Atmospheric Environment Pergamon Press 1972, Vol. 6, pp. 61-63. Printed in Great Britain.

A NOTE ON THE SIGNIFICANCE OF PARTICLE CHARGING TIME IN ELECTROSTATIC PRECIPITATION

(First received 12 July 1971 and in final form 4 August 1971)

Abstract-A question is raised regarding the validity of the recent claim that particle charging time due to ion bombardment in electrostatic precipitators is greater than generally supposed. Associated with the effective migration velocity of a real precipitator, an effective charging time can be postulated. It is suggested that this effective value may be si~~~ntly less than its theoretical counterpart.

particle radius (m) NOMENCLATURE

precipitator collecting surface (m*) ion mobility, (m s-l) (V rn-‘)-l electronic charge (C) charging electric field (V m-l) precipitating electric field (V m-l) relative dielectric constant of particle (dimensionless) precipitator length (m) distance from precipitator inlet at which P is maximum (m) ion concentration (ions rne3) precipitate density (kg m-? precipitator radius (m) time after entering precipitator (s) gas velocity (m s- I> volumetric gas flow rate (m” s-l) instantaneous particle migration velocity (m S-l) theoretical particle migration velocity for saturation charge (m s-‘) effective particle migration velocity for saturation charge (m s-‘) permittivity of free space (F m-l) fractional collection efficiency, dimensionless gas viscosity (daP) (dekapoise) theoretical particle charging time constant (s) effective particle charging time constant (s)

INTRODUCTION IN A PAPER presented recently at the Second International CIean Air Congress, NICHOLS and OQLKSBY (1970) have emphatic~ly drawn attention to a point which, at least for industrial electrostatic pre- cipitators, had, heretofore, with but one or two exceptions (B&i& 1968; HIGNETr, 1967), neither been adequately documented nor seriously regarded. The work reported by these authors raises a question which should be considered both for its inherent interest and possible practical importance.

It is a consequence of the Nichols-Oglesby argument that, in the design of a precipitator, one must now know two intensive characteristics, particle migration velocity and charging time constant, in place of the traditional migration velocity alone. But just as the designer’s effective migration velocity differs from its theoretical counterpart, often by a factor of several-fold, we may wonder whether a corresponding condition prevails vis-d-vis the charging time constant. Specifically, the postulated effective charging time constant might be so much smaller than its theoretical value, that the constant can continue to be disregarded in practical design cases. In other words, in practice, the effective migration velocity is, perhaps, still the only precipitator “constant” we need to know to size a precipi- tator in accordance with the Deutsch efficiency equation.

EFFECTIVE CHARGING TIME CONSTANT Some indications of the relative magnitudes of the effective and theoretical time constants may be

had from the following. If. in addition to the assumptions usual in the derivation of the Deutsch e&lciency formula for S tubular precipitator

f = 1 - e-“ws’Y = 1 - e_2W&jm, (1) 61

62 Technical Notes

it is supposed, in accordance with the law of field-dependent [ion-bombardment) charging that

t w=wr---

f-i-7

then equation (1) is modified to (ROBINSON, 1961)

(2)

By de&&ion, the effective migration velocity w,’ at zero time constant is that value of W, which causes equation (I) to fit the experimental data. By analogy, for a time constant greater than zero, the effective values of time constant and migration velocity, i and w,‘, respectively, are those values of 7 and w, yielding a good match between equation (3) and experiment. One way of obtaining effective vatues is by measuring the area1 density of precipitated material P on the collecting electrode as a function of downstream distance from the precipitator inlet. If the entering aerosol is initially uncharged, P rises rapidly from zero at L = 0, reaches a peak at L = L, a short distance downstream of the inlet, and then drops off asL increases further [Experimental P&.-L curves are shown by KALMCHMKOW (1933) and ROBINKIN (1961, 1967)]. Analysis of equation (3) shows that the effective migration velocity is readily calculated from the slope of the In P-vs.-L curve at large L (ROBINSON, 1961)

w,’ = - - ‘2” lim L--tCC

2 (In PI,

in contrast to the theoretical value

Similarly, the effective charging time constant is found from the point of occurrence L, of the maxi- mum precipitate density on the same curve (ROBMSON, 1961)

2w,’ Lp = 7’ = -

( 1 r v’ (6)

as opposed to the theoretical value

The extent to which the effective and theoretical time constants might differ is suggested by equation (6): assummg L, remains essentially constant, effective charging time T’ would be expected to be smaller by the same ratio that the effective migration velocity w,’ is smaller than the theoretical. In terms of the modified Deutsch model, then, the possibility is raised that arguments in behalf of inordinately long charging times-whatever their theoretical merit-lose some of their force.

Both the interesting conclusions reported by NICHOLS and OGLFSBY (1970) and the point made here remain to be corroborated experimentally. It is hoped that these authors will presently be able to provide further data on the basis of work that is now in progress.

Health and Safety L&oratory, U.S. Atomic Energy ~ornrnis~~~, New York, New York 10014, U.S.A.

MYRON ROBINSON

Technical Notes 63

REFERENCES

B&XM J. (1968) Delay of particle charging in an electrostatic precipitator. Stab (English Transl.) 28 (7), 10-14.

HIGNET~ E. T. (1967) Particlecharge magnitudes in electrostatic precipitation. Proc. Inst. elec. Engrs 114,1325-1328.

KALASCHNIKOW S. (1933) The effect of field strength and gas treatment time on precipitation efficiency. Z. Tech. Phys. 14,263-270.

NICHOLS G. and OGLESBY S. (1970) The significance of the particle charging time in electrostatic precipitation. Second Znt. Cleun Air Congress, Washington, Paper EN-41D. To he published in Proceedings, Academic Press, New York.

ROBINSON M. (1961) A miniature electrostatic precipitator for sampling aerosols. Anal. Chem. 33, 109-113.

ROBINSON M. (1967) A modified Deutsch efficiency equation for electrostatic precipitation. Atmospheric Environment 1,193-204.