Title:
METHOD FOR INDUCING AGGLOMERATION OF PARTICULATE IN A FLUID FLOW
United States Patent 3755122


Abstract:
A method of facilitating removal of particulate from a fluid stream whereby individual particles of the particulate are agglomerated to form larger and therefore more easily removable particles. The particulate is passed through a zone which contains electric charging regions disposed at locations transversely spaced across the fluid stream and adapted to charge the particulate. Charge regions are alternately charged across the stream; that is, contiguous charge regions contain oppositely polarized electric fields, thereby to create transverse to the stream small regions where the particulate is charged positive, say, immediately adjacent to regions where it is charged negative. The thusly charged particles are then mixed to bring the oppositely charged particles into close proximity, one with the other, and small particles of the particulate agglomerate upon larger particles. The agglomerated particulate is then precipitated or otherwise removed from the fluid.



Inventors:
Melcher, James R. (Lexington, MA)
Sachar, Kenneth S. (Cambridge, MA)
Application Number:
05/109615
Publication Date:
08/28/1973
Filing Date:
01/25/1971
Assignee:
MASSACHUSETTS INST OF TECHNOLOGY
Primary Class:
Other Classes:
95/57, 95/64, 95/70, 204/571
International Classes:
B03C3/66; B03C5/00; (IPC1-7): B03C5/00; C02B1/78
Field of Search:
204/186-191,302-308 55
View Patent Images:
US Patent References:



Foreign References:
GB846522A
GB464192A
GB183768A
JP45028480A
Primary Examiner:
Tufariello T.
Claims:
What is claimed is

1. A method of electrically inducing agglomeration of particulate in a fluid flow, that comprises, charging particles of the particulate in some regions of the fluid positive and charging other particles in other regions in the fluid negative, mixing the charged particles to cause oppositely charged particles to mingle sufficiently to provide electric interaction therebetween, and agglomerating particles of the particulate upon other particles thereof, and feeding back at least some of the agglomerated particles into the fluid flow for subsequent agglomeration with smaller particles therein.

2. A method as set forth in claim 1 wherein a portion of the fluid containing the last mentioned agglomerated particles is fed back into the fluid flow for said subsequent agglomeration.

3. A method as claimed in claim 1 in which the mixing is enhanced by temporally alternating polarity of the charge regions thereby to achieve a homogeneous system of charged particles, through cross-streaming of the fluid.

4. A method as claimed in claim 1 in which the regions are alternately maintained at positive and negative DC potentials to enhance said mixing by cross-streaming of the fluid and thereby achieve a homogeneous system of charged particles.

5. A method as claimed in claim 1 in which mixing is enhanced by creating turbulence in the fluid thereby to achieve a homogeneous system of charged particles.

Description:
The present invention relates to precipitator apparatus wherein particulate in a fluid flow is induced to agglomerate by virtue of electric forces between particles carried by the fluid stream.

In a book entitled "Industrial Electrostatic Precipitation" by Harry J. White, published by Addison-Wesley Publishing Company, Inc., in 1963, the author discusses electrostatic precipitators for removal of suspended particulate from gases. It is noted in the book, and is discussed in detail hereinafter, that such precipitators do not remove particulate below certain sizes. This holds true for other types of particle removers (e.g., centrifuges and scrubbers), as well. Accordingly a principal object of the present invention is to provide means for reducing the population of small particles by increasing the average size of particulate in a fluid flow.

A further object is to provide a method and a means for effecting electrical attraction between the individual particles of the particulate in the fluid, thereby to cause them to unite to form larger particles.

A still further object is to provide a method and means for creating a zone in the fluid stream wherein there are positively charged particles mingled or intermixed with negatively charged particles, to allow agglomeration of small particles of the particulate upon larger particles thereof.

These and other objects are evident in the following description of the invention and are particularly delineated in the appended claims.

The objects of the invention are attained by a method of electrically inducing agglomeration of particulate in a fluid flow that comprises charging adjacent transversely spaced regions, in a pattern alternately positive and negative, thereby to charge particles in such adjacent regions respectively positive and negative. The particulate, once charged, moves out of the charging region, thereafter being mixed to cause oppositely charged particles to mingle sufficiently to provide electric interaction therebetween. The electric interaction agglomerates small particles of the particulate upon larger particles thereof. In this way, the size of the particles in the particulate is increased to facilitate removal thereof from the fluid and to make possible removal of the very small particles which are not removable at all using most commercial removal systems.

The invention is discussed herein upon reference to the accompanying drawing, in which:

FIG. 1 is a system diagram in block diagram form, embodying the concepts of the present invention;

FIG. 2 is a partial sketch, partly cut away, and shows a portion of the system of FIG. 1, particularly to illustrate in simplified form a charging zone wherein particles in a fluid flow are provided with positive and negative electric charges, a mixing zone, and an agglomerating zone;

FIG. 3 is a view taken upon the line 3--3 in FIG. 2 looking in the direction of the arrows;

FIG. 4 is a schematic circuit diagram of a simple electric circuit for use in connection with the charging zone of FIG. 2;

FIG. 5 is a schematic representation of two of the charging electrodes shown in FIG. 2 to illustrate electric charge distribution about the electrodes in the charging zone;

FIG. 6 is a modification of the electrode array shown in FIG. 2 and shows an electrode array or matrix wherein short charging electrodes are oriented parallel to the fluid flow, rather than orthogonal thereto as shown in FIG. 2;

FIG. 7A shows the natural size distribution of particulate in a typical dirty gas and FIG. 7B shows a more desirable distribution for particulate removal purposes;

FIG. 8 shows, schematically, a single electrostatic agglomerating stage embodying the present inventive concept;

FIG. 9 shows a vortex sheet and charge distribution emanating from a single wire electrode in the charging zone of FIG. 8, the wire being driven by a DC or a sinusoidal AC voltage;

FIG. 10 shows charge distribution at one instant for superposition of vortices from several of the wires shown in FIG. 8;

FIGS. 11A and 11B are discrete spectrum approximations used to break integral-differential equations into a system of coupled differential equations representing families of particles of the particulate;

FIG. 12 is an agglomerating zone or section zone or section, performance characterized by spatial distribution of two particles families injected at x =0 in FIG. 8 with particle densities [n1 (0), n2 (0)] and charges per particle [q1 (0), q2 (0)], and the associated two-family distribution function;

FIG. 13 shows the effect of multi-staging the single stage shown in FIG. 8;

FIG. 14 shows, schematically, a feedback system whereby some particles of a multi-stage agglomerator are fed back from the output to the input thereof; and

FIGS. 15A and 15B show typical mass distribution for fly ash from combusted pulverized coal and a discrete spectrum approximation thereto.

Before proceeding with a detailed discussion of the underlying principles involved in the present inventive concept, there follows in the next few paragraphs a brief preliminary description of the apparatus involved, particular reference being made to FIGS. 1-6 of the drawing. In the discussion, the term "particulate" is used to define the overall collection of material in a fluid flow, and "particle" is used to define the individual elements of said material. The term "fluid" embraces both gas and particular liquids; however, the largest part of the discussion relates to gas, such as flu gases and the like.

Turning now to the drawing, apparatus is shown generally at 101 in FIG. 2 for inducing agglomeration of particulate in a fluid flow. The apparatus 101 includes a charging zone 2 that includes an array of electrodes comprising electrodes 5, 5', 5" and 5"'. A source of DC electric potential 11 in FIG. 4 is connected to render the electrodes 5 and 5" positive, and a source of DC electric potential 12 is connected to render the electrodes 5' and 5" negative. (As hereinafter discussed, the voltage sources 11 and 12 can be AC, in which event the indicated polarities in FIG. 4 are momentary in nature.) Thus, adjacent electrodes as, for example, the electrodes 5 and 5', are connected to the potential source in such fashion as to apply alternately positive and negative electric potential at any instant of time thereto; i.e., the electrodes 5 to 5'" are alternately positive and negative in space, the electrode source 5 being positive in the illustrative example, the electrode 5' negative, the electrode 5" positive, etc. In this way, as the particles designated 10 of the particulate flow in the longitudinal or x direction in FIG. 2 past adjacent charged regions (e.g., the positively charged region designated 14 and the negatively charged region designated 15 around electrodes 5 and 5', respectively, in FIG. 5), the particles take on the charge of the particular region through which each passes. As shown in FIG. 5, the particles designated 10' which have passed through the positive polarity region 14 are positively charged, and the particles designated 10" which passed through the adjacent or contiguous, laterally displaced, negative polarity region 15, are negatively charged. The charged particles flow into a mixing zone 3 where, as later explained with particular reference to FIG. 10, they are mixed to cause oppositely charged particles 10 to mingle sufficiently to provide electric interaction therebetween. The particles 10 then pass into an agglomerating zone 3, to allow precipitation of the small particles 10' in FIG. 5 upon the larger particles 10". In fact, the zones 3 and 4 really are one drift zone in which, first, mixing predominates and then agglomeration predominates. Following agglomeration, the particulate may be precipitated by electrostatic precipitator means, by scrubbing, in a centrifuge, or by some other means applicable to removing large particles, the alternate means being designated 6 in FIG. 1; and the fluid thereafter can be discharged. In FIG. 1 there is also shown a source of particulate, entrained in the fluid, and a source of electric potential 7; the latter may be connected to an array of electrodes in the manner before discussed. The electrodes 5, 5', etc. can be strung in the y-direction shown in FIG. 3, to provide contiguous regions 14, 15, 22, and 23, transversely spaced (i.e., in the z-direction), in which the electric field spatially alternates from positive to negative potential across the space in the z-direction. The field may, however, be temporally alternating in a periodic fashion or static. The wires 5-5'" are secured to the inner walls of a conductive chamber or conduit designated 16 by insulators 9, 9', 9", and 9'" on the left side and insultors 8, 8', 8", and 8'" on the right side, respectively, or the chamber 16 can itself be insulating. The adjacent electrodes may be shielded from one another by a shield 18 in FIG. 4, which is grounded at G. The electrodes may be oriented orthogonal to the fluid stream, as shown in FIG. 2, or they may be short electrodes oriented parallel to the stream, as shown at 50, 50', 50", 50"' and 50"" in FIG. 6, the latter being laterally separated in the 2- y plane, again to provide areas of alternate polarity at laterally separated regions, as shown. Turbulence means 3' may be provided.

There now follows a more detailed explanation of the invention. Small particles in a gas stream are typically the last to be removed from the flowing gas in a conventional precipitator. Among other factors contributing to this phenomenon is the relatively low mobility of small particles. This can be illustrated by a simple but useful model in which particle precipitation to the walls of a tube or conduit having cross-sectional area A and precipitating perimeter S is considered. If there are n particles per unit volume of the particulate to be collected, and the electrically-induced radial velocity at the precipitation wall is taken as w(the product of the particulate mobility b and the radial electric field intensity at the wall), then in distance dx, there is a change in particle density dn given by the expression for steady-state precipitation

AUdn = - Swndx , (1)

where U is the mean (of the turbulent) flow velocity.

With the assumption that w is independent of x, and hence not influenced by n, for example, it can be seen from Eq. (1) that the particle density decays with distance at a rate typified by the decay length ln

ln ≡ UA/Sw (2)

The smaller w, the greater the decay length ln, and therefore the greater the tube length required to achieve a given removal of the particulate.

The particle conductivity is also a problem in a conventional device, because the charge precipitated with the particles on the walls fails to leak away if the particles are highly insulating. The resulting space-charge-induced contribution to the electric field tends to cancel the volume field, and hence cut off the precipitation.

For purposes of discussion, suppose that a size distribution function for the particulate is defined by f(r,a,t), where r is the position in space, a is the particle "radius," and t is the time. The number density of particles in the radius range a to a +da at the position r, and time t is:

f(a) da particles/unit volume. (3)

Typically, the particle distribution function might depend on size as sketched in FIGS. 7A and 7B. An object of the present invention is to describe a device which tends to attenuate the particle population at low radii by achieving attachment of the particles to larger ones. Hence, the distribution function is skewed toward the higher radii shown in FIG. 7B from the distribution in FIG. 7A.

Note that the decrease in numbers at low a could be dramatic without much of an increase in f at large radii: the attachment of a large number of small particles to a larger particle would result in relatively little shift to the right in the larger particle range.

Particles themselves can be collection sites for smaller particles, much as the precipitator electrodes are conventionally the collection sites. In such a device, the larger particles are essential, hence must not be precipitated. By contrast with the conventional precipitation approach, wherein the small particles are the last to be removed, here the smallest particles are reduced in population first. Hence, the device agglomerates small particles onto larger ones as a conditioning process, prior to filtration by conventional techniques: electrostatic precipitators, cyclones, etc.

Fundamentally, the particle surfaces replace the collection electrode surfaces, and a decay length analogous to that given by Eq. (2) could be defined. If the collection particles (having radius R, number density N, and charge such that their surface electric field is Ep) are thought of as being sites tantamount to removal of the particulate (having density n and mobility b), then the particulate collected by a single collecting particle per unit time is 4πR2 bEp n and NAdx times this quantity is the total particulate number collected in the distance dx. Instead of Eq. (1), the following expression obtains:

dn =- ndx/lp ; lp = (U/4πR2 NbEp) . (4)

A test of the advantages inherent in using the particles as collection sites rather than walls is made by comparing lp and lw. If Ew is defined as the electric field at the wall of the conventional precipitator, then w =bEw, and the ratio of collection lengths is

lp/ lw = [(S/A)/4πR2 N] (EW /Ep). (5)

The surface-to-volume ratio of the conventional precipitator collection channel is S/A. Becuase 4πR2 N is the surface-to-volume ratio of the collecting particles, it can be seen from Eq. (5) that any advantage obtained from using particles as collection sites comes from having a high relative surface-to-volume ratio. Note, however, that there is an additional advantage if the collecting field Ep can be made large compared to that practical in a conventional precipitator collection channel.

Although the simple model resulting in Eq. (5) gives no clue as to how the particles are to be used effectively as collection sites, it does illustrate that a new type of scaling is introduced. The collection of ultra-small particles takes place in a region occupied by the system of particles; no electrodes are required. But to be efficient, a population of collecting sites must be maintained. Large sized particles are desirable, and should not be removed until after the small radii part of the particulate has been collected.

The mixture of large and small particles (the dirty gas) is shown in FIG. 8 entering the single stage or section 101 from the left. In the charging zone 2 of the section 101, all sizes are charged in a manner that insures oppositely charged particles distributed throughout the size range. This is done in one of two ways by means of corona sources: (a) the corona wires are driven by alternating voltage, so that they charge particles in their vicinity positively and negatively as they stream by. The result is a traveling wave of charge immediately following a given wire. The homogeneous system of charged particles is achieved by mixing in the zone 3 just downstream; wires are driven alternately out of phase, so that mixing is augmented by cross-streaming of gas between regions downstream of neighboring charging wires; (b) wires are alternately maintained at positive and negative DC potentials. Thus, a stream of particles having the same sign of charge emanates from a given wire, but is mixed with the streams from the oppositely charged neighbors as the gas passes through the mixing region.

Once the particles have become mixed -- and hence essentially neutral conditions are obtained at the macroscale -- the agglomeration process caused by relative motions of the particles at the microscale takes place. For convenience, this process can be envisioned as occurring in the agglomerating region 4 following the mixing region 3 shown in FIG. 8. Actually, both mixing and agglomeration should occur in a distributed fashion throughout these regions. The mixing predominates at first, the agglomeration later. The regions are not distinguished by any electrode structures, but rather are simply drift zones occupied by the flowing dirty gas. It is this lack of components that makes the agglomerating mechanism proposed here an attractive one.

In the following paragraphs, design considerations are discussed for each of the regimes shown in FIG. 8, so as to answer the important questions: How much charge per particle can be obtained in the charging section? What length of mixing region is required and how does that depend on the construction of the charging grid? and, What length of agglomeration section is required to achieve a given clearance of small particles from the gas?

The charging mechanism in the immediate vicinity of the charging electrodes is essentially of the conventional type. As mentioned before, ions generated by corona discharge on the wires in the charging zone 2 drift through the region (e.g., 14, 15, 22 and 23) traversed by the particles, and hence charge the particles, either diffusively or by impact. The particles having sizes greater than about 0.5 μm are charged by impact, while those that are smaller are charged by diffusion.

In fact, other means of charging might be employed, and the agglomeration mechanism would still be effective. For example, the collection particles could be liquid drops, and then an optional mode of charging would be to use charge induction as the particles are formed, or to use condensation on charge sites.

An estimate of the agglomerator performance requires the dependence of particle charge on particle radius, a. If it is assumed that the effective charging field in the corona region is Eo, then an impact charging model leads to a charge-per-particle that saturates at the value

q(a) = 12 πε0 a2 Eo . (6)

Hence, with the assumption that Eo is set by the charging section arrangement and voltage, Eq. (6) gives the charge dependence on radius at the inlet to the mixing region. Note that once the particles have been mixed, there is no macroscopic field. The effective collection field is that at the particle surface. For the charge given by Eq. (6), that field is simply

Ep = [ q(r,a,t)/4πεo a2 ]; q(rc a, t) = 12 πεo a2 Eo . (7)

where rc signifies the position of the charging saturation. In what follows, it is assumed that the mixing zone 3 is crossed by the particles without decay of this saturation charge, so that rc is the plane x + 0 at the inlet of the agglomerating section. Any conglomeration in the mixing zone would tend to increase the effectiveness of the device. The following might be considered a worst-case analysis in that respect.

If the gas stream is operated at a large enough Reynolds' number (Re = Ud/υ > 50, where d is the wire diameter and υ is the kinematic viscosity of the fluid), the alternately positive and negative vortices will tend to mix the fluid to a certain degree. In the case that the wire voltages are driven sinusoidally at line frequency, the distance downstream over which the charge changes sign is considerably larger than the scale of eddies. For a 10 m/sec. flow, the former will be λ = U/f = 0.167 m, and for a wire with 10-3 m diameter, the latter will be on the order of a few millimeters. Thus, this mechanism alone will not produce a zero net charge distribution.

Consider the fact, though, that the width of the wake increases in proportion to √x, where x is the downstream distance from a wire. That is, b/d =√x/d where d is the wire diameter and b is the wake width. The wakes from the two neighboring wires will intersect each other when x = xo such that b = D, with D the wire spacing. Since the voltages of the neighboring wires will be 180° out of phase, with either AC or DC excitation, the mixing initiated at this point should tend to decrease the net charge distribution. By the time that the flow reaches x = 10xo, the mixing nears completion. That is, the flow approaches net charge neutrality at a given point viewed on the scale of the most dilute particles. Thus, for d = 10-3 m and D = 10-2 m (see FIG. 10), the required mixing length xc is

xc = 10xo = 10(b2 /d 2 d) = 10 [(10-2 ) 2] / 10-3 = 1 m

The latter figure should be considered an upper bound on the mixing length, since the flow is considered to be initially laminar when incident on the wires. Typically, it would be turbulent before reaching the charging zone 2. Other means to create turbulence and mixing may be used, as well.

As outlined above, the purpose of the agglomerating zone 4 is to achieve an attentuation of the low particle size densities, as characterized by the shift in distribution function f(a) sketched in FIGS. 7A and 7B. Hence, it is desirable to establish expressions that describe the distribution of f(r,a,t). Because the charge per particle is also varying in the agglomerating process, a description of q(r,a,t) is also required. To this end, there is stated below physical laws accounting for the migration of particles and the conservation of their associated charges.

Thus, a means velocity for particles v, which for the present purposes is the gas velocity, is defined. Assume that the electrical forces have a negligible effect on the gas motion, so that v is a function of space and time determined by the flow characteristics alone. More properly, when conservation of a certain size particle with a certain sign of charge is applied to a given volume, the effects of both turbulence and the inter-particle electric fields average to zero. Taking this function as known in describing the agglomerating zone, then conservation of the number of particles in a size range Δa is accounted for by

-δfΔa/δt = ∇. (f av) + SΔa . (8)

Here, SΔa is the number of particles per unit volume per second lost from Δa to other size ranges, minus a similar number brought in by collection from other size ranges.

A second equation is best written by considering an individual particle and requiring that its increase in charge, q, be accounted for by the current carried by particles of the opposite sign impacting (or diffusing to) its surface:

Dq/Dt = -i . (9)

Actually, for each equation written for the positively charged particles of radius a, its twin expression can be written for its oppositely charged counter-part. The particles changing the charge q of Eq. (9) are oppositely charged from it, and hence belong to the twin system. Assuming success in creating equal quantities of oppositely charged particles of every size, then the particle distributions of each system will be perfect images of each other.

In the following, the approximation is made that in any range of interest of the radii distribution, the number of particles leaving because of collection by larger particles greatly exceeds that coming in, because smaller particles have collected yet smaller particles, with a resulting increase in their size. Similar arguments pertain to the electrical current carried by particles as they are collected. The current collected by a single particle of radius a', due to image particles in the size range Δa, is:

KΔa = q(a)b(a)f(a) Δ aEp (r,a', t) 4πa' . (10)

Similarly, the number of particles/sec. collected by particles having radius a' from the range Δa(per unit volume) is

ΓΔa'= b(a)f(a') Δa' Ep (r,a',t) 4πa' (11)

Note that Ep = q(r,a', t)/4πεo a' .

From Eq. (11), it follows that ##SPC1##

and from Eq. (10). the single-particle current due to all smaller impacting particles is: ##SPC2##

Thus, there is a pair of integral-differential equations governing f and q in the agglomerating section. These are obtained by inserting Eq. (12) and Eq. (11) into (8), to get: ##SPC3##

and Eqs. (13) and (10) into (9) to get ##SPC4##

Note that, in writing Eq. (14), it is assumed that the gas moves at sufficiently low velocities, relative to the speed of sound, to justify setting ∇. v v = 0. Also, all symbols used to represent charges are defined such that they are positive. Use is made of Eq. (14) to find the distribution function for the smaller particles, and to do so, the term on the right couples to the larger particles through their instantaneous charge distribution. That distribution is brought in by Eq. (15) written for the larger particles. The formulation is then complete, because the integral on the right in Eq. (15) requires the particle distribution function for the smaller particles.

In view of the difficulties encountered in solving the coupled integral-differential equations, Eqs. (14) and (15), it is convenient to approximate the continuous distribution of radii by a discrete spectrum as shown in FIGS. 11A and 11B. The continuous distribution is represented by breaking it into p discrete spectra, formally: ##SPC5##

where integration over the neighborhood of one impulse shows that nm is the number density of particles within the spectral range Δam. Also, qm ≡ q(am) is the average single-particle charge over that same range, and accordingly, b(am) ≡bm.

For a spectral pair separated by many times the radius of the smaller range of particles, the approximation mentioned previously of neglecting increases in particle density (at a specific radius) produced by coagulation of smaller sized particulate becomes increasingly accurate. Substitution of the impulse train of Eq. (16) for the density spectrum in the coagulation and charging equations, (14) and (15), provides a system of coupled differential equations ##SPC6##

Thus, a representation in terms of 2p nonlinear partial differential equations is evolved.

Of greatest practical interest is the steady-state condition. If, in addition, the agglomerating geometry is essentially dependent on only the one spatial coordinate x, the system of Eqs. (17) and (18) reduces to ##SPC7##

where U is the mean gas velocity in the x- direction.

To obtain both physical insight into the significance of the model and preliminary quantitative assessments of the potential of the device, it is in order to consider the one-dimensional, steady-state system characterized by Eqs. (19) and (20). The approach also exhibits the essential nature of the particle interactions predicted by a p family set of equations, if attention is limited to the interactions of two families, a1 and a2, as sketched in FIG. 12.

For the present purposes, it is assumed that the mobilities of both families are representable in terms of a simple Stokes' drag model

bm = (qm /6πμ am) , (21)

where μ is the dynamic gas viscosity. Then, Eqs. (19) and (20) reduce to the 2p = 4 expressions

dn1 /dx = - [ q1 n1 n2 q2 /6πμεo Ua1 ] (22) dn2 /dx = 0 (23) dq1 /dx (24)

dq2 /dx = - [ q2 q12 n1 /6πμa1 εo U] . (25)

notice that modeling of the present system is again evident. The charge on the smaller particles and the number density of the larger ones is predicted by Eqs. (23) and (24) to be constants: n2 = constant and q1 = constant.

Equations (22) and (25) can then be combined and solved in terms of the inlet values n1 (0) and q2 (0). It is then possible to show that ##SPC8##

That these are solutions is evident by simply substituting Eqs. (26) and (27) into Eqs. (22 - 25).

A useful relation between the particle density n1 (x) and the charge per particle q2 (x) is obtained by observing from Eqs. (22) and (25) that 1/n2 dn1 /dx = 1/q1 dq2 /dx. Because n2 and q1 are constants, this relation can be integrated and the initial conditions used to show that

[n1 (x)/n1 (0)] = (η+1) [q2 (x)/q2 (0)] - η (28)

Note that physically interesting values of the loading parameter range from -1 to infinity. Over this entire range, the number density and charge per particle are decreasing functions of x. However, η = 0 demarks a regime in which the charge decay limits the degree to which the particle density is decreased from a regime in which all of the particles can be removed without completely discharging the large particles. That is, as x ➝∞

η n1 (x)/n1 (0) q2 (x)/q2 (0) ≥0 ➝0 η/(η + 1) ≤0 ➝-η 0 (29)

Thus, η is an essential design parameter. Assuming that all particles are charged to saturation by the same effective field Eo in the charging section, then q1 and q2 (0) are given respectively by Eq. (6) and q2 (0)/q1 = a22 /a12 . Further, V2 /V1 = (n2 a23)/(n1 a13) ... where V2 /V1 is the ratio of total particle volume concentrations at the inlet to the section, and we can write the loading parameter as

η = a1 /a2 V2 /V1 - 1 (30)

this last expression makes it clear that the price paid for being able to completely collect the smaller particles in a single section is a volume loading of V2 /V1 = a2 /a1. If the particles are to be effectively changed in radius by a factor of 10 in a single stage, then the ratio of volume loadings of the large to the small particles must be in the same factor of 10. This statement uses the fact that η = 0 is the least value of the loading factor that gives a distribution of n1 (x) approaching zero as x➝∞. In fact, for η = 0, Eqs. (26) and (27) assume the simple forms

[n1 (x)/n1 (0)] = [q2 (x)/q2 (0)] = 1/[1 + x/l*] (31)

Just how rapidly the density of small particles approaches zero in this delimiting case is clearly a function of l*. A convenient form for l* is found by making use of the charging equation, (6), and defining n1 = 1/(α1 a1)3 such that α1 is the number of particle radii, a, by which particles are typically spaced when they are in the number density n1 (0). Then,

l* = (α13 μ U/24πεo Eo2) (32)

Note that this expression does not depend on the size a1. The following equation can be taken as a typical value:

l* = [(100)3 (5 × 10-5)(5)/(24)(π)(8.85 × 10-12) (106)2 ]≅ 3 × 10-1 m (33)

This is a reasonable, typical length for a practical device.

There is a discussion in the paragraphs that follow of how feedback can be used to further enhance the rapidity of agglomeration. That the length l* is of a significance similar to that illustrated in the introduction by lp is seen by noting that b = q1 /6πμa1. If it is further recognized from Coulomb's law that 4πR2 Ep = q/εo, it follows that lp in Eq. (4) can be written as lp = μo U/bNq. For the particular case η = 0, Nq ≡n2 q2 (0) = q1 n1 (0), and hence lp = εo U/b1 q1 n(0), which is seen to be identical to l*.

For optimal use of a given volume, it is likely that agglomeration is best achieved by having several, or perhaps many, stages 101 in series. An index as to the necessity of using series staging is the loading parameter η . Clearly, if η is considerably less than zero, staging is required, or only fractional clearance of the small particulate will be achieved, no matter how long the agglomeration section, but, even if η is on the order of zero, it may be desirable to use some form of multiple staging.

There follows a discussion of the manner in which the previous derivations give the performance of stages, as shown in FIG. 9, or series, as shown in FIG. 13. There then follows a discussion of an alternative or complementary approach in which feedback of particles is used to improve efficiency. Staging, whether by means of series sections, feedback or both is a trade-off with loading and, ultimately, overall systems considerations will dictate which combination of equipment and loading should be used.

A series of s stages is shown in FIG. 13. Each stage consists basically of charging wires and a drift space for mixing and agglomeration, as sketched in FIG. 8. Parameters for each stage are summarized with the figure. It is assumed that each charging section renews the charge/particle to the same value as that achieved at the inlet to the first stage. Thus, q2 (0) is the same for each stage, but in general, the loading of n1 at the stage inlets varies, hence each stage has its associated loading parameter and characteristic decay length l*. For the i'th stage, [from Eq. (26)]: ##SPC9##

and hence the removal of particulate for the system as a whole is ##SPC10##

where the parameters are defined such that

n1i = number density of particles n1 leaving i'th stage,

li = length of i'th stage,

q2 (0) = saturation charge per particle of q2 family entering an agglomeration zone,

ni = [q2 (0)n2 /q1 n1i- 1 - 1], and

li * = 6πμa1 εo U/q12 n1- 1

Another way of increasing the efficiency of the system is to use the large and quite valuable particles more than once in a given section. This is accomplished if some of the particles at the outlet of the total agglomerator section (perhaps itself consisting of a series of stages) are fed back to the input as illustrated in FIG. 14. The feedback is illustrated for the two-family system, but the general approach which is outlined could be equally well applied, with some complication, to a larger number of families.

The relation between input and output number densities njin and njout is required. A fraction χj < 1 of the j'th spectrum is separated and fed back to the inlet of the agglomerator (0 < χj < 1). The general problem is complex, because the relationship between nj and njs for a given family depends on the resident number densities of other families. However, in the two-family picture of the agglomeration process, the number density of the largest family of particles is uncoupled from those below, and the feedback relations are

n2s = n2o (36) n2e x = n2s - χ2 n2s (37)

n2o = n2in + χ2 n2s (38)

from which it follows that n2ex = n2in, but more important, that:

n2s = n2o = n2in /1 - χ2 (39)

Thus, the large particle number density in the agglomerator is enhanced.

Now, a "gain" G > 1 for the agglomerator section is defined such that

n1s = n1o /G1 (40)

where, from Eqs. (26) and (35), ##SPC11##

and the effect of feeding back the large particles is to increase η and hence increase G1 as computed from Eq. (41). But, in addition, a fraction χ1 of the small particles is fed back. This fraction might be most conveniently selected as equal to that for the large particles. In any case, feedback relations for the small particles are, in addition to Eq. (40):

n1ex = n1s - χ1 n1s (42) n1o = n1i n +χ1 n1s, (43)

and it follows that the output number density is related to the input density by

n1ex /n1in = (1 - χ1)/(G1 - χ1) (44)

thus, the feedback accomplishes an improvement in the efficiency of particle agglomeration by subjecting the small particles to more than one pass through the agglomerator, as reflected by Eq. (44), and also improving the effect of the agglomerator in attenuating the small particles because of the residence of a larger number of large particles [Eq. (41) with η computed using n2 = n2s from Eq. (39)].

To estimate the effectiveness of such a device in an industrial application, it is in order to examine a one-stage device which operates on the fly ash produced by burning pulverized coal in an electric power station. The size distribution in such a flow is given in FIG. 15A. Notice that all sizes from less than 1μ to greater than 100μ are represented. In order to transform the distribution to make it compatible with the two-family analysis, the following identification is made. The particulate mass distributed between a = 0 and a = 1μ is redefined as the small particle density m1 centered at a1 = 0.5μ. The remaining mass, which in this case represents 99 percent of the total, is defined as the large particle mass density, with an effective radius of 10μ. This redefined distribution is shown in FIG. 15B.

For a typical total particulate loading of M = 7 × 10-3 kg/m3, that part attributed to the small particles is: M = 7 × 10-5 kg/m3. The loading factor in this case is:

η = [(a1 /a2) (V2 /V1) - 1]= [(a1 /a2)(M2 /M1) - 1]= [(5 × 10-7 /10-5) (7 × 10-3 /7 × 10-5) - 1]= 4 (45)

the spacing factor α1, (see paragraph before Eq. 32) can be determined from the following relation

n1 1/(α1 a1)3 = M1 /m1 ➝ α13 = m1 /M1 1/a13. ##SPC12##

Finally, the decay constant is now seen to be:

l* = (α13 μU/24πεo Eo2) = [(242)3 (5 × 10-5) (5)/(24)(π)(8.85 × 10-12) (106)2 ]≅ 5.3m (48)

Using the results of Eqs. (26) and (27), we can determine the density and charge distributions down the channel:

n1 (x)/n1 (0) = { - 0.25 + 1.25 e0.75x }-1 ≅ 0.8 e-0.75x (49) q2 (x)/q2 (0) = e0.75 {- 0.25 + 1.25 e0.75x {-1 ≅ (50)

To achieve a removal efficiency of 99.9 percent for the small particulate, ie., have n1 (x)/n1 (0) = 0.001, requires that the agglomeration region be at least 8.9m in length. Because only a single stage is required, this is a feasible length for a practical device.

The above conclusion pertains to operation of just one stage. Suppose that two stages are cascaded, each a meter in length. The output small particle concentration is given by Eqs. (34) and (35) for s = 2 and l1 = l2 = 1:

∴(n12 /n1o) = (n11 /n1o) (n12 /n11) ≅ (0.8 e-0.75 )(0.92 e-0.75 ) = 0.145 (51)

Notice that, in cases like this where η > 1, the effect of adding more stages rather than just extending the length of the first, is not particularly significant.

To make it possible to meet specifications with a shorter length of a single-stage system, part of the large exiting particles can be fed back to the input. Thus, let χ2 = 0.9 and χ1 = 0. From Eq. (39),

n2s = n2o = n2in /(1 - χ2) = 10n2in

Thus:

G1 ≅e +η li /li* = e+9.25 l (52)

To meet the same efficiency requirement as before, n1 (x)/n1 (0) = 0.001, the length of the agglomeration region must be at least 0.72 m. This is a significant reduction in the required length of the system and, again, indicates practical device dimensions.

In passing, it should be pointed out that, even though there is an increase in the large-particle concentration by a factor of ten, they are still fairly well dispersed. Feedback has reduced α2 from 52 to 24.

In the foregoing, it is assumed that the incoming stream contains a sufficient number of large particles. If this is not the case, then some such large particles are introduced at the entrance, artificially. However, most industrial particulate flows contain sizes covering a rather substantial range. For example, fly ash from pulverized coal contains one percent by mass of submicron sized particles, and a full 50 percent by mass of particulate larger then 10 microns. Even if this concentration, n2, occurring naturally in the stream is not as large as desired for a direct-coupled device, the feedback mechanism analyzed just before will allow an increase by a factor of 1/1-η of the effective large particulate concentration.

As alluded to in the last paragraph, most gas flows contain a distribution of radii, rather than contributions from just two widely separated ranges. To predict the alteration of the particle distribution, the full integral-differential equations should be used. However, a reasonable picture of the nature of the operation can be generalized from the two-particle case. The smaller particles will tend to attach themselves to the larger ones. The extent of this process can be increased by increasing the large particle concentrations and their charges, using them repeatedly, or even introducing large particles by a seeding process, or lengthening the effective agglomeration section. In any case, it is evident that output distribution will be a skewed version of the input one. The extent of the distortion will be in proportion to the system properties mentioned above.

Before concluding, it should be pointed out that this system also does much to alleviate the problem caused by high resistivity material. In ordinary electrostatic devices, the dust can accumulate on the side walls to such an extent that the corona may be turned off. The arrangement disclosed herein has no such walls. In addition, the reintrainment problem which causes inefficiency in other devices is actively sought here. The turbulent flow tends to keep the corona wires clear of resistive buildup, preventing shutdown and loss of many of the large, and quite valuable, particles.

The output of the cross-spectrum agglomerator can be fed into a conventional precipitating device. This might be an electrostatic precipitator, a scrubber, a cyclone, a settling chamber, etc. It is required that such a device be just about 100 percent efficient in removing the larger sized particulate. Since these may be on the order of 10 to 100μ or larger, this task is certainly within the abilities of devices currently available.

In the foregoing description, and as previously mentioned, the discussion is primarily relevant to a system wherein the fluid is a gas; however, the fluid may be a liquid such as, for example, hydrocarbon fuels, which are an example of relatively insulating liquids and the particulate can be solids, liquids, or even biological particles. Also, as should be quite evident from the discussion, the terms "transversely" and "laterally" apply to both the z-and the y-directions in the drawing and the charged regions are spaced transversely or laterally, one from the other, adjacent regions being oppositely polarized; that is, if one electrode is charged with a positive polarity, all the electrodes adjacent to that electrode are charged with a negative polarity to provide contiguous regions of positive or negative polarity as before discussed (e.g., see the electrode 50 in FIG. 6). Of course, each charging electrode can be made in any specific region, as is known, of a plurality of individual electrodes, all bearing, at one instant of time, the same polarity. The foregoing technical description emphasizes agglomeration wherein smaller particles attach themselves to larger particles; however, the mechanism holds true for agglomeration between particles in the same size range as well.

Modification of the invention herein described will occur to persons skilled in the art, and all such modifications are deemed to be within the spirit and scope of the invention.