Figure 1 shows a front view c~f arse embodiment of the apparatus of the
present inver~tian
25 far creating miczobubbles of gas , said apparatus in the embodiment shown
using a cylindrical
pipe member and a plurality of harixaataily-extending ayliridrieal apertures;
Figure 2 is an enlarged view of area °°A'' of Figure 1;
_ ~3
CA 02460123 2004-03-08
figure 3 is an enlarged view of area "B" of Figure', sharwing i~ detail
circular apertures
farmed ire the pipe member;
Figure 4 is a view of an alternative embodiment of the g~resent invention,
similar to that
shown in higt.tre l, showing utilization of an inclined but substantially
vertical baf#le member;
Figure 5 is ae1 enlarged view of a partiettlar embodiment showing of a pipe
member of
the present inventiax! of circular cross-section, further showing an
embodiment of the pipe
member having horizontally-extending rectangular slots formed i:n such pipe
tz~ember 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
3C-~C;
Figure 58 is a section through the pipe member of Figure 5, taken along plane
Y-Y;
Figure G is an enlarged view of a particular embodirttent shs~wir~g of a pipe
member of
the present invention of Square CraSS-SeGtIO~, further showing an embodiment
of the pipe
member having horizontally-extending rectangular slots fptmed in such pipe
member f4T acting
as apertures to permit the expulsion of a gas-liquid mixture from sixth pipe
member;
Figure ~A is a section through the pipe member of Figure i5, talcen albng
plane X-~;
Figure 7 is an enlarged view of a particular embodiment showing of a pipe
member of
the present invention of triangular gequal sided) cross-section, further
showing an etnbadimertt
of the pipe member having horizantallywextending rectangular slots formed in
such pipe member
for acting as apertures to permit the expulsiazi of a ;as-liquid rnixtare from
such pipe tztember;
p'igure 7A is a section tluaugh the pipe member of Figure 7, taken along plane
X-;
_2q._
CA 02460123 2004-03-08
Figure $ is an enlarged view of a particular embodiment showing of a pipe
meraber of
the present invention of rectangular cross-section, further showing an
emb~iment of the pipe
member having horizontally extending rectangular slots farmed in such pipe
tnertxber far acting
as apertures to permit the expulsion of a gas-liquid mixture from such pipe
member;
Figure 8A is a scetion through the pipe met~ber of Figure 7, taken along plane
X-~
Figure 9 is a side view similar to Figure 1. showing another embodiment of the
apparatus
of the present invention, wherein the apertures far farming the microbubbles
axe situate in a plug
1D member which is itself situated at the extreme lowermost distal ezid of the
plug meruber;
Figu~ rr 1 A is an cnlar,~ed view of area "A" of Figure 9;
Figure II is yet a further side view similar tp Figure l and 9, showing yet
another
embodirrsent of tha apparatus of the present invention, in this case having
circular apertures
situate in the plug rxaember at the extreme ldwermosi end of the pilae member;
Figure ~ 2 is art enlasged view of area "A" of Figure 1 l;
Figure 1~ is an enlarged view of the baffle plate member shown in. Figs. 1,9,
and I I;
Figure I4 is a cross-sectional view of a particular embodiment of the
apparatus of the
present in.ventian which was selected to conduct tests on;
Figure 1S i5 scherrsatic view of additional test apparatus used to test the
operability of the
apparatus and method of the present invention;
Figure 7.b is a table setting out test data obtained. using the test apparatus
of Figure 1~
and 15; and
-25-
CA 02460123 2004-03-08
figure 17 is a graph showing a plat of ap~tuue exit aree~ Ae as a fiittction
of bubble
diameter; such data atstained from data using the test apparatus shown in
Figure 14 and IS; and
.detailed ~escriptinu s~f the ~.uvetteion
Fig, 1 shows arm embodiment of the apparatus 10 of the present invention for
producing
micrabubbles 12 in a liquid l~.
A means 1~ for introducing gas bubbles 20 into such liquid I~ Hawing in pipe 9
is
provided_ Means 1G may ba a verituri , namely a Converging-dive;rgit~g node,
as known in the
1~ aft, having at the canvergirtg portiau an alaerture l~ through which gas,
typically althou,~;h not
always air, is drawn and flows in the form of bubbles 2Q iota the liquid, xo
form a gas-liquid
mixture 2w. Alternatively, and mare typically, meaxts 1f is simply an orifice
to pctrru.t the
injection of gas under pressure into said liquid l~ itt pipe member 12,
resulting in formation of
gas bublsles 2~ within liquid ~.4, which is under a resulting pressure.
2~
The supply 4f gas xnay be from ambient sit, if air is the desired ,gas to be
introduced, as
shown in .Fig. 1, or alterr~uvely may be Pram a pressuaized tanlk a.f gas {not
shown), if sonic
other form of gas (such as Hx or Cue) is desired to be iztiroduced.
25 Gas bubbles 2E1 enuained in such gas-liquid mixture 22 in the above mazu~er
are typically
of a size greater than 1 ~ microns, ar at Ieast a majority of gas bubbles 2Q
entrained in such gas-
liquid mixture 22 are a f a size greater than I4Q microns, at typical ambient
temperature and
pressure (?2° C and I atmosphere).
_?~_
CA 02460123 2004-03-08
One pf the purposes of the apparatus 10 of the present invention is to reduce
the bubble
size of the gas bubbles 2~ within the gas-liquid mixture 22 to a sxxe less
than 10t? ttucrops, and
preferably to a size in The range of 5-Stt 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,
S for the purposes of purifying andlor causing certain entrained substances in
such liquid 14 to
precipitate out of such gas-liquid mixture ~2, thereby ridding such liquid 1~
of such substances.
The gas-liquid mixture 22, having gas bubbles 2fl therein the majority of
which are of a
site greater than 104 microns, is thereafter conveyed typically by means of a
hollow pipe 4r
14 conduit Z4 to an elongate, hallow pipe member 2~, typically although not
necessarily, situate
within a contaiiune~t vessel 4a, as shown in Fig. 1.
pipe member ~4 contains aperture means cousistiul; of a one or more apertures
~~,
extending from an interior ~3 of such pipe member ~4 to an exterior ~7 of pipe
member 24 (see
15 enlarged view of one embodiment of pipe meFaber ~4 sbowxt in Fig- 3,
wherein pipe member 2~
is cylindrical in cxoss-section, having a plurality of cylindrical apertures
therein). Each of
apertures 3Z may be of any geometric shape, but preferably are a~f a
cylindrical shape as shown
in Fig. 3, a cylindrical aperture being the resultant shape that results from
drilling of such
apernue 32 during manufacture using ~ circular Grill bit, cuilling being one
of the easiest means
2~ of forming such apertures 32. teach of said apertuxxes 32 ex#exul
horizAntally outwardly and
substantially perpendicular to a longitudinal axis of the pipe member 24, Pipe
member 2~ is
positioned. substantially vattically, as shown in .Fig. 1, and is adapted to
receive the liquid-gas
raixture 22 and supply same under pressure to aper;ures 32. Each of apertures
32 extend
horizontally outwardly from interior 33 of pipe member 24 to exterior 37 of
pipe metrtber 24.
2S Pipe member 24 further possesses a plug member ?~, situate at a lowermost
distal end thereof far
preventing egress of liquid-gas. mixture 2~ &ottr said pipe trternl~r~ 2~i.
As hereinafter explaixted, the sire tbQth width and cmss-sectional area) of
such apertures
3? is dependent in a preferred embodiment an certain formulae which are
preferably maintained
3Q to allow foTtr~at~C?Fi Of rnicrobul~bles 12 of a desired size, namely less
than 100 microns, and
-27-
CA 02460123 2004-03-08
p~referahly 5-50 microns, when the gaa-liquid mixture ?2 is expelled under
pressure from the pipe
member 24 via apertures 32 .
A containment vessel ~0 is further provided. In a prefwed embodiment,
containment
S vessel. 4Q is an elongate, vertically-extending column, co~gtuvd so as to
receive therewithin
pipe member 24 in an upper portion 42 thereof. Specifically, ixt the
embodiment shown in Fig.
1, containment vessel 4Il is fotxned of a vertical ca»duit ~i~, having
threaded flange members
43 affixed din the preferred embodiment by welding for conduits of weldable
metallic material
and witem such conduits are of a plastic material such as polyvirxyl
chloride(PYG), by an
1 ~D adhesive or a batxding agent such chlaroform~ at each a f a bottom and
top end X4,45 respectively
. Flanges 41,43 are aclapte~l to receive plate members 47,45 at each of skid
top and bottom ends
44,45 which may be bolted to flange members 43 respectively by means pf bolts
57, with an
intervening gasket i;9, so as to form an enclosed vessel ~~.
15 The purpose of vessel 4D is to receive and contain for a tune liquid lei
expelled from sand
apertures 32 at a given level "x" within said vessel 40. The resulting
micmbubbles 12 produced
in the gas-liquid mixture 22 which fall from apertures 22 into vessel 40 may
react in the bottom
portion 41i of vessel 40 with substances within the liquid 14, so as to cause
imgurities to
precipitate out. The remaining (purified) liquid 15 may then be removed froth
vessel 40 via a
20 lower liquid mihdrawal pipe 5l.
Alternatively, or in addition, the vertical length 5rp of the botxottt portion
~+8 of vessel 4Q
may act as a stratificat#on column and take advantage of a "sorting'°
with respect to gas bubbles.
In this regard, arty remairuxrg gas bubbles lei of a relatively large size (ie
in excess of 100
25 microns in size) which uiay 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 wild
tend to fall into
bottom gorhon ~8 of vessel 4(!. .t~awever, larger gas bubbles tend to fall to
or above a level
namely above line "X" as shown in Fig. 1) before begintzbxl; to rise in the
liquid column
contained in the bottom portion of vessel a0 . On the otlser hand, smaller
sized gas bubbles tend
_2g_
CA 02460123 2004-03-08
to fall to a level "Z" ar below such level "Z" before hegictning; to rise
within such liquid, as
shown to Fig. 1.
Accordingly, by positioning withdrawal pipe al at a level below a level "~" to
which
the majority of larger gas bubbles fall, only liquid 1S subsT~ttially having
gas Gobbles of a size
less than 100 micmtts may be oGtained when withdrawn from withdrawal tube 5x.
Such liduid
14, having a majority of gas bul~hles therein of a size less Fhan lU0 microns,
rosy then he
transported vix withdrawal pipe S~ to a further contaixuxtent vessel 52 (not
shown] where such
gas microbubbles entrained in the liquid 14 may then react (or further react)
with substances
1~? within such liquid l~, such as iron bacteria or other undesirable
s:ubstaarCes, so as to render such
substances harmless sir Cause tltetn Y.o pFecipttate Dut of solution, leaving
a purified liquid 15.
Although ii is not necessary 'that vessel 4I! be an enclosed vessel, in the
preferred
embodiiuent it is desirable that vessel gill he an enclAsed vessel, as shown
in Fig, 1. This allows
two advantages to be realized.
Firstly, to improve the fonrtation of gas micmbubbles upon the liquid-gas
mixture ~~
being expelled from aperture msarts within pipe tnetnber 2~i, the side walls
55 of an enclosed
vessel 4A may be used, where the pressure in pipe member ~4 is sufficiently
high, as a vertical
surface against which resuliiu$ jets SG of gas~Iiduic3 rttay impinge against
prior to falling frara
upper portion 42 of vessel 4d to bottom portion 48 of vessel 4~" A depictiozt
of this preferred
embodiment is shown in enlarged view in Fig. 2. 'fhe impaCtio» of the jets Sb
of gas liquid
agaizlst side walls S~ tends to cause larger gas ?~uGbles entraixted in liguid
14 to break into
micrabubbles, thus aiding the formation of gas micrabubbles.
Secondly, the utilixxtiou of an enclosed vessel 40 assists in maintenance of
gas
microbubbles witl;jn liquid 14 in the hottotn portion 48 of vessel 40, as the
vessel 44 may be
maintained under a relative pressure. In this regard, in a preferred
embodiment, rite internal
relative pressure in the upper p4rtion 42 t~f vessel 40 is in the range of ~5
prig or above, with the
3~ pressure of the gas-liquid mixture 22 in pipe ~nemher 24 being in the range
of S prig or higl3et
-29-
CA 02460123 2004-03-08
than the internal relative pressure within vessel 4t1, to permit the gas-
liquid mixture Z2 within
such pipe member 24 to be expelled into upper pardon 42 of vessel 4Q via
apertures 32. The
maintenance of a pressure within vessel 40 less than the supplied pressure
within pipe member
2~ assists in formation of gas bubbles in liquid 14. The maintenance of a
pressure within such
vessel 4(l higher than ambient assists in maintaitiiug babbles of a small sixe
within the bottom
portion of the vessel 44, which is useful ifthe carting feature desc~bed above
is not desired to be
used and instead the b4ttotn gartion ref vessel 4t1 is used as a type of
coutaixunent vessel to allow
reaction of the gas microbuhbles with substances within liquid 14 , as further
explained below.
lfl The embodiment of the apparatus and the method of the present invention
where the
"sorting" of bubbles accardixtg to size is etnplayed and the withdrawal pipe
~i is situated at a
level below level "Z" to withdraw only those gas bubbles the majority of which
have a size less
than 10U microns, is particularly Suited to a continuous as opposed to a batch
process.
specifically, because the liquid which is withdrawn from withdrawal pipe Sl is
st<bstantially
comprised of microbubbles, liquid 14 having such microbubbles entrained
therein may he
continuously withdrawn from vessel 4A far subsequent pxocessing in a reaction
vessel (not
shown ) elsewhere.
Where the bottom portion 4$ of vessel ~0 is itself used as s reacCi4rt vessel
to allow the
txticrobubbles therein to react with substances in such liguid 14, either a
"batch" or a
"continuous" pmcess may be employed. ~pecificatly, where a batch process is
employed,
sufficient gas-iidttid mixture ~2 is discharged through apertur~a ~2 to allow
the liquid-gas
mixture ~2 to rise in vessel 4d to a level "x" approximately one-ltalf to two-
thirds the height of
vessel 4D. A period of time is allowed to pass, namely the period. of time
which it tales for
2S ttticxobubbles of a size leas than 14~ microns to rise from a level at or
below level "Z" (see Fig.
3) to level "X". Thereafter the liquid 35 may be withdrawn fronx vessel 44 by
withdrawal pipe
S1 at a position att such vessel anywhere izttermediate level x and the base
of the vessel 4A, and
preferably at a level close tp level "Z".
_3p_
CA 02460123 2004-03-08
Where a continuous process of treatixig liquid 14 is containment vessel aU is
desired to be
employed, liquid 1~ in the liquid-gas mixture 22 is supplied to the vessel 40
via pipe member ~4
at a rate apprs~xirnaiely equal to a rate at which the liquid iS is withdrawn
from vessel 40 via
withdrawal pipe 51, In addition, the rate of withdrawal of liquid iS (and the
rate of supply of
liquid 14) is adjusted so that at a time when liquid is removed fxom said
bottosrr porti~aa 4$ of
vessel 4A the microbub>xles will have travelled. upwardly a distance tbraugxi
liquid 14
substantially equal to a majority of the depth of liquid 14 an said bottom
portion of said vessel,
namely from approximately level "z" to approximately level "~."_ irl order to
facilitate the
removal of liquid 15 which has been exposed lo micrabubbles for such period of
time, a vertical
1~ baffle plate member bt? may be employed as shown in Fig. 4 to direct the
flow of liquid hxvitig
micrabubbles eutFairsed therein as shown in Fig. 4. In such embodiment
withdrawal tube Sl is
preferably situate close to, but below level "7C", and withdraws liquid 15
which has beers expciaed
to gas microbubbles for the time that it takes such tnicrobubbles afrer
havixag 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
1~ member 40 .frorri level "Z" to level "X".
In a further embodiment, the apparatus 1U 4f the present invention further
includes a
horizontal laaffle plate member ~0 iref Fig. 1 and Fig. 4), positioned
intermediate upper portion
42 and bottom portion 4f of vessel 40, arid above level "x" of liquid I4 in
the vessel 44, so that
24 gas-liquid mixture sprayed from pipe member 2~+ is permitted to pass
throug3x such baffle
member 8fJ when falling to bottom portion 48 of vessel 4t1. $able plate member
go is provided
with a series of orifices ~2 (see Fig. 13 showing enlarged view of hari2antal
baf#le member 8(1)
to permit ,has-liquid mixture 22 to further fall to bottotu pot3ian 48 of
vessel 44. F3aftie plate
mertiber 8t1 further assists in converting gas hu6bles ~0 in gas-liquid
miacture 22 to tnicrobubbles.
Pipe member 24 hawing orre or more apertures 32 thereon may he any ho~Iaw
elongate
tubular member, substantially sytt~rnetric$1 in cross-sectiati. Figures 5, fi,
7, and 8 show tbtu
separate embodiments, where such pipe member 24 is alternatively c~f, but not
limited to, having
a circular, square, triangular, and xectangular cross-sectional area
respectively
-31 -
CA 02460123 2004-03-08
.1n vrc3er for the apertures to best form mi~ct~bubbles, in a prefexxed
embodiment a specific
mathetuatical relationship exists between the interior area of the pipe member
~4, and the
combined exit area Ae of apertures ~~, where such pipe member 24 has a maximum
exterior
width Des and maximurrc interior width Vii. Such relationship between the
combined exit area Ae
of the apertures ~2 and the inlet area Ai of the gipe member 24 is essentially
a functipn of the
thickness of the pipe member {namely the ratio of 1~i to Do) , and is ~.
cie~nite relationship for
symmetrical pipe members 24 of unifatut wall thickness.
Specifically, it has been found experimentally (see examples 1 and ?, below)
axed
confumed by derivatis~n (see summary of invention, above) that for pipe
metxtbers 24 of uniform
wall thiclmess and having a ma.xiuit)m interior width Di and a ttzaximutn
exterior width Do,
where the pipe member 24 has identical moments of inertia about at least two
separate axis in a
plane of cross-section through such pipe tner#tber ~4, that for formation of
tnicrobubbles of gas
in a liquid 14 (ie bubbles of less than 104 micrntts) under conditions of
standard temperaxure and
pressure, Ae can he less than or edual to, but no greater than Ai x I~iIDo
where there exist a
plurality of apertures 32 in pipe member 2$. Where only one aperture 32 exists
in pipe member
~4, such aperture may only have a cross-sectional area no greater than Ai x
DiI2Do.
Figure 5 shows ~ detail view of a pipe member 24 of the present itmentioal,
having a
cixeular arose-section, of maximum x~z~ernal width Di, and maximum exterior
width Do, and
internal area Ai= ~c x Di ~ 1~.. Figure 5 also shows the confiSura#ion of pipe
member 2~ and
apertures ~2 used to deterntine the relationship between inlet arcs Ai and
combined aperture exit
area Ae. Two rectangular slots 90 were formed in pipe member 24, on apposite
sides thereof,
each to a depth of ~~z ~o. 8ach rectangular slot 9p forms an exit wee equal to
r~gapr~ x ~ x pi (see
?5 Fig. 5f3) , so as, in the case of two rectangular slots 94, to form a
combined exit area Ae= 2 x
rr,7apn x '1r ~ f-rl
It was experimentally found tree example 1, below) that the maximum combined
exit
area far at least two err more apertures was Ae can be no greater tYian Ai x
DiIDo where babbles
of a sine less than 1(10 microns are desired.
- 32 -
CA 02460123 2004-03-08
~aviug a raaximum combined exit axes Ae means that the aperture "gap" shown in
Figure 5 will be a maximum. Accordingly, whzre maximum throughput of gas-
liquid mixture 22
is required through apparatus 10 of the present mventi~azt, the maximum
combined aperture exit
area Ae is used. Where Ae ~Ai x lSi/Do, setting this equal to 2 x ;;ap x n x
Ai and salving for
the gap, this means the "gap" can only be ~Ai x L?ilpQJl2 x ~ x Iii which
stated more simply is
equal to Ailn x Do., where 7t x lrlo is the outer circumference of pipe member
~4.
Accordingly, in a further embodiment, a further restriction exist on the width
of the
14 ''gap" shøwn in Fig. .~, namely that the "gap" be no greater than the
quotient of Ai and the outer
circumference of pipe member 34, namely n x lots. Stated ~ other terms, to
form bubbles in the
extruded jets S6 of gas..liquid mixture 22 urhich is expelled Exam rectangular
slots 90 camgris~rig
apertures 32, such apertures 32 raay only be of a txcaximum vertical depth
("g.ap") of .AiIC,
finely ~ 1t x Di a I4 JI ~ ~ x poJ (ie I1i 214 .Do ). Thus where the maximum
aperture distance (ie
1S the maximum "gap") of l~i Z !4 Do is used, so as to be required to drill
the fewest slots or
apertures 3~, the maximum "gap" of aperture is typically used, na~n.ely
Ai~circum~'erence o f pipe
member 24, which for a cylindrical pipe member 24 is simply Di z !4 'po.
As may be seen froxri Figure 5, pipe member 24 possesses unifarEn wall
thiclmess (ie Do
20 less lei is always a cbnstant). Moreover, as may be seen from Fig. 5A, such
pipe mexttber 24
possesses ax least two identical morr~enls of inertia in a plane of cross-
section, namely the
moments of inertia about axis xt and Iz are identical, namely n16~ [Dog - lai
~
The same relationship applies in the case of pipe memba;r 2~ of square crass-
sectional
25 area Ai, as shown in Figs b and 5A, of uniform iluc~ess "t". Tlt.us for two
rectangular slots qa
within square pipe member 24, as may be seen Pram Fig. GA, ~e corrtbined
aperture exit area Ae
may be calculated as Z x "gap" x. ~I12 Di -r ~1i t l~ ,pi ]. ~Nhere the
maxitnutn "gap" is
detexmitted by the surprisingly- found relationship of Ai!(circuxaference of
pipe), namely Ail4
f.?a , then A.e thus becomes 2 x Ai/4Do x [ 2Ai~= Ai x Bili~a. Again, a square
pipe metnher 24
- 33
_. . ~__._.. _ _,. " ~~~,.n~,~~,~~, ~._ .. ..._ .__ _ .
CA 02460123 2004-03-08
has identical moments of inertia abQUt two identical axis I1 and Ia; in a
plate of crass-section,
namely It = Iz = [Dap - Di° ~Il~
The same relationship applies in the case pf pipe member ~4 of triangular
(equal sided)
S cross-sectional area Ai, as may be seen from. Fig. 7 and 7A. ~'hus for rwo
rectan~xlar slots 90
within equilateral triangular pipe member 2~i of depth equal to f2 Do on one
side as shown in
Fig. 7A, as may be seen from Fig. ~A, the cotubined aperture exit area znay be
calculated as 2 x
"gap" x ~11~ Di t Did. Where the maximum "gap" is detertnixted b;y the
surprising relationship of
AiIC, which en the case of an equilateral triangle of interior maximum width
Di equals Ail3lao,
then Ae= 2 x gap x 3!2 l:~i= 2 x Ail3Do x 3/? Dl , which reduces again to
Ae=Ai x Dil~o. Again,
as may be seen from Figure 7A, an equilateral sided txiat~gulax' pipe member
24 has identical
moments of inertia about two axis h and Iz in a plane of crass-section,
rtapnely It = Iz .
t5 For a symmetrical pipe member 24 which does oat have identical morrtents of
inertia
about two axis irt a plane of cross-section, such as a rectangular pipe member
24 as spawn itt Fig.
8 and 8A (namely h ~I2 ~. the derived relationship of Ae=Ai x DiIDo does not
apply.
T~owever, in the case of a rectangular pipe rrtember ::~ having maximum
exterior
dimension 15t , rrtinimum exterior dimension Da , maximum interior dimension
D~ , and
mittitxtum interior diFrtension D~ , as shown in Fi,g_ 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 [ %'~
?~4-r D3 -r %z D4 ~. Agaixt,
using the surprising result that the maximum " gap" equals AiIC, namely Ail[2x
(Dz+ .D,)~, then
Ac = 2 x gap x [p3+ Da ] = Ai x [D~t D3 ~! [D2+ ~1t ~-
With respect to the location of the apertures 32 of the present invention,
from which gas-
liquid anixture 23 is expelled, aperGttres 32 may be formed wirllin pipe
member 24, as shown in
Fig. 1 attd particularly in enl$rged view shown in Figs. 3 and Figs. 4 throw 8
inclusive.
Alternatively, apertures 32 rnay be formed in plug member 2~.. Fig. 9, and
Fig. 10 showing
3~3 enlarged detail, illustrate formation of a pair of rectangular slots 9f1
which serve as apertures 32
-~4-
CA 02460123 2004-03-08
in plug means 25. Fig. 11, and Fig. 12 shaving enlarged detail , :illustrate
the ~employrrtent of a
pluralixy of cylindrical apcrlures 32 in plug txtember 2S. 4f course, as in
Tlre case where the
apertures 32 are situate within the pipe >:aember 24 itself, such apertures
may he of any
geometrical cross-sectional area, wish circular cross-sectional area being
preferred due to the
S ease in creating cylindrical apemtres 32 having circular cross-sectional
area, ouch as by drilling
with circular drill bits.
~x~r~tpte 1
A series of seventeen various-sited apparatus 14 were can5trueted in
accordance with one
of the embodiments o f the invention as contemplated ?tereirt, namely that
etnbadiment shown in
Fig, I, having a pair of apertures 3z in the form of horizontally attending
recta~agular slots 90,
as shown in Fig. ~.
l3ach of the aforesaid seventeen test units comprised a shell (referrs~d to
above and below
as a vessel 40~, having itt an upper portion 42 thereof a downwardly
extending, substantially
ve~ical cylindrical pipe tnernber 2~ s~f various Di and Do, ranging from
nominal pipe nominal
diameters of O.St? inches ur I~.O inches.
Each of pipe members 24 for the various fast units had a ps~ir of rectatagular
pppased
2Q slots 90 therein, as shawu. in Fig. S. xhe exit area Ae for the pair of
slots was set as the
ma~:imam., in accordance with the requirement Ae {maxi = Ai x Dillao. »ecause
the width of
each of the slats 9I1 was the width Di of rah pipe member 24 as shown in Fig.
5, the vertical
dePTh tie "gap") of each of the slats 9Q was accordingly thereby pry.-
detertatined dire to the
requirement that A~A.i x DiIDo, and was gap~~,~",a= Ai!{ou;er circumference of
pipe member
Z4).
Vessels 4p of var;ous notxrinal diameter sizes were used arid matched. with
correspondi>xg
pipe members 24, with the vessel 4A having a nominal diameter of approximately
six times the
pipe lnenzber 24 nnminlal diameter . This resulted in a thatching of vessels
4Q with pipe nzenlbers
_3g_
CA 02460123 2005-02-25
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.
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 sizf; greater than 100 microns therein the majority
of which were of a
range of size between about 100~.m to 3mm, and under a pressure slightly
exceeding 20 psig,
was provided to pipe member 24, and sprayed into an upper portion of vessel 40
via rectangul~~r
slots 90, such upper portion of the vessel containing gas, under a pressure of
approximately 20
psig, which uses slightly less than the supplied pressure due to the pressure
drop across the
aperture(s), and a lower portion of said vessel containing water having
microbubbles therein.
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, which was then provided
in a holding
tank (not shown) at ambient atmospheric pressure.
In all seventeen instances for the devices tested, microbubbles were formed in
vessel 40
over each of the four volumetric flow rates, of dimensions less than 100
microns.
-36-
CA 02460123 2005-09-15
Example 2
Purpose
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.
~pa~atus
Apparatus of the type shown in Fig. 14 was selected, and in particular an
apparatus of Fig. 14 having the dimensions for inlet pipe member OD and ID and
(upper)
impaction pipe length, as well as shell (vessel) height and diameter.
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
-37-
CA 02460123 2004-03-08
10b. Additional piping 10$ pernaittecl supply , via a globe valve 1.10 and
venturi nozzle 11~ to
pipe member 2~ of apparatus 10. Water exiting vessel ~p of apparatus 1 Q
passed through a flow
meter 115 and pressure gauge 117, and then through a globe valve :t 18 to
Plexiglas tank 100.
Procedure
pipe mexrtbers 2~ ware created, haul g horizar~tall~e~tending cylindrical
apertures ~2,
of diameter, number, and comlained exit area Ae as recorded in Fi~,~re 1G.
l0 Each coc~ribination of bole (aperture) size and exit area was tested with
the same standard
procedure set out below. Each test was run under the same caxu3itians of back.
pressuFS (i.e.
pressure of gas is the upper portion of vessel ~0, narxtely appro~ciirtately
20 psi), Flow rate, water
volume, water temperature, and pressttxe dz~ap across the Venturi nozzhe. The
same apparatus 10
was used for all the tests, and pipe iuemher 2a was chaxrged between rues.
lvleasurir~g the rise of the bubbles against time permitted determina.tian the
size of the
average bubble in the tank.
~ The apparatus 10 was connected to the Plexiglas pump x.00 and pump X06.;
~ Valve 1 i8 from tanl:100 was opened tn allow equilibrium level between tanla
1011
and vessel 4A of apparatus 10;
~ Pump lOG was started and allowed to run until constant level was achieved in
vessel
~40 of apparatus d0 ;
~ Valve 130 couttnlling claw through venturi nnz2le 1I2 was adjusted to create
a 20
psi drop across the nozzle X12 ;
~ The back press~ire ozy vessel 40, namely the pressure of the gas itt upper
portion of
vessel 40, was then adjusted to 20 psi;
~ The apparatt 10 and test equipment was lei to trot for 3.~ minutes;
~ Pump lilt was turned o#fand valve 118 between vessel 44 and tank 1i10 was
closed;
_~g_
CA 02460123 2004-03-08
~ Once a clear view at the bottom to the rear of the tank 11?~ was established
huhble rise
was monitored and recorded at the given time intervals;
~ Once tank ~fHa became clear ofbubbles the tap ofves:~el 4I! was removed and
pipe
member 24 was changed t4 a pipe member having differing cumber and for
diameter
pf apertures;
The above procedure was xepeated far pipe members 34 having agertures 32 of
various
rzeunber andlar diameter, to determine the effect of area and hale size ors
the vessel's
perforrtiatice.
1~ 'I've results afthe measurements, and. resulting calc~latiaus, are compiled
in Table I6.
C~lculatian~
The design uses the formula
Egu.1
_ ~ x~7~, ~
~''' 4
where: A;=ix~.let area
1~, = inside diameter afpipe
This forxxl~a defines the inlet area of pipe on the vessel 40. The inlet area
Ai is used. to
determine the gap size or tnaxixnutu hale dimension.
Eclu.~
Gap_~ ~''oo
where: Gap = hale dimension or Gap size
Al= izilet area
~5 ~p = outside diameter of pipe;
This formula defines the maximum length of one afthe holes°
damertsians. The
maximum combined aperture exit area Ae is determined usixig the pipes°
dimensions in the
following formula
-39-
CA 02460123 2004-03-08
Eqa.3
x. ~ pi 3
A a = pi ~ n x Gad
a
W114Ie: Aa'~1"laXil'riltlxl exit area
Di ~ i.x~side diameter of pipe
Do = outside diameter of pipe
This formula defines the zrzaxi~lum area: that will produce the desired
micrabubbles. bait
areas less than this value are capable of pro~.ucing the micrabubbles whereas
any area greater
than this does nQt produce bubbles t#tat are cuff ciexttly small. Both the
hole site arid exit area are
parameters that effect ibe size of the bubbles that are produced by the
vessei_
la
Using Stokes 1'raw the si2.e of the bubbles produced is determined by the iise
velocity of tl:cese bubbles. Stones Law states
Eqn.4
3 tRa -
1~ ~.~N
whew: v = velocity of bubble rise
g = gravitational cqnstaxit
Fw~ pa ~ deilsily Qf wafer and air
~, = viscosity of fluid
2Q )~ _ diameter ef has bubble i~z fluid
each of the experimental rues produced data which appear iri Figure 16. >rach
experimental run is also accompanied by a corresppudirig hole diaxrteter,
cumber ofholes acccl
25 exlt area.
Tirrie and distance traveled were used to calculate the rise velocity.
.Eqii.S
- ~a -
CA 02460123 2005-12-13
where D = diameter (cm)
v = velocity (cm/s)
~, = viscosity of water (Poise) = 0.0112 P
g = gravitational constant = 981 cm/s2
pW = density of water = 0.99913 g/cm3 @ 15°C
pa = density of air = 1.239 mg/cm3 @ 15°C
The number of holes, the hole diameter and the resulting exit area were
determined using
the following equation.
Eqn.7
Ae= NH'' DA24
where: A.e = exit area
NH = number of holes
DA = hole diameter
Sample Calculations
The first calculation needed was to determine the maximum exit area
D; = 0. 824 Do =1. 05 Ae= '~xD' 3
4 x Da
~ = 0 . 418487 in2
The following calculations are those used to determine the exit area at a
given hole size
and number.
NH=21; Dia=532 ~~ P~=NHXD,~2 X 7f
4
1~=0.4026inZ
-41 -
CA 02460123 2005-02-25
D;= 0.824 Do=1..05 ~_ ~xD~3
4 x Do
~ - 0 . 4184 8 7 in2
The following calculations are those used to determine the exit area at a
given hole size;
and number.
NH= 21; Dia=532 ,~ ~- ~xDA2 X 7~
4
P~=0 . 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; tl=5~ tZ=lOt v= ~
to - t1
v-_ 0.2~m~s
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 inz , the
bubble size was
greater than 50 microns. (ref. those tests where bubble diameter was 68.26,
53.2, 68.45, 53.6,
58.71, 65.60 and 82.44~n respectively).
-42-
CA 02460123 2004-03-08
As may also be seen froze Figure 1 f>, where the aperture dia~Erteter was
:'eater than
Ail(auter circumference of pipe member ZA), namely greater than 0. Z 61
inches, the average
bubble size was ~reateF t#~ 50 tnicrans.
Where the combined aperture exit area Ae was less than or approxiu~ately equal
to Ai x
lail:Da, namely less than or equal w x.41$487 in'' and the aperture diameter
less than or equal to
Ail(auter circumference of pipe merriber 24), bubble site was less than 5~
microns.
Figure 1'7 is a graph prepared &ortt that illustrates a relationship between
combined exit
area Ae and bubble diameter. The average diameter front the first ~0 seconds
(in most cases)
was platted agains; the exit area. Figure 17 demo~stra~tes a def ned
relationship betureen ttxe rwo
variables that occurs while the hale diaxne#er is held constar#t. '1'his
,gives evidence of'the
ia#luence of exit area an bubble size. The larger the exit area the larger the
siie of the bubbles
prr~c#wGed.
1S
Figure 17 has an area that is below and to the right of the doted line. such
represents a
design co~guratian afthe apparatus 1d of the present invention which produces
micrnbubbl$s in the desired range al less than SQ microns.
2Q
:~
Although the disclosure describes and illustrates selected emlsodiments of the
invention,
it is to be understQad that the iitve~tian 1s Rt~t limited to these pat~ieular
selected embodiments.
2S Many variations and modiftcatiQns will now occttx to those skilled in the
art . Far a complete
definition of the scope of the invetttian, reference is tp further be had to
the summary of the
invention and in particular the appended claims.
- ~3 -
