Modeling of Saturation Characteristic of an Aspiration Condenser

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1 PIERS ONLINE, VOL. 6, NO. 1, Modeling of Saturation Characteristic of an Aspiration Condenser Z. Roubal, M. Steinbauer, and Z. Szabó Faculty of Electrical Engineering and Communication, Brno University of Technology Kolejní 296/4, Brno 612, Czech Republic Abstract It was confirmed that light air ions have positive influence on human health. For its appraisal it is necessary to know the concentration of air ions and air ion mobility spectrum. This spectrum is usually found out using the saturation characteristic measurement with a gerdien tube; another design option consists in the aspiration condenser with a segmented inner electrode. The second method is faster, but the resolution of air ion mobility spectrum shows worse characteristics.. This paper deals with the mathematical analysis and numerical modeling of saturation characteristic evaluation for this aspiration condenser with a segmented inner electrode. Using a combination of both methods may increase the resolution of air ion mobility spectrum, and the progress of measurement is still better than with the gerdien tube solution. 1. INTRODUCTION The presumption that ions contained it the air have significant influence on living organisms has been discussed in a large number of scientific papers with a focus on the problem of concrete effects of ions on bacteria, animals, and humans [1 3]. Light and negative ions feature positive effects on the human organism, whereas their heavy and positive counterparts bring about negative impact. It was shown by N. I. Goldshtein [3] that the complete absence of negative air ions in the inhaled air is fatal to animals. Any evaluation of air ions and their impact on the human organism is only made possible after and on the basis of air ions concentration measurement and air ions spectrum mobility. One of its methods is based on measurement using the aspiration capacitor. In a simple aspiration condenser gerdien tube the internal electrode is not divided into several segments. This method will be modeled saturation characteristics for the natural spectrum of negative air ions measured in [4]. Here, the disadvantage consists in considerable time consumption inherent with the measurement of air ions spectrum. However, if an aspiration condenser with a segmented inner electrode is applied, the pace of measurement can be substantially accelerated. We will obtain an estimation of the air ions spectrum in the given interval, whose accuracy can be further advanced by measurement at several voltages. For the purpose, saturation characteristics will be modeled again of individual segments of the aspiration condenser inner electrode. 2. THE ASPIRATION METHOD PRINCIPLE The basic principle of the aspiration method is shown in Fig. 1 on an elementary aspiration condenser gerdien tube; the principle (model) was taken over from [1] and [5]. Here, it holds that d 1 inner electrode diameter, d 2 outer electrode diameter, L length of gerdien tube, v x air flow velocity, + positive air particle (ion), negative air particle (ion). The gerdien tube consists of two electrodes. There is an electric field between the inner electrode (the collector) and the outer electrode. The field is imposed by voltage source U. The air mass with ions is actuated by a fan through the gerdien tube. Negative ions in the electric field impact the collector, and the current produced is measured by an electrometer. The measured current is proportional to air ion concentration [2]. By means of the change of polarity it is also possible to measure positive air ions. An important parameter of the aspiration condenser is the air flow volume rate M defined as M = ( r 2 2 r 2 1) π vx. (1) In [7], the equation of motion was derived for a ion entered to gerdien tube with a segmented inner electrode for initial point A[, y ]. y 2 = 2 x k U v x ln ( r2 r 1 ) + y 2. (2)

2 PIERS ONLINE, VOL. 6, NO. 1, (a) Figure 1: (a) An elementary aspiration condenser. (b) The coordinates for boundary mobility determination. It is possible to establish by the help of this equation whether a given ion will impinge upon the internal collecting electrode and whether, thus, it will share in the current passing through the aspiration condenser. If we need to determine the current induced by ions entering the gerdien tube, it is advantageous for us to define. From coordinates A[; y ] and E[L; r 1 ] it can be derived that = ε ε r M C U. (3) All ions with a mobility higher than will impinge upon the inner electrode. From the group of ions with k < only a proportionate part will impinge upon the inner electrode. Applying the cylindrical condensers volume ratios, we can establish I k<km = k n q M, (4) I k km = n q M. (5) Let us assume a continuous spectrum. The current, then, will be determined by the sum of ions with a given mobility; for ions with k < there will hold Equation (4), for ions with k will hold (5). It is good to start with the charge concentration density [8]. Then there holds I = M 1 And after substituting for the boundary mobility k ρ (k) dk + M (b) ρ (k) dk. (6) I = C U ε k ρ (k) dk + M ρ (k) dk. (7) It is advantageous [2] to express the characteristics of the aspiration condenser by the help of function G. Equation (7) can be modified to the form I = G(k) ρ (k) dk, (8) for the gerdien tube, function G is given C U k k < G = ε (9) M k 3. MODELING OF THE GERDIEN TUBE SATURATION CHARACTERISTICS For the new gerdien tube type (Fig. 1) designed at the Department of Theoretical and Experimental Electrical Engineering, Brno University of Technology, the ratio was described in Fig. 2 of

3 PIERS ONLINE, VOL. 6, NO. 1, function G to air flow volume rate M directly from the motion Equation (2) for the polarization voltage of 25 V. Fig. 3, then, shows the Matlab-modeled saturation characteristics with a natural concentration of negative ions in the laboratory. For the spectrum determination, the saturation characteristics must be measured in the pointto-point mode; after that, it is possible to determine the spectrum of air ions from the constructed tangent lines. The first derivation, however, highlights the fluctuations and noises. A detailed description of the method can be found in [1, 2, 5, 7]. Figure 2: The ratio of function G to air flow volume rate M. Figure 3: The saturation characteristics with a natural concentration of negative ions in the laboratory. 4. SATURATION CHARACTERISTICS MODELING FOR AN ASPIRATION CONDENSER WITH A SEGMENTED INNER ELECTRODE For the motion equation pertaining to the aspiration condenser with a segmented inner electrode there holds Equation (2). With that said, it should also be noted that it is necessary to establish a new initiatory distance y for each segment. The measuring connection of electrometers and polarization voltage for an aspiration condenser with four segments of the inner electrode (currently under development at the DTEE) is described in Fig. 4. The G i functions for the individual segments are modeled (for the voltages of 12 V and 25 V) in Figs. 5 and 6. Function G 1 of the first segment is highlighted in red, while for the second segment it is depicted in green, for the third in blue, and for the fourth in black. As is obvious from images 5 and 6, direct establishment of the spectrum from G i functions is inconvenient because all G i functions interlap markedly and are permeable for heavy ions too. The solution to the problem consists in measuring the currents that pass through the individual segmented electrodes at two voltages and deducting these currents suitably from one another. In [7] there are introduced relations necessary for the spectrum estimation. Fig. 7 describes the acquired function G for a small voltage ratio a = U 2 /U 1 ; Fig. 8 represents function G for a large ratio a. Even though the spectrum determination from Fig. 7 appears to be more favorable thanks to a Figure 4: The trajectory of air ions in the gerdien tube is shown on the left, whereas the measurement of individual segment currents of the inner electrode and the applied polarization voltage are shown on the right.

PIERS ONLINE, VOL. 6, NO. 1, 21 29 lesser degree of interlapping of G functions, the measurement shows a considerable error owing to small differences in currents I 1 and I 2. In Fig.

4 PIERS ONLINE, VOL. 6, NO. 1, lesser degree of interlapping of G functions, the measurement shows a considerable error owing to small differences in currents I 1 and I 2. In Fig. 8, the estimation of air ions mobility spectrum is encumbered with the error of interlapping of functions G that have passed from the trapezoidal to Figure 5: Function G i for individual segments of the inner electrode and polarization voltage of 25 V. Figure 6: Function G i for individual segments of the inner electrode and polarization voltage of 12 V. Figure 7: The deduction of functions G i for U 1 = 2 V and U 2 = 25 V. Figure 8: The deduction of functions G i for pro U 1 = 12 V and U 2 = 25 V. Figure 9: Saturation characteristics of the aspiration condenser with a segmented inner electrode. Figure 1: The new gerdien tube designed at the Department of Theoretical and Experimental Electrical Engineering, Brno University of Technology.

5 PIERS ONLINE, VOL. 6, NO. 1, 21 3 the triangular shape. Here, however, the error caused by the deduction of currents is lower. For the optimal ratio of voltage it is appropriate to start from the saturation characteristics modeling for all segments of the inner electrode. In Fig. 9, the saturation characteristics were described for the natural concentration of ions in the laboratory as measured in [5]. 5. CONCLUSION The problem of suitable selection of the voltage ratio as well as of the absolute magnitude pertaining to U 1 and U 2 is dependent on the type of ions assumed in the measured environment. For this reason it is advantageous to establish, by means of modeling the saturation characteristics of the related aspiration condenser with a segmented inner electrode, the optimum working area in such a way that the measured currents are not too small and their variance for the given voltages is sufficient. Through repeated measurement for other pairs of voltage, the estimation of the air ion mobility spectrum can be gradually made more accurate. ACKNOWLEDGMENT The research described in the paper was financially supported research plans MSM and MSM of the Ministry of Education, Youth and Sports of the Czech Republic. REFERENCES 1. Charry, J. M. and R. Kavet, Air Ions: Physical and Biological Aspects, CRC Press, Inc., Boca Raton, Florida, Steinbauer, M., P. Fiala, K. Bartušek, and Z. Szabó, Experiments with accuracy of air ion field measurement, PIERS Proceedings, , Hangzhou, China, March 24 28, Goldstein, N. I. and T. V. Arshavskaya, Is atmospheric superoxide vitally necessary?, Z. Naturforsch, Vol. 52, No. 5 6, , May June Bartušek, K., Měření spektrálních charakteristik iontových polí, 21, 5. Vojtek, T., T. Skoupil, P. Fiala, and K. Bartušek, Accuracy of air ion field measurement, PIERS Online, Vol. 2, No. 4, , Roubal, Z., M. Steinbauer, Z. Szabó, and R. Kubásek, Real-time measurement of air ion spectrum using gerdien tube with segmented inner electrode, PIERS Proceedings, , Moscow, Russia, August 18 21, Tammet, H. F., The Aspiration Method for Determination of Atmospheric-ion Spectra, IPST, Jerusalem, 197.

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