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1 Aerosol Science and Technology ISSN: (Print) (Online) Journal homepage: May an Increase of the Effective Migration Rate Observed in Electrostatic Precipitators with Wider Plate Spacings or Faster Gas Streams Really Be Termed Non-Deutschian? Claus Riehle & Friedrich Löffler To cite this article: Claus Riehle & Friedrich Löffler (1992) May an Increase of the Effective Migration Rate Observed in Electrostatic Precipitators with Wider Plate Spacings or Faster Gas Streams Really Be Termed Non-Deutschian?, Aerosol Science and Technology, 16:1, 1-14, DOI: / To link to this article: Published online: 11 Jun Submit your article to this journal Article views: 466 Citing articles: 11 View citing articles Full Terms & Conditions of access and use can be found at

2 The Effective Migration Rate in Electrostatic Precipitators May an Increase of the Effective Migration Rate Observed in Electrostatic Precipitators with Wider Plate Spacings or Faster Gas Streams Really Be Termed " Non-Deutschian"? Claus Riehle and Friedrich Loffler Institute fur Mechanische Verfahrenstechnik und Mechanik, Universitat Karlsruhe, Postfach 6980, 7500 Karlsruhe I, Germany In recent years, experimental investigations concerning electrostatic precipitators have repeatedly confirmed an increase in the effective migration rate upon widening the plate-to-plate distance or raising the average gas flow velocity. An increase in the effective migration rate with increasing passage width or gas velocity is interpreted as an improvement in precipitator performance. This seems to contradict the traditional Deutsch equation. As a result, one often refers to these as "non-deutschian phenomena." It can be demonstrated that a certain part of the above experimental observations may, indeed, be explained within the scope of the Deutsch concept and hence must not be termed "non-deutschian." This is achieved by considering the influence of the particle size distribution when calculating the effective migration rates. These calculations are based on logarithmic Gaussian distributions, without any restriction of their global applicability. The effective migration rates calculated in this manner are presented as a function of the plate spacing and the average gas velocity and are compared with published data. This reveals that the original Deutsch model yields a correct qualitative description of the actual state, although quantitative deviations do, indeed, exist. INTRODUCTION Electrostatic precipitators are excellently suited to high-grade, fine-dust separation. They are not actually a filter in the standard fashion, i.e., where the flow is obstructed by a perpendicularly orientated filtration area, but rather are figuratively "electrostatic cross-flow filters." As such, electrostatic precipitators hardly impede the gas stream. Contrary to cake-forming filters, electrostatic precipitators therefore possess the advantage of efficiently cleaning large gas flow rates (over lo6 m3/h) with extremely low pressure losses (< 400 Pa). Before an electrostatic precipitator can purge an exhaust gas of particulate matter, the particles must initially receive an electrostatic charge. They are then deflected from the main gas stream by an electric field, to be collected on a metal sheet. In the case of a so-called two-stage electrostatic precipitator, the particle charging and collecting is executed separately, i.e., successively (Figure 1 a). Single-stage electrostatic precipitators, however, conduct both processes simultaneously (Figure I b). Two-stage electrostatic precipitators are mainly of interest for small-scale applications such as the cleaning of welding smoke in workshops. The single-stage precipitators (often referred to as wire-plate precipitators) are of greater industrial significance and are therefore the subject of the present investigations. For example, they are used to clean industrial exhausts that result from coal-fired power stations, cement and smelting works, or refuse incineration furnaces. The discharge electrodes are situated be- Aerosol Science and Technology 16: Elsevier Science Publishing Co., Inc.

3 C. Riehle and F. Loffler 1. stage / 2. stage \ dust / electrodes in a liquid film into a suitable receptacle. In order to clean an exhaust gas stream of 1000 m3/h, a separation area of between 20 and 50 m3 will be required, depending on the desired separation efficiency and the collection characteristics of the specific dust in question. In addition to the operational parameters, the dust concentration in the clean gas is essentially influenced by the length of the collection zone: the so-called field length, which may be as long as 30 m. The usual average gas flow velocity is - 1 m/s for plate spacings of between 200 and 450 mm. raw gas clean gas FIGURE 1. (a) Schematic diagram of a two-stage electrostatic precipitator. The particles are charged and collected in successive, separate chambers. (b) Schematic diagram of a single-stage electrostatic precipitator. The particles are charged and collected in one single operation. tween the earthed collecting electrodes and are connected to a negative high potential of kv. This creates a negative corona discharge, i.e., an electric current flows from the discharge electrode to the collecting electrode, electrically charging the particles as they pass. These are then deflected from the main flow direction by the electric field to be deposited on the collecting electrode. If the gas flow contains solid particles, then a dust layer of several millimeters to some centimeters forms. So-called rappers periodically strike the lower edge of these plates to dislodge the dust layer, which subsequently falls into a dust collecting hopper located underneath. When the gas contains droplets, then these flow down the collecting THE PROBLEM The selection of an applicable plate spacing has, in past years, been the subject of extensive discussion. Although passage widths of between 200 and 250 mm were customary, mm wide plate spacings are now seen to prevail on the European market. Nevertheless, a number of aspects indicate that the optimal passage width actually lies between 400 and 600 mm (Mayer-Schwinning and Rennhack, 1980; Mayer-Schwinning, 1985; Petrol1 et al., 1985). In practice the wide-spacing concept has proved more efficient since, at a constant electric field strength, an increase in the effective migration rate (explained in more depth in the following section; see Eq. 4) may be observed. The separation hence improves with respect to the volume flow rate-specific collecting area, which recoups the investment necessary in increasing the high tension supply. In connection with this, D. 0. Heinrich (1963, 1978) noted that G. Heinrich observed an increase in the effective migration rate for wider plate spacings as far back as the late 1950s, which led to patent applications in England and France. In the 1970s, systematic investigations were conducted by Aureille and Blanchot (197 I), Giipner (1976), and Masuda (1979). Each observed

4 Effective Migration Rate in Electrostatic Precipitators 3 an effective migration rate increase which was approximately proportional to the widening of the plate-to-plate distance. Whereas Aureille and Blanchot and Masuda maintained a constant electric field strength, Giipner's experiments were based on a constant discharge electrode current density. Furthermore, the effective migration rate has also been observed to rise with increasing average gas flow velocity. In the early 1960s, Dalmon and Lowe (1961) had already published results from which it was plain that an increase in the average gas velocity initially increased the effective migration rate up to a certain point beyond which a reduction ultimately commences. In the first years of the past decade, Wiggers (1982) comprehensively investigated the influence of the average gas velocity and the channel width on the effective migration rate. He too verified the frequently observed increase, as Figure 2 illustrates. These observations seem to contradict the Deutsch concept. As such, they were originally referred to by Cooperman (1976) and Heinrich (1984) as "non-deutschian phenomena. " Various hypotheses were propounded for their explanation. For example, Misaka et al. (1978) demonstrated that a wider passage width leads to a greater electrostatic field strength in the vicinity of the collecting electrodes. On the other hand, investigations have also shown that denser particle concentrations then arise close to the collecting electrodes which could induce a particle back-diffusion. This behavior is strongly influenced by the turbulent mixing within the precipitator's passage width (Gross, 1980; Crowe and Bernstein, 1981; Yamamoto and Velkoff, 1981 ; Cooperman, 1984; Self et al., 1984; Shaughnessy and Davidson, 1986). Although it is an accepted fact that the electrostatic field strength, turbulence, and particle back-diffusion in the proximity of the collecting electrode decisively affect the collection behavior, the quantification of this influence is, even today, scarcely possible. plate-spacing (a) average gas velocity (b) - mm - FIGURE 2. (a) Wiggers's 1982 experimental results. The measured effective migration rates are plotted as a function of the plate spacing for various average gas velocities. (b) Wiggers's 1982 experimental results. The measured effective migration rates are plotted as a function of the average gas velocity for various plate spacings. This article nevertheless demonstrates that the effective migration rate increase which results when widening the plate spacings or increasing the average gas flow velocity can at least partly be explained without the necessity of introducing non-deutschian phenomena. Both effects may indeed be described by the Deutsch concept upon combining the original Deutsch law with m/s

5 4 C. Riehle and F. Loffler the practice-orientated equation. DEUTSCH EQUATION applied Deutsch The first particle collection modeling in electrostatic precipitation was undertaken by Deutsch in The equation that now bears his name specifies the grade efficiency, i.e., the particle size- specific separation efficiency: T(X) = 1 - exp - w,(x) su [ "I Here, the theoretical migration velocity w,, is the steady-state particle velocity within the boundary layer of the flow. This is established between the equilibrium of forces, i.e., the electrostatic force and Stokes's resistance force. Since the electrostatic charge and the flow resistance of the particle both depend on its size, the migration velocity is therefore a function of the particle size x, the electrostatic charge Q,, the local electrostatic field strength E, and the dynamic fluid viscosity p. In the case of spherical particles of a diameter x, and under consideration of the Cunningham correction Cu (in which X represents the average free wavelength of the air molecules), Eq. 2 holds Instead of characterizing filter equipment by means of the grade efficiency, one often uses total separation efficiency. In contrast to the grade efficiency, the total separation efficiency depends on the kind of quantity (i.e., number, length, surface area, or mass) specified by the parameter r. In general, the mass-specific total separation efficiency is favored, i.e., r = 3. The total separation efficiency is evaluated by weighting the grade efficiency with the relative frequency of the kind of quantity r, given by the particle size distribution qr(x). This is followed by a summation over the particle size range in question, as demonstrated in Eq. 3: Hence, the particle size distribution must be known before the Deutsch equation can be applied to determine the total separation efficiency of an electrostatic precipitator. In practice, the particle size distribution is not always at hand, so that the following simplified version of the Deutsch equation is often applied: The difference between Eq. 4 and the original Deutsch Eq. 1 is that the exponent now includes the so-called effective migration rate we,. This cannot be calculated in advance for a specific exhaust gas, but must be determined by inserting a measured total separation efficiency into Eq. 4 and solving according to we,. Hence, Eq. 4 may also be observed as a definition of the effective migration rate. Since all influencing parameters are incorporated in the measured total separation efficiency, this also holds for we,. Past attempts to improve the total separation efficiency for a specific exhaust by enlarging the filter collecting area according to Eq. 4 often did not yield the expected benefits. This is actually not surprising, since this equation does not take the effect of the particle size distribution into account. An enhanced compliance between the projected goal and the actually attainable collection efficiency emerges from the modified Deutsch equation suggested by Matts and Ohnfeld ( ).

6 Effective Migration Rate in Electrostatic Precipitators 5 This equation may also be interpreted as a definition of the effective migration rate w,. Because Eqs. 4 and 5 differ by the exponent k, one must accordingly differentiate between the two effective migration rates we, and w,. Experience has shown that satisfactory results emerge when k assumes the value of (Maartmann, 1974). In general, the value for k and these for we, and w, are dependent on the specific dust in question. Since Eqs. 4 and 5 both utilize the effective migration rate as an adaption parameter, no fundamental difference really exists between them. In publications, Eqs. 1, 4, and 5 are not always meticulously differentiated; indeed, each has been referred to at some time as a "Deutsch equation. " Independent of which equation one favors, the so-called specific collecting area (SCA) is inevitably included in the exponent. In the following its reciprocal is defined as y and is termed a ' 'design parameter. " If one wishes to assess the collection characteristics of an electrostatic precipitator with the aid of one of these equations, then a widening of the plate spacings or an increase of the average gas velocity should inevitably lead to a reduction of the particle collection. The goal of this article is to reveal the fundamental correlations between the parameters of the original Deutsch model and the effective migration rate. Especially interesting is the question of whether the observed increase of we, with decreasing SCA (Figure 2) really does contradict the Deutsch model? METHOD OF APPROACH The original Deutsch equation fundamentally allows the total collection efficiency to be predicted for specific precipitator parameters and exhaust gas particle size distributions. In practice, however, Eqs. 4 and 5 serve to evaluate an effective migration rate from a measured total separation efficiency. Hence, a mass-specific total separation efficiency is initially calculated according to Eq. 3, for which the separation function parameters and particle size distribution must be defined. The result can then be converted to an effective migration rate. In a second step, total collection efficiencies, and effective migration rates are calculated as functions of the design parameter y; i.e., the separation function is varied, the parameters of these investigations being the median values and the particle size distribution width. Total Separation Efficiency The precipitator geometry (plate spacing and precipitator length) and the operational parameters (i.e., the average gas velocity, the mean electrostatic field strength, and the electrostatic charge as a function of the particle size) define the separation function. Filter Parameters Since electrostatic precipitators generally operate with field strengths of 1-5 kv/cm, an average value of 3 kv/cm was chosen. A gas velocity of 1 m/s represents a normal situation, as does the selected plate spacing of 300 mm (= 2s). The length of the precipitator was calculated from Eq. 1 for particles of 10 pm in diameter and a required collection efficiency of 99.9 %. From this, a length of 2.39 m results. Thus, the design parameter yo = m/s emerges (Table 1). Particle Charge The calculation of the theoretical migration velocity postulates the Deutsch assumption that the particles enter the separation zone with their maximal electrostatic charge. This maximal charge can be calculated either by the classical field-charging theory (Eq. 7), which offers an adequate accuracy for particles larger than 1 pm or by Cochet's (1961)

7 6 C. Riehle and F. Loffler TABLE 1. Filter Parameters Electric field strength E, = 3 kv/cm Average gas velocity u = 1 m/s Plate spacing Precipitator length L = 2.39 m equation (Eq. 8). The latter takes into account the fact that particles smaller than 1 pm display a progressive stochastic diffusion motion with decreasing size, and hence offer an enhanced absorption cross-section to the ionic current than equally-sized stationary particles. The permittivity of vacuum is E, = As/ Vm and the permittivity of the particle material is described by 6,. (For the calculation of the theoretical migration velocity (Eq. 2), the following parameter values were used: X = 0.1 pm, = 1.84 E - 5 kg/ms, E, = 10.) FIGURE 3. Separation functions of an electrostatic precipitator calculated according to the classical field-charging theory and Cochet's equation (see Table 1). persed in the raw gas may be described by logarithmic Gaussian distributions. Here, it is not the parameter itself, but its logarithm that is subjected to the Gaussian distribution, which makes allowance for the fact that the particles always possess a finite size. The logarithmic Gaussian distribution is derived from the standard Gaussian distribution with the aid of the following transformation: A In the fine particle range, different separation curves result depending on which model is applied to describe the particle charge (see Figure 3). If not otherwise stated, the calculations presented in the Results section are all based on the separation curves derived from Cochet's model (Eq. 8). (Originally all calculations were performed using the classical field charging theory. These results showed the same tendencies but they were even more pronounced than that ones we present here.) Particle Size Distribution For the calculations it is assumed that the volume distributions of the particles dis- Under consideration of the standardization criteria, the logarithmic Gaussian distribution is described by: The parameter x5,,, is the volume distributions median, i.e.:

8 Effective Migration Rate in Electrostatic Precipitators Furthermore, the parameter a,, ( = In a,) is the logarithmic Gaussian distribution width defined as: While the median values x,,,, depend on the kind of quantity r, the spread of lognormal distributions a,, is the same for volume, area, or number distribution. Table 2 is intended to give the reader a concept of the extent of the x,, lx,, ratio for various distribution widths. A spread of a,, > 2.5 will hardly occur in reality, since x, > 12x5,. In other words, if the median value x5,= 10 pm, then X, would be larger than 120 pm. Such extreme particle size distributions will only occur in a few isolated cases. However, if the median value x,, = 1 pm, then x, > 1 pm, and then x,, > 12 pm. In this case, the spread a,, = 2.5 now presents a feasible situation. Figure 4 demonstrates logarithmic Gaussian distribution for various spreads a,, for constant median values of x,, = 0.5 pm and x,, = 5.0 pm. With the aid of these assumptions, the mass-specific total separation efficiency may be calculated for y =yo as a function of the spread for different median values. Effective Migration Rate The combination of Eq. 4 or 5 with Eq. 3 for the total separation efficiency will respectively deliver an algorithm for the calculation of the effective migration rate. The uncommon feature is that the effective migration rate, which according to definition is a measured (properly stated, indirectly meas- TABLE 2. Logarithmic Gaussian Distribution Width FIGURE 4. Logarithmic Gaussian distributions plotted on a linear scale for various distribution widths. (a) The volume median value of all curves is 0.5 pm. (b) The volume median value of all curves is 5.0 pm. ured; see Eqs. 4 and 5) parameter, can be calculated using the Deutsch model: When k = 1, Eqs. 4' and 5' are identical. Hence, we, and w, are both quantitatively equivalent functions of the precipitator parameters and the particle size distribution. For the sake of simplicity, Eq. 4' has been favored for the subsequent calculations, although if necessary, both migration rates

9 8 C. Riehle and F. Loffler may be interconverted with the aid of the following relationship: Should one wish to investigate the influence of the plate spacing or the mean gas velocity on the effective migration rate (Eq. 4') or the respective total separation efficiency (Eq. 3) then, under the precondition that the average electrostatic field remains constant, three free parameters remain: the design parameter y, and the two particle size distribution parameters x5,,, and a,,. RESULTS Initially, the total separation efficiency was calculated according to Eq. 3 for y =yo. The integration limits were chosen such, that in each case % of all particles were included, or in other words, that the standardization conditions for the logarithmic Gaussian distribution were fulfilled to at least Figure 5a illustrates the total separation efficiencies for various median values as functions of the distribution width a,,; the design parameter yo = m/s. One can immediately observe that the total separation efficiency can either increase or decrease with progressive distribution width, depending on the median value in question. This behavior may be more easily understood upon regarding Cochet's separation function depicted in Fig. 3. Hence, if the numeric integration is correct, then for the distribution width a,, = 0 (i.e., a monodisperse particle size distribution) the "total" separation efficiency of the x5, fraction must yield the same value as that delivered by Cochet's separation function at the corre- FIGURE 5. (a) Mass-specific total separation efficiency of an electrostatic precipitator calculated according to Eq. (3) with y =yo, as a function of the logarithmic Gaussian distribution width for various volume median values. (b) Effective migration rates of an electrostatic precipitator calculated according to Eq. 4' with y =yo, as a function of the logarithmic Gaussian distribution spread for various volume median values. sponding location, which is indeed the case. Whether the total separation efficiency increases or decreases with progressive particle size distribution width is determined by the relative positions of the median and modal values with respect to the separation curve's minimum. For example, the curve of the 10.0-pm median value clearly illustrates how the total separation efficiency continuously decreases with increasing spread. In this case, an increase in the spread causes the modal value to shift nearer to the

10 Effective Migration Rate in Electrostatic Precipitators 9 separation function's minimum (cf. Figures 3 and 4 b) so that the separation deteriorates. The curve for the 3.0 pm median demonstrates an analogous although somewhat weaker behavior, provided a,, < 1.8. If, however, the median value happens to be in the vicinity of the separation function's minimum, then a wider particle size distribution can obviously do nothing but improve the total separation efficiency. This behavior is clearly demonstrated by the curves with the median values of 1.0, 0.3, and 0.1 pm. In the instance where the median values are to the left of the separation function's rninimum, then the total separation efficiency must increase for constant distribution widths, which is verified by the curves with the median values 0.1, 0.03, and 0.01 pm. Because the separation function increases rapidly again towards smaller particle sizes, the total separation efficiency must again be reduced for a particular median value onwards with increasing particle distribution width. This is illustrated by the curves with the and 0.01-pm media. If the results plotted in Figure 5a are converted to effective migration rates via Eq. 4', Figure 5b will emerge. Here, one can observe that the effective migration rate either slightly increases or substantially decreases, depending on the median value in question. Since Figure 5b does not present any new results, but only reflects the situation already discussed in Figure 5a, the interpretation of the effective migration rates is subject to the same argumentation as above. Finally, the mass-specific total separation efficiency has been calculated as a function of the design parameter y. The results are plotted in Figures 6 and 7 for various distribution widths of specific media. The results of the calculation for the 5.0- and 0.5-pm volume media may be observed in Figures 6a and 7a, respectively. Both graphs display the " Deutschian behavior, " i. e. higher gas velocities, wider plate spacings, and shorter collection electrodes reduce the total 0 0 I I I I I JviL denlgn parameter (a) I I I I I I & deslgn parameter lnls FIGURE 6. (a) Mass-specific total separation efficiency of distributions possessing a volume median value of 5.0 pm calculated according to Eq. 3 as a function of the design parameter y for various distribution widths. (b) Effective migration rate for distributions possessing a volume median value of 5.0 pm, calculated according to Eq. 4' as a function of the design parameter y for various distribution widths. separation efficiency. Hence the total separation efficiency decreases, as expected with increasing design parameter y. Wider particle size distribution can provoke either a deterioration or an improvement of the total separation efficiency, depending on the median value, the distribution width, and the design parameter y. In the case of the particle size distribution possessing the 5.0-pm median (Figure 6a), progressively wider distributions decrease the total separation efficiency, when a,, < mi3

11 10 C. Riehle and F. Loffler 0.0 I I I I I I & derlgn parameter ds (a) 0 00 I I I I I E & design parameter d s (b) FIGURE 7. (a) Mass-specific total separation efficiency of distributions possessing a volume median value of 0.5 pm, calculated according to Eq. 3 as a function of the design parameter y for various distribution widths. (b) Effective migration rate for distributions possessing a volume median value of 0.5 pm calculated as a function of the design parameter y for various distribution widths The curves for which this holds intersect at - y = 0.26 m/s. When y > 0.26, this behavior is reversed; i.e., wider distributions improve the total separation efficiency. Incidentally, when calculating according to the classical field-charging theory, the curves for different distribution widths intersect all in one dot, say y,. The actual y, value depends on the median value in question. This unexpected behavior is explained by the fact that wider particle size distributions incorporate a larger quantity of larger and smaller particles, since according to the Deutsch model, larger particles possess higher migration velocities, they will therefore be more rapidly deposited. For this reason, one can observe that the average particle size in the dust collecting hoppers decreases over the precipitator length. To the right of the intersection y,, the total separation efficiency change caused by the accumulation of coarser particles outweighs that of the larger y value. To the left of y, just the opposite occurs. The fact that the curves intersect at a single location, irrespective of the spread a,, means that an electrostatic precipitator could (provided the Deutsch concept holds!) be conceived with the total separation efficiency remaining independent of the distribution width. However, since the total separation efficiency at y = y, falls so far short of normal requirements, this aspect is of no practical relevance. Returning to Figure 6 a (presenting calculations using Cochet's equation), we see that an increase in the distribution width from a,, = 1.5 to a,, = 2.5 brings Cochet's separation curve minimum to bear. Some of the particles are now included in the increasing curve section, which must lead to an improvement in the total separation efficiency. The conversion of these results to effective migration rates according to Eq. 4' delivers Figure 6b. Here, one can observe an effective migration rate increase with increasing design parameter y. This implies that higher gas velocities and wider plate spacings will, when consequently calculated according to the Deutsch concept, yield higher effective migration rates. The rate of increase strongly depends on the particle size distribution width and the value of the design parameter y. The various curves which emerges for al, < 1.5 hence also intersect at y,. Their interpretation may be conducted in the same manner as for Figure 6 a. If one selects a median value which lies closer to the separation curve minimum, then for a specific y value, a widening of the particle size distributions must lead to an improved total separation efficiency. This is

12 Effective Migration Rate in Electrostatic Precipitators 11 clearly demonstrated for x,, = 0.5 pm in Figure 7a. The reason for this behavior is, in the same manner as above, to be found in the influence exerted by the separation curve's minimum. Here, the total separation efficiency also decreases with decreasing design parameter y for all curves; i.e., the Deutschian behavior may again be observed. Upon comparing Figures 6a and 7a, one can see for a particular filter parameter y, that the coarser particles are more effectively collected. For example, the total separation efficiency for y = 0. l l m/s and a,, = 0.7 drops from 83% for a median of 5.0 pm to 32% for a median value of 0.5 pm. This is to be expected for these particle size values, since according to Eq. 2, the smaller ones possess smaller theoretical migration velocities and are hence, as verified in practice, more poorly collected. The results of a conversion into effective migration rates according to Eq. 4' are displayed in Figure 7b. One may observe for uln values below 0.7 that the effective migration rate remains relatively constant. This is due to the fact that the total separation efficiency decrease is just compensated by the design parameter increase. An increase in the design parameter only then significantly increases the effective migration rate for wider particle size distributions. A comparison between Figures 6b and 7b will reveal that in both cases, the effective migration rate increases with increasing plate spacing or higher gas velocity, whereby the rate of increase mainly depends on the particle distribution width. The absolute effective migration rates are substantially lower for the particle size distribution possessing a median value of 0.5 pm than those with a 5.0 pm median. This is again reasonable since the finer particles are not so effectively captured owing to their low theoretical migration velocity. mined mathematically is only possible when the raw gas particle size distribution in question is known. Nevertheless, most publications concerning (measured) effective migration rates do not include the particle size distribution data. One exception is Wiggers's (1982) publication, which contains all necessary data. Here, the measurements were conducted using a quartz dust with the cumulative mass distribution shown in Figure 8 (extracted from the original publication). The given particle size distribution was divided into discrete sections and the mass-specific total separation efficiency was calculated by summing up the respective contributions. These experimental parameters were used for the calculations for which the electrostatic field E, (= U/s) was approximately constant (see Table 3). A relative dielectric constant of E, = 10 was assumed for the quartz dust and the classical field-charging theory (Eq. 7) was applied. The results are shown in Figure 9. The circles represent Wiggers's experimentally determined effective migration rates which increase in a rough approximation linearly for y < 0.13 m/s. This increase appears to weaken for y values above 0.13 m/s, but one should consider the high degree of scattering. The effective migration rates calculated from the discrete cumulative mass distribution (Figure 8) have been plotted as full dots. Their evaluation was based on the electrostatic field strength, mean gas veloc- COMPARISON WITH PUBLISHED DATA A description of the experimentally derived effective migration rates with those deter- FIGURE 8. Cumulative mass distribution of the quartz dust used by Wiggers (1982) determined by sedimentation analysis.

13 12 C. Riehle and F. Loffler TABLE 3. Wiggers's Experimental Parameters Electric field strength E,, = ( ) kv/cm Mean velocity Plate Spacing Precipitator length L = 3 m Y ~iggers ity, and plate spacing, which were specified for each experiment. The drawn line results from an average field strength of 6.4 kv/cm. The calculated effective migration rates increase in an almost linear fashion with increasing design parameter y, but somewhat weaker than the measured effective migration rates. The calculation does, however deliver an increasing deviation from the measured values with increasing y. When y is small, the differences are either low, or the curves actually intersect. One particular feature is that the absolute values of the calculated effective migration rates are, for the largest part of the investigated y range, lower than those experimentally derived. If the curves could be extrapolated down to Wigged experiments calculated with eq. (3) and (4') dto. with average el. field 6,4 kv/cm design parameter - m/s FIGURE 9. Effective migration rate as a function of the design parameter y. The circles represent Wiggers's 1982 experimental results. The dots are the values calculated for Wiggers's parameters. The drawn curve represents the values derived from the calculations for an average field strength of 6.4 kv/cm. even lower y values (i.e., larger specific collecting areas) then a reversed behavior is to be expected. The calculated effective migration rates will then be greater than the experimental values. This could indicate that a certain range of specific collecting areas exists for electrostatic precipitators in which the measured values may be satisfactorily described with the Deutsch model. In contrast, however, other ranges also exist where the results yielded by the Deutsch model are either higher or lower than reality will supply. It should also be noted that the measured effective migration rates are usually compared with theoretical migration velocities (Eq. 2), whereby one single particle size must be chosen for the calculations. Although this should be a particle size which is "representative" for the separation process, nobody has been successful in devising a suitable axiom. As a result, the cumulative mass distribution median value is usually selected. In the case of the above example for instance, the median value of x,,,, is, according to Figure pm. Upon calculating the theoretical migration velocity for Wiggers's experimental parameters according to Eq. 2, then w,( x,) = 1.43 m/s will emerge. This value is far higher than the effective migration rates measured and calculated. Hence the question must arise whether the comparison between effective migration rates and theoretical migration velocities is of any practical relevance. From Figure 9, it would appear to be more appropriate to compare measured and calculated effective migration rates or to directly regard just the total separation efficiency alone. SUMMARY The mass-specific total separation efficiency of an electrostatic precipitator was initially calculated using the original Deutsch model. The electrostatic particle charge was derived according to Cochet's equation. This takes the diffusion movement into account, hence

14 Effective Migration Rate in Electrostatic Precipitators 13 also describing the field-charging of fine dusts below 1 pm. Contrary to the classical field-charging concept, the separation function therefore possesses the typical local minimum in the region of 0.2 pm. The strong influence of the particle size distribution is mirrored by the calculated total separation efficiency. Depending on the median value of the particle size distribution, the total separation efficiency can either increase or decrease with increasing distribution width. The second step involved the calculation of the mass-specific total separation efficiency as a function of the precipitator design parameter y for constant electric field strengths. The design parameter is the reciprocal of the specific collecting area (i.e., is proportional to the plate spacing and the mean gas velocity). The results reveal that the total separation efficiency decreases with increasing plate spacing and increasing gas velocity, whereby the rate of decrease depends on the parameters of the particle size distributions. This behavior is also known as ' ' Deutschian behavior. ' ' The combination of the total separation efficiency consequently calculated according to the Deutsch model with an equation often used in practice by electrostatic precipitator constructors (also often referred to as the Deutsch equation) yields an effective migration rate. This is, in one respect unusual, since an effective migration rate is otherwise an exclusively indirectly measured parameter. The results show that the calculated effective migration rates increase with increasing plate spacing and average gas velocity. The rate of increase is chiefly dependent on the particle size distribution width. As a result, this phenomenon cannot be termed from the beginning as ' 'non-deutschian. " Finally, the effective migration rates experimentally determined by Wiggers (1982) for a laboratory scale precipitator were compared with calculated effective migration rates. This was possible since the applied particle size distribution and the respective experimental parameters were specified in Wiggers's publication. The comparison reveals that the qualitative trend of the effective migration rate is correctly described by a consequent calculation according to Deutsch. Wider precipitator plate spacings and higher average gas velocities lead to higher effective migration rates. Certainly the slope of the calculated values is weaker than that one of Wiggers's experiments. Thus the Deutsch model does not correctly predict the quantitative trend of the effective migration rate. The experimentally observed stronger increase can be termed at best as "non-deutschian. " Therefore in future models additional parameters must be taken into account. To summarize: an increase of the effective migration rate with increasing plate spacing and increasing average gas velocity can partly be explained with the Deutsch model. For this reason the term "non- Deutschiali phenomenon" should not be used in this connection. A final point of this article might be the following: any interpretation of measured effective migration rates should be done with much more care than was done previously. REFERENCES Aureille, R., and Blanchot, P. (1971). Staub-Reinhalt. Luft 31: Cochet, R. (1961). Colloq. Intern. Centre Natl. Rech. Sci. 102: Cooperman, P. (1976). Presented at the 69th Annual Meeting of the Air Pollution Control Association, 27 June-1 July, Cooperman, G. (1984). Atmos. Environ. 18: Crowe, C. T., and Bernstein, S. (1981). Environ. Int. 6: Dalmon, J., and Lowe, H. J. (1961). Ed. Centre Natl. Rech. Sci. 102:363. Deutsch, W. (1922). Ann. Phys. 68: Gross, H. (1980). Dissertation, UniversGt Stuttgart. Giipner, 0. (1976). Dissertation, Universitiit Essen.

15 14 C. Riehle and F. Loffler Heinrich, D. 0. (1963). Staub-Reinhalt. Luft 23: 83-91, Heinrich, D. 0. (1978). Staub-Reinhalt. Luft 38: Heinrich, D. 0. (1984). Presented at the International Conference on Electrostatic Precipitation, Kyoto, 1984, pp Maartmann, S. (1974). Staub-Reinhalt. Luft 34: Masuda, S. (1979). Presented at the EPA Symposium, Denver, CO, July, Matts, S., and ~hnfeldt, P. ( ). Flakt Mayer-Schwinning. G. (1985). Chem.-1ng.-Tech. 57: Mayer-Schwinning, G., and Rennhack, R. (1980). Chem.-&.-Tech. 52: Misaka, T., Sugimoto, K., and Yamada, H. (1978). Pre- sented at the CSIRO conference on Electrostatic Precipitation, Leura, Petroll, J., Borgwardt, V., and Schroter, K. (1985). Staub-Reinhalt. Luft 45: Self, S. A,, Mitchener, M., Khim, K. D., Choi, D. H., and Leach, R. (1984). Presented at the 2nd International Conference on Electrostatic Precipitation, Kyoto, pp Shaugnessy, E. J., and Davidson, J. H. (1986). Exp. Fluids 4: Wiggers, H. (1982). Dissertation, Universitat Essen. Fortschr. Ber. VDI-Z. Reihe 3, Nr. 67. Yamamoto, T., and Velkoff, H. R. (1981). J. Fluid Mech. 108:l-18. Received December 28, 1989; accepted May 7, 1991.