18 P 10 Particle transport in an inhomogeneous electrostatic field under laminar flow conditions

J. Aero.~ol Sci., Vo[. 24. Suppl. I, pp. S I 3 g - S I 4 0 , Printed m Greal Britain.

1993

0 0 2 1 - 8 5 0 2 / 9 3 $6.00 + 0 . 0 0 Pergamon Press Ltd

18 P 10 Particle Transport in an lnhomogeneous Electrostatic Field under Laminar Flow Conditions J. Dixkens, C. Strzeletz, F. Stratmann, H. Fissan Process and Aerosol Measurement Technology, University of Duisburg, Germany

Keywords ESP, Inhomogeneous Electric Field, Particle Transport Introduction For particle multi-element analysis it becomes important to sample directly on analytically suitable sample supports. This reduces the risk of contamination and the loss of the material to be analyzed. Dixkens et. al. (1993) developed an electrostatic precipitator (ESP) to deposit particles homogeneously on chemical resistant and analytically suitable samples carriers. This particle sampling technique for direct multi-element analysis avoids chemical preparation and consequently contamination. The basic idea of the ESP is the use of electrostatic forces to deposit unipolarly charged particles on a sample support (f.i. quartz-glass). To get a better understanding of the particle transport processes within the ESP a mathematical model has been developed. ESP-Model Investigations, dealing with the transport of charged particles in systems with external electrical fields must account for fluidmechanical (flow) and aerosoldynamical effects (convection, diffusion, external forces). For modelling the particle transport in the ESP it is necessary to find solutions for the simplified Navier-Stokes, the particle transport and the electrical potential equations. __ ~PG UU)=-~P-~C

(1)

(2)

Cp : Cq+C~

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=

0

(3)

u=fluid velocity, z=stress tensor, p=-pressure, pa=$as dens/ty, pp=particle density, nr=particle number concentration, Dr=Diffusion coefficient, Cp=parlicle velocity, Cq=coulomb velocity, C =sedimentation velocity, do=el,potential

This equations are solved numerically assuming Newtonian fluid, steady state, incompressible S139

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flow, diffusion and external torces. The developed numerical model (ESP-Model) is based on the extended Simpler-Algorithms ( Stratmann and Otto, 1992; Stratmann and Whitby, [989).

Verification and Results Figure 1 shows a schematic illustration of the ESP. Unipolarly charged particles flow through the nozzle into the ESP tube, where the flow velocity is reduced. Within the ESP, particles are transported due to the electrostatic force to the sample carrier which is fixed on the electrode. To verify the ESP-model investigations where performed. At first the electric potential was calculated by finite element method and by finite difference method (Simpler-Algorithms). Both Methods showed an excellent agreement. The equipotential lines of the ESP are shown in figure 1. At second the particle transport influenced by diffusion, sedimentation and the coulombic force for singly charged particles was calculated and the determined collection efficiency of the ESP was compared with the measured collection efficiency. In figure 2 the collection efficiency of the ESP with different electrode diameters is plotted versus particle diameter. It is evident that the experimental and calculated results agree well. The collection efficiency is larger with larger electrode diameter, This is an indication that the distribution of the particles on the sample carrier may be influenced, too. Aerosol

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Fig. 2: Comparisonof measuredand calculatedpartmlecollectionefficiency

The performed investigations demonstrate that the developed numerical model is feasible to describe the particle transport and deposition inside the ESP. Future work will concentrate on the particle distribution on the sample carrier in dependence of ESP geometry and sample carrier material (conducting, non-conducting). Reference J.Dixkens,

T.l~)se and H.Fissan, A new particle sampling technique for direct analysis using total-reflection X-ray fluorescence spectrometry, Spectrochemica Acta, Vol. 48B, No.2, pp. 231-238, 1993

F.Stratmann.

E.Otto and H.Fissan, Theoretical Investigation of Ion and Particle Transport in Space Clmrge Fields, J. Aerosol Sci., Vol. 23 Suppl. 1, pp. 101-104, 1992

F.Swatmmm

and E.R.Whitby, Numerical Solution of Aerosol Dynamics for Sunultaneous Convection. Diffusion and External Forces, J. AeroSol Sci., 20(4), pp. 437-440, 1989