EXPERIMENTAL TECHNIQUES
Conductivity Measurement Method by Means of Multivibrator Frequency Control Louis A. Rosenthal Department of Electrical Engineering, Rutgers University,New Bruns wick, New Jersey 08903
An electrolyte conductivity probe controls the frequency of an astable multivibrator and provides simple stable waveforms. Conductivity can be interpreted as a frequency (or period) measurement. Circuits to restore the signal to analog form are described. The measurement method may provide rapid conductivity measurements in a simple manner for certain mixing salinity studies.
Introduction In a program concerned with the mixing of fresh and salt waters, the need for a simple, rapid, direct-reading instrument for the measurement of electrolytic conductivity or resistivity was required. Since many locations were to be measured, the instrument had to be low-cost and simple in concept. The local conductivity measurement had to be indicated a t a speed commensurate with the mixing action, yet insensitive to the probe signal noise. There are well-established methods for electrolytic conductivity measurements and a variety of commercial instruments to provide such measurements typified by the product lines of Beckman and Leeds and Northrup. By making the electrolytic cell part of a Wheatstone bridge circuit and manually balancing the bridge, a static, high-accuracy volume resistivity measurement can be made. The cell constant must be known to convert the measured resistance to a volume conductivity or resistivity. By making the bridge self-balancing through a servo loop, it is possible to automate the readout. For many cases, electrical bridge accuracy is not warranted except for calibration procedures. The mixing of salt and fresh waters results in a dynamic resistance range of several decades. As another procedure, similar to an ohmmeter, a voltage is applied to the conductivity cell and the current flowing is a direct measure of conductance. This method is rapid and direct-reading, but requires a stabilized cell voltage drive signal and current-measuring means. Khang and Fitzgerald (1975) describe a variation of this procedure based on the application of operational amplifiers. The ohmmeter methods require a stabilized voltage or current source, a low-pass filter to average out the probe dynamic noise, and some form of signal detector. All of the measurements described must be made a t ac, since the electrolytic cell must not be allowed to polarize. The typical cell employs platinum electrodes that have been passivated by a platinum black surface to eliminate any unilateral effects or polarization. Frequencies from 60 Hz and up are used, and in certain cases the frequency is increased as the conductivity range increases, to minimize the effect of an electrode surface capacitance. A method will be described wherein the cell resistivity is converted to a variable frequency signal. The period of this
signal is linearly related to resistivity and the frequency is linearly related to conductivity. Many advantages of this system will become apparent, and the method is particularly amenable to the salinity study mentioned.
The Method One form of a free-running astable multivibrator similar to that described by Wittlinger employs an operational amplifier with an RC feedback network, as a single time constant, establishing the oscillation period. Figure 1 shows this circuit with certain improvements where R1, the probe, and C1, a range capacitance, determine the operating frequency. An important feature of this circuit is that the probe is grounded and can be located a t the end of a shielded cable. The operating period for this circuit follows
and for the case shown where R2 = R3
T = 2R1C1 In 3 Although the amplifier A1 alone is sufficient for oscillation, the additional stage A2 acting as a limiter and low-impedance output unity buffer is essential for improved performance. Amplifier AI is driven between +I- saturation states and produces a square-wave output which is clipped to f0.6 V by the diode D1, D2 network. This new square-wave signal is fed back through the linear unity buffer stage (At) which provides low impedance, output isolation, fast slew rate, and improved waveform. All amplifiers can be the popular 741 variety. The amplifier A1 is driven between voltage saturation levels, but never current saturation levels, in a square-wave manner. This signal is clipped and at unity gain, provided as the output ( e o ) signal square wave of amplitude equal to the clipping diode voltage drop (i.e., approximate 0.6 V = V). The change 2V is returned to the probe appearing as the exponential waveform shown in Figure 2. As capacitor C1 charges, the probe voltage decays from 3V/2 to V/2, a t which time amplifier A1 (having a gain of 2) switches polarity. It is as though the composite amplifier were output-limited to f V due to the Ind. Eng. Chem., Fundam., Vol. 16, No. 4, 1977
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Figure 1. The circuit for conductivity measurement is shown. A +/-15 V supply is required for the amplifiers A1 and A2 (MC1558 Dual 741 operational amplifiers). Silicon diodes D1 and D2 limit the amplitude swing to +/-0.6 (VI.
Figure 3. A calibration curve of period vs. probe resistance shows over three decades of linearity. Capacitor C1 can shift the calibration to higher or lower frequency ranges.
Figure 2. The electrolytic conductivity cell probe waveform uniquely defines proper operation and stays constant for the entire resistance range. action of Az. If the gain of the amplifier AI, (1 t Rs/Rz), is increased from 2, then the exponential will decay to a lower trip point and the peak probe voltage will approach 2V. For improved stability and negligible jitter, it is desirable to trip a t a high level in the exponential decay. As an example of stability, from a cold start at a period of 7.291 ms, the period increased to 7.309 (0.25%) in 2 h. This change was attributed to component temperature sensitivities. The clipping level of the diode network D1, Dz will not influence the frequency (see eq 1)since a voltage ratio establishes the waveform and timing. The probe experiences a symmetrical constant waveform of peak value equal to 3V/2 or approximately 0.9 V. The period or frequency of the circuit can be readily determined by any commercial counter/timer as a direct readout. Such instruments are becoming commonplace in the typical laboratory. Other methods of converting the signal to an analog output will be discussed later. Figure 3 is an experimental plot of the probe resistance terminating 4 ft of coaxial cable vs. period for the circuit shown. Over three decades of linear relationship are observed, during which time the waveforms did not deteriorate from those discussed. At the low end of resistance (high conductivity) at 50 ohms, the output resistance and the current limitation of the A2 operational amplifier degrade the performance. For the high-resistance (low-conductivity) 500 000-ohm region, the input impedance of the operational amplifier A1 deteriorates the linearity. I t would be possible to extend the linear range if deemed necessary by employing F E T input operational amplifiers (e.g., RCA CA3140) and higher current output stages. Capacitor C1 sets the scale, and for the data presented the frequency extends from 3 Hz to 8.4 kHz, proportional to conductivity. Decreasing C1 will increase the frequency accordingly, but the frequency and slew rate limitations of the operational amplifiers must be respected. Features of This Method Certain useful and novel aspects of this measurement method are noteworthy. The conductivity cell waveform is amplitude-stabilized so that voltage coefficient and such nonlinearity effects are eliminated. A cell that is polarizing or improperly passivated will produce an asymmetrical 484
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I \
I.
(b)
Figure 4. Circuits for converting the square-wave signal available to a direct reading of resistance (part a, period) or conductivity (part b, frequency) employ constant current charging for improved performance. Diode D5 (IN5308) in the bridge circuit shown sets the current Io at about 3 mA.
waveform in that the positive area and negative area are unequal. This check was employed to cull an improperly prepared cell. Since frequency increases with increased conductivity, the cell electrode capacitance effect is offset in the correct direction. Similarly, the shielded lead capacitance errors did not appear meaningful a t increasing frequency, since this shunt capacitance can be lumped with C1. By cycle or period counting, the equivalent of low pass filter action is obtained. The averaging process associated with the time interval measurement will minimize all fluctuation noise. It is also true that this averaging process will limit the speed of response. Employing a counterhimer as an output indicator is not a negative feature of this method, since such equipment is common in the laboratory. One counterhimer can be multiplexed to read several outputs for various locations. The four-digit accuracy is of course hardly necessary in a conductivity measurement, but the stability of the circuit is sufficiently good so that with a stable resistor replacing the cell, the measured jitter is trivial. For a conductivity measurement, drift in the observed readings were traceable to unclean cells or liquid agitation. Since the information is contained in a frequency or period measurement, the conductivity measurement can be accurately transmitted to remote locations, over wire or by auxiliary wireless means. The power requirements are +15 and -15 V at 5.0 mA, so that battery operation is reasonable for por-
table and remote-location operation. The problem of converting a conductivity signal to the standard 4.0 to 20 mA for remote monitoring, as well as the general problem of transmission of information over wire lines, can be minimized. Since electrolytic conductivity is very sensitive to temperature, the circuit offers promise in providing compensation for modest temperature variations. At 1%salinity (15to 35 "C) the temperature coefficient of resistivity (TCR) was found to be approximately -1.25%/"C and a t 3% salinity -1.45%/"C. Unfortunately, the temperature coefficient varies with salinity and is not a simple correction; the resistance decreases with temperature increase. If Rp is made temperature-sensitive and mounted in a probe in juxtaposition with the conductivity probe having a common ground return circuit, a possibility for limited temperature compensation exists. A negative TCR is required for Rp to compensate for a negative TCR for the probe R1, and the balance is typically critical and limited in tracking and range. With R2 made equal to R3 for the waveforms discussed, it is possible to realize only two-thirds of the TCR for resistor Rz. For perfect temperature compensation, the TCR of R2 should be 1.5 times that of the solution conductivity monitored. Conversion to an Analog Signal In the event that an analog output, rather than the digital signal of the counterltimer, is required for recording or automatic monitoring, certain simple circuits are available. Circuits that give a direct reading of period will follow the resistance of the electrolytic cell, and those that read frequency follow conductivity. Two such circuits are shown in Figures 4a and b. A meaningful improvement is achieved by using a constant current diode as described by Botos to limit the charging/discharging current of the series capacitor. For both circuits it is necessary to drive them with a clipped or bounded signal, and as shown in Figure 4, a square-wave (+I-) A volt signal is provided for this drive. Note that the analysis depends only on the peak-to-peak voltage of the signal, and if the signal is asymmetrical, performance is unchanged. Referring to Figure 1,such a signal (>*lo v) is available at the output of AI. It is also possible to amplify the eo signal to a similar level at the amplifier A2, or after a transmission path, square the signal in a Schmitt trigger circuit. Many conventional schemes are capable of providing the (+/-) A volt signal. In Figure 4a, the square-wave voltage signal is converted to a +/- constant current ZOby means of the bridge rectifier driving the constant current diode D5. The full-wave bridge circuit converts this device to a bilateral constant current source with a zero conduction band equivalent to two diode voltage drops. Charging the capacitor in a linear manner produces a triangular waveform of amplitude
The amplitude should be limited to A less two diode drops to maintain constant current charging. For example, with IO at 3 mA, CI = fd, and T = 2.5 ms, the peak amplitude (E,) is 1.88 V. Any ac voltmeter based on a full rectified average principle but calibrated in rms volts will read (Erm8)
E,,,
= aEp/4 fi = 0.5563,
The rectified average value of the signal eo is directly related to period and hence electrolytic resistivity, once the calibration has been set. A direct measurement of the circuit frequency can be related to electrolytic conductivity. In the circuit of Figure 4b, the same (+/-I A signal is provided and capacitor C2 is charged, or discharged, via the constant current diode (D5)
arrangement. As the capacitor is charged between the voltage levels + A and -A (2A is the excursion), a rectangular slug of current is required equal to a charge
Zotl = 2ACp
(3)
Ample time must be allowed for a complete charge and charge reversal so that C2 establishes the highest operating frequency. The current pulse as portrayed is of amplitude IO,and the falling edge is slightly rounded as the capacitor Cz charges to A and leaves insufficient voltage for proper operation of the constant current diode arrangement. It is proper to correct eq 3 according to
where V corresponds to a diode drop of about 0.6 V. The average current flowing through the resistor R is
.
,,z
2z,t, =-
T
(4)
for full-wave action of the bridge circuit. A scaling equation can be provided according to
i, = 4(A - 2V)Czf where f is the frequency, proportional to electrolytic conductivity. As an example, a 1mA dc meter is used in place of R, and if Cp = 0.1 X fds, A = 10, and f = 200 Hz
i, = 4(10 - 1.2)(0.1 X 10-6)200 = 0.705 mA
(4b) Excellent linearity was obtained as a frequency meter in support of eq 4a, and by scaling Cp, average current can be related to conductivity directly. I t should be noted that the charge 81required to reverse the capacitor C2 voltage is Q1 = 2(A - 2V)Cp = 1.76 MC if A = 10 V. By limiting IO to 3 mA, the pulse nominal time t l is 0.59 ms and the upper limit of frequency ( f ) is achieved when t 1 approaches 1/2 f . Both of the indicated circuits behaved in an exemplary manner and by limiting the circulating current to IO, in a constant current manner, the circuit loading was reduced and impulsive current waveforms avoided. Performance T o date, the measurement method has been used under static conditions to measure salinity with a commercial bridge measuring apparatus as the standard reference. Simple probe-type cells were constructed to provide large cell constants (i.e., small electrode areas) compatible with the resistance range of the oscillator. In certain crude experiments in mixing, rapid indications of change in conductivity were observed. Analog recording would be desirable, since the period or frequency measurement is not continuous but is based on the gate sample rate. Using commercial conductivity probes or properly prepared equal area probes excellent performance was obtained. However, when the cage probe described by Khang and Fitzgerald (1975) was employed, an asymmetric waveform, traceable to an electrolytic generated emf, resulted. This probe design has a point electrode inside of an outer spiral shield electrode. The circuit design presented cannot tolerate a dc input offset voltage and as shown cannot be used with any electrode which has a generated emf. Although the described electrode was carefully prepared and platinized for passivation, a significant voltage (0.2 V) was generated. It was possible Ind. Eng. Chem., Fundam., Vol. 16, No. 4, 1977
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to insert an adjustable cancellation dc voltage to restore the circuit to proper operation. However, this additional zero or balance adjustment is an inconvenience. At times, measurements of salinity profiles or stratification require the use of multiple probes. Multiple probes wherein each has its own cagehhield or needle probes to a reference distant ground plate have been employed. Using the frequency control method, only the cage electrode configuration provided the proper isolation between probes. Cross-talk can be very serious in this measurement method where frequency lock-in effects can take place. The multiple unguarded probe technique with a common ground plate cannot be employed in this conductivity measurement method. Further use of this measurement method will provide the full evaluation as to limitations and potential.
Acknowledgment The efforts of Siva G. Thangam, of the Department of Mechanical, Industrial, and Aerospace Engineering, in evaluating this method are appreciated, as well as the support of NSF Grant ENG73-03545-A01. Literature Cited Beckman Instruments. Inc., Cedar Grove, N.J. 07009, Technical Literature. Botos, B., "FET Current Regulators-Circuits and Diodes," Motorola Application Note AN-462. Khang, S. J., Fitzgeraid, T. J., lnd. Eng. Chem., Fundam., 14, 208 (1975). Leeds and Northrup, North Wales, Pa. 19454, Technical Literature. Wittlinger, H. A., Application Note CAN-5641, RCA Solid State Division, Somerville, N.J. 08876.
Received for review March 7, 1977 Accepted July 11,1977
A Transient Technique for Measuring Diffusion Coefficients in Porous Solids. Diffusion in Carbonaceous Materials Ralph 1.Yang,' Rea-Tiing Liu, and M. Stelnberg Department of Applied Science, Brookhaven National Laboratory, Upton, New York 7 1973
A transient technique has been developed for measuring effective diffusion coefficients of gases in porous materials. The technique is appropriate for measuring De in the range of low2to cm2/s. Comparisons between this technique and other techniques are discussed. Diffusion of two binary gaseous systems in a nuclear graphite and in a bituminous coal has been studied with this technique.
Introduction Problems connected with diffusion of gases in porous solids occur in many technically important areas. The voluminous literature published on this subject has been recently reviewed (Satterfield, 1970; Smith, 1970; Aris, 1975). Most of the research, both theoretical and experimental, has been concentrated on diffusion in catalysts. The results on various catalysts have been summarized (Satterfield, 1970). A standard experimental technique adopted in this area has been of the steady-state type which was perhaps first used by Buckingham (1904) and referred by many as the Wicke-Kallenbach technique (Wicke and Kallenbach, 1941). This technique employs flows of gases of different composition over two sides of a cell separated by a porous solid. Composition changes between gases entering and leaving the cell are measured and are related to the mass flux and the diffusion coefficient by using the solution to the governing diffusion equation. A problem arises when the diffusion coefficient is small. In this case, the gas flow rates must be kept low to effect a measurable change in the concentration of the diffusing gas. However, low flow would cause serious errors in data analysis because of the boundary layer problems. Here one recalls that in solving the diffusion equation of the system, the concentrations at the two boundaries are assumed to be equal to those of the bulk streams. A diffusion equation for this system with other boundary conditions has not been solved. With low flow rate, it can be shown that an error of 10-20% in diffusion coefficient can result from the boundary layer problem (Yang et al., 1977). With this constraint, the Wicke-Kallenbach technique is suitable and is normally used for measuring diffusion coeffi486
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cients of greater than cm2/s. It is, therefore, desirable to develop a rather simple technique with which diffusion coefficients of smaller than cm2/s can be accurately measured. This communication summarizes a transient technique which is suitable for diffusion coefficients in the range of 10-2 to 10-8 cm2/s. Diffusion in some technically important materials in this category, such as coal and graphite, has been studied and the results are discussed. It should be noted that some techniques for measuring very small diffusion coefficients have been developed previously and have been employed successfully for zeolites (Ma and Lee, 1976; Sarma and Haynes, 1974). It should also be noted that a transient technique similar to this one was published by Gorring and deRossei (1964). A comparison between these two transient techniques will also be given in the Discussion. Experimental Section Apparatus a n d Procedures. As shown in Figure 1, the apparatus consisted of a hollow, spherical chamber. The spherical solid sample was placed in the central portion of the chamber and was supported by three small posts. The chamber had a diameter of 2.54 cm and the spherical samples were of the sizes of about 2 cm in diameter. Temperature in this work ranged from 23 to 75 "C. The sweeping gas, gas B, was preheated with copper coils immersed in a constanttemperature oil bath. The line leading to the diffusion chamber was heated with heating tapes whose temperature was controlled. The diffusion chamber was also heated with temperature-controlled heating tapes. The temperaturecontrolling thermocouples were placed at the inner surface
