Pressure Effect on Microwave Heating of Gas

Javaid Iqbal QureshiFAST National University of Computer and Emerging Sciences

ST-4, Sector 17-D, Shah Latif Town, Karachi, Pakistanjavaid89marq*yahoo.com

Abstract

In connection to microwave heating of gasmolecules, characterizing equations of microwaveattenuation of gas filled media under molecularresonance and off-resonance were derived. Theattenuation constant was found to be an increasingfunction with pressure when the molecule is at off-resonance. The attenuation constant was a decreasingfunction with pressure when the molecule is atresonance. This result supports previously reportedexperimental observations.

1. Introduction

Techniques of microwave heating of gaseous orvapor media have been investigated for a variety ofindustrial applications in the past [1]-[8]. In thesetechniques efficient transfer of microwave energy togaseous particles are important. The microwave energytransfer to the gaseous particles can be monitored byobserving the attenuation constant of microwavepropagation through the gaseous media [9]-[1O].It has been known that the particles absorbmore microwave energy if the frequency of microwaveequals the resonance frequency of the particles than thecase of off-resonance [11]-[14]. However, it has notbeen well investigated as to the effect of gaseouspressure on this microwave energy absorption by thegas molecules. For the initial thinking, the microwaveabsorption is proportional to the molecular density,therefore the absorption will be proportional to thegaseous pressure. But some experimental resultsreported indicated that under a certain condition, theamount of absorption decreaseswith the increasing pressure [1]-[15]. This paper is tocharacterize the pressure effect on microwave energytransfer to the gaseous molecules when heating gas orvapor by microwave power.

2. Microwave attenuation in gaseousmedium

A conceptual model to explain the behavior ofmicrowave attenuation constant vs. gas pressure will bepresented. The model is a cubical model and says thatwhen each oscillator mass M in the system is oscillatingat a frequency f, the amplitude of oscillations of eachoscillator is the same in each of the three orthogonaldirections. The oscillator is then said to have cubicaloscillations of amplitude (x/2) in each of the sixdirections. Now suppose that the oscillator exerts apressure P on any one of the sides of the cube having anarea A. The total force F exerted by the oscillator onthat side is

F =Ma =PA (1)

WhereA= x2 (2)

a = !2 (x/2) = 2 2 f2 x (3)

Substituting both Eqs. (2) and (3) in Eq. (1),

M = P(x2- n2-2

(4)

Since the microwave attenuation in gaseous medium isproportional to the mass of the oscillator and inverselyproportional to the amplitude of the oscillator, it can bestated that the attenuation constant EX is

cr=kM(xl2) (5)

where k is a proportionality constant. Each oscillator ofmass M is assumed to be composed of a group of atomsor molecules which take part in the transition process.

The dimensions ofa should be (m- 1). So

k =k'M

(6)

where k' is a proportionality constant.Substituting both Eqs. (6) and (4) in Eq. (5),

at = k' . Pnj2 M

(7)

It should be emphasized in Eq. (7) that the attenuationconstant a is proportional to the (P/M) ratio. Whenpressure is increased, the mass M increases as well. Butthe (P/M) ratio is not necessarily constant. It ispostulated that at a resonance frequency, due to thesynchronization effect of particles, the (P/M) ratio isdominated by M. The majority of the mass of theoscillator oscillates in the same direction at the sametime in this case. Hence attenuation constant decreasesas pressure increases. It is further postulated that at off-resonance frequency, due to the randomness of particlemotion, the P/M ratio is dominated by P. In this caseonly a part of the mass of the oscillator oscillates in onedirection at the same time. Moreover, not all the masstakes part in the transition. Hence, attenuation constantincreases as pressure increases.

3. Attenuation constant.

Calculations have been made for OCS (Oxy- CarbonylSulfide) gas, and following results were found for theattenuation constants

Calculated results from Eq. (9) were plotted in Fig.2together with the measured results from Ref. [15] . Asseen from Fig. 2 both the calculations and experimentalresults agree reasonably well in the mid pressure range.Visible deviation of experimental data fromcalculations at the low pressure range can be attributedto the absorption loss of the empty test cell itself. Thedeviation at high pressure range is attributed to non-linear effect of the refractive index of the gas.

5. Remarks and discussion

As clearly shown in Fig. 1 and Fig. 2 that theattenuation increases with the pressure when themolecules are at off- resonance and attenuationdecreases with pressure when the molecules are atresonance, respectively.

Equation (9) is not accurate for P-0O. It is reasonablehowever at low pressure. If P-40, then the attenuationobserved is not zero dB. At P *0, the observedattenuation is a finite value which is equal to theattenuation of the empty test cell.

Equation (9) is not accurate for P-poo either. There willalso be an additional apparent attenuation at highpressure region in reality. The high density gas presentsa different impedance of the test cell when compared tothe same test cell filled with the low pressure gas. Thiseffect of impedance change is also not considered inEq. (9).

.L [dB] = 5.69 * 10-3j p(at Off- Resonance)

.L [dB] = 150 ( 1/ P)(at Resonance)

(8)

(9).12j

'IY'is the attenuation constant with the dimension [m-'].'L' is the length of test cell for the OCS gas.'P' is the pressure ofOCS gas in 'Torr.'

4. Correlation to experimentalobservation.

4.1. At off- resonance.

Both the experimental results from Ref. [15] and thecalculated results from Eq. (8) were plotted in Fig. 1. Asseen from this figure, experimental results agreereasonably well with the calculated results.

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z~ ltvmo

._ IqE4TT

m20 S

PRESSURE MARP

4.2. At resonance.

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6. Conclusions

As seen from the reviewed experimental data andpresented analysis, a conclusion can be made thatmicrowave absorption by gas molecules increases withgas pressure at off-resonance and, at resonance, themicrowave absorption decreases with gas pressure forcertain types of gases. The dependency of microwaveattenuation on gaseous pressure has been characterized.Thus the dependency of gaseous pressure on theeffectiveness of microwave heating of gas has beenanalytically characterized.

7. References

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