Ultramicroprobe Method for Investigating Mass Transfer through Gas

Industrial & Engineering Chemistry Fundamentals .... Ultramicroprobe Method for Investigating Mass Transfer through Gas-Liquid Interfaces. Young H. Le...
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Ind. Eng. Chem. Fundam., Vol. 17, No. 1, 1978

59

EXPERIMENTAL TECHNIQUES

Ultramicroprobe Method for Investigating Mass Transfer through Gas-Liquid Interfaces Young H. Lee, George T. Tsao,* and Phillip C. Wankat School of Chemical Engineering, Purdue University, West Lafayette, Indiana 47907

The construction of probes with tip diameters of 0.2 to 0.6 p m is described for measuring concentration fluctuations of a dissolved gas in the liquid diffusion boundary layer adjacent to the gas phase. With suitable instrumentation this probe can be used to construct local concentration profiles inside the boundary layer under various liquid velocities. From the data obtained, it is possible to elucidate the mass transfer mechanisms at the gas-liquid interface more clearly than has been possible previously.

Introduction Gas-liquid mass transfer which is of considerable importance in the chemical industry has been subject to numerous investigations. Starting with the film model of Whitman (1923), various models have been proposed for predicting the liquid side mass transfer coefficient, k ~Among . the classical ones are Higbie’s penetration theory (1935) and Danckwerts’ surface renewal theory (1951). These models did not consider liquid hydrodynamics in their formulation. Scriven (1968, 1969) critically reviewed earlier models and emphasized the importance of hydrodynamics. Recent models increasingly incorporated turbulence parameters of the liquid (Fortescue and Pearson, 1967; Theofanous e t al., 1976) in the expression of mass transfer coefficients. In spite of all these efforts, experimental investigation of the liquid diffusion boundary layer next to the gas phase has not appeared in the literature. One of the difficulties for direct investigation is that the thickness of the boundary layer is very thin even a t relatively low Reynolds numbers. By employing the film theory of Whitman, k L = D/6, the diffusion boundary to 10-2 cm thickness, 6, is calculated to be on the order of for h~ of to low3cm/s, which is in the range of industrial importance. In the above estimation, the value of gas diffusivity in liquids, D , was taken as 10-5 cm2/s, a reasonable value for a dissolved gas in a not too viscous liquid. This means that the dimension of the sensor has to be much smaller than cm in order to give meaningful measurement of concentrations inside the boundary layer. Probeless technique such as holographic interferometry (Masliyah and Nguyen, 1976) can be applied to such measurements but the local detection of eddies a t different positions of the liquid surface may become difficult, if not impossible. Furthermore, a special experimental setup is required for such measurements in addition to sophisticated calibration procedures. Turbulence parameters of the bulk liquid such as liquid velocity fluctuation and concentration fluctuation have been measured by using probes such as conductivity probes and hot-film or hot-wire anemometer probes. The disadvantage of using probes is that they make a significant perturbation in the velocity field of the liquid such that the detection of smaller eddies may not be possible. 0019-7874/78/1017-0059$01.00/0

This problem can be avoided by making the probe size smaller than the size of the smallest eddies of practical importance. Among the spectra of different size eddies produced by liquid turbulence, the smallest eddies of importance are those whose eddy Reynolds number equals unity. For such eddies viscous forces are as important as inertial forces. Kolmogoroff defined the velocity scale, u k , of these eddies when the eddy distribution has come to equilibrium (Hinze, 1959).The importance of this velocity scale is that sometimes it appears . example, Lamont and explicitly in the expression for h ~For (W bubble ) ~ / ~flow Scott (1970) obtained h~ = O . ~ ( S C ) ~ / ~for and Calderbank and Moo Young (1968) obtained k L = O . ~ ( S C ) - * / ~ (for W )mass ~ / ~ transfer from submerged solid surfaces to liquid in stirred tanks, where 6 is the rate of energy dissipation per unit mass and u is the kinematic viscosity of ~ and is equal to uk. liquid. In both expressions ( E V ) ~ / appears The eddy length scale, lk, corresponding to u k is (v3/t)1/4 since the eddy Reynolds number is unity. At relatively high turbulence, the value of lk is on the order of several microns to several tens of microns depending on the rate of energy dissipation. For instance, if the power dissipation is 1 W/kg of water, lk is approximately 30 km. In order not to give significant perturbation to the eddies of this size, the dimension of the sensor has to be less than a few microns. Microelectrodes of 1 to 100 km tip size has been widely used in the field of physiology (Feder, 1968) for measuring ions, membrane potentials, and dissolved gases in cellular levels. With a proper modification, this type of microelectrode can be made to detect concentration changes due to eddy motions in the liquid diffusion boundary layer adjacent to gas phase. Principle of Measurements Polarographic measurement (Kolthoff and Lingane, 1951) of dissolved gases, notably oxygen, is well established in the field of medicine and physiology (Silver, 1974). A polarographic cell consists of a noble metal cathode (platinum or gold) immersed in an electrolyte solution, to which a bias voltage is applied with respect to a suitable reference electrode (calomel or Ag/AgCl) as shown in Figure 1.The concentration of the electrolyte has to be more than 100 times that of the

0 1978 American Chemical Society

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Ind. Eng. Chem. Fundam., Vol.

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No. 1,

1978

GLASS IRSLUTION

'\ CAS In EQUILIBRIUH WITH SOLVCIOW

w

SOLVTION COI(TNM1LC OLPCTROLXTE Ag.b@l

Figure 3. Model of bare cathode. RJXlEWCE ELZTRODE

EXPOSED PWTINUM TIP

Figure 1. Polarographic cell.

disturbed partial pressure of the dissolved gas is Po (Figure 3). The radius of the cathode is ro and the values of the gas diffusivity and the solubility of the medium are Do and So, respectively. The governing diffusion equation is aP - = Do at

($+ -r2 -)apdr

In order to solve the above equation, appropriate boundary conditions are needed. If the bias voltage is applied to the cathode a t time zero and if the voltage is sufficient to make the partial pressure of the dissolved gas a t the cathode surface zero, which is true for a well-polarized cathode, then the boundary conditions become (a1 (b) (C 1 Figure 2. Shapes of cathode tip: (a) Transidyne microelectrode; (b) recessed cathode without membrane; ( c ) recessed cathode with membrane.

reactive species under measurement so that most of the current is carried by the electrolyte species (Skoog, 1971). Depending on the level of bias voltage, sometimes called polarizing voltage, the current output of the cell becomes proportional to the concentration of a specific gas dissolved in the electrolyte solution. For example, in the voltage range of -0.6 to -0.8 V a t the cathode, the current becomes proportional to the activity of the dissolved oxygen. When the platinum cathode is palladinized and impressed with a bias voltage in the range of +0.3 V a t the cathode, the current becomes proportional to the activity of dissolved hydrogen (Baumgartl and Lubbers, 1972). Carbon dioxide can also be measured by slightly modifying the operation of the hydrogen electrode (Severinghaus, 1968). I t has to be noted, however, that the current output of the polarographic cell corresponds to the activity or the equivalent partial pressure of dissolved gas but not to the concentration. Solubility data are needed for the conversion of partial pressures into concentrations. Miniature polarographic electrodes with cathode diameters of 1 to 25 pm have been used for measuring oxygen concentrations in blood and tissues (Silver, 1974). This type of microelectrode is available commercially (Transidyne Corporation, Ann Arbor, Mich.) and was used by Bungay e t al. (1973)for detecting concentration fluctuations a t the liquid surface. Tsao and Lee (1975)employed the same type of microelectrode for investigating concentration fluctuations in the liquid diffusion boundary layer with added proteins. Although the tip diameter of this electrode was claimed to be on the order of 1pm, the overall size was rather bulky as shown in Figure 2a. The other disadvantages were that the calibration was not possible and the use of bare platinum as an active sensing area resulted in a poor spatial resolution as will be shown below. Bare Metal Cathode. The properties of the bare metal cathode can be analyzed by using a model cathode of halfspherical shape immersed in an infinite medium whose un-

P(ro,t) = 0

(2)

P(r,O) = P o

(3)

P ( m , t ) = Po

(4)

The solution is

An expression for the electrode current is obtained as follows (Kolthoff and Lingane, 1951) Z ( t ) = nFADo($)

r=ro

= n F A D o & (dP z)

r=ro

where n is the number of electrons per mole of gas reduced a t the cathode surface, F is the Faraday constant, and A is the cathode area in square centimeters. From eq 5 and 6 , the steady-state pressure, P , and the steady-state current, I,, are P, = P o ( l

-

3)

I , = 2nrFDoSoPoro

(7)

(8)

The distance from the center of the cathode to the point where the steady-state partial pressure reaches 0.99Po can be calculated from eq 7 dg9%

= lOOro

(9)

The time t , required to reach within 5% of the steady-state value is obtained from eq 6 (10)

Hence, for a cathode of ro = 0.5 pm, which is measuring oxygen cm2/s),t , will become 0.016 in water at 25 "C (Do = 2.0 X s and a t 50 pm from the center of cathode, steady-state partial pressure of the dissolved gas will reach 0.99Po. Therefore, even a cathode of 1pm diameter has a poor spatial resolution, since it reads the concentration of dissolved gas at 50 pm away from the cathode a t steady state. If the thickness of the hydrody-

Ind. Eng. Chem. Fundam., Vol. 17, No. 1, 1978

namic boundary layer around the cathode is less than 50 pm, the output current of the electrode will increase with the stirring of the liquid making the calibration of the probe difficult. This occurs because a fresh supply of dissolved gas brought in by the moving liquid compensates for the consumption by the cathode, thereby steepening the pressure gradient a t the cathode surface. A second problem is that the current output of the probe changes in liquids with different D o since the current is a function of DOas shown in eq 8. Spatial resolution of the cathode can be improved by further reducing the radius of the cathode. For ro of 0.1 pm, d9gYbwill become 10 wm and t , will be 6 X lop4s. If there is a stagnant liquid layer of 10 pm thickness in front of the cathode surface, a cathode of this size will show high spatial resolution with a fast response time. This condition can be achieved by making a 10 pm recess of insulation in front of the exposed cathode surface (Figure 2b). The rate of dissolved gas consumption by the cathode can be estimated by using the equation

J = -AD0

(E)

r=ro

= -ADOSO

(z) aP

r=ro

61

Figure 4. Model of membrane-covered cathode.

(11)

At steady state, this becomes as follows from eq 7

When measuring dissolved oxygen in air-saturated water a t 25 "C, a cathode of ro = 0.5 pm will consume approximately 5X g of 02/s, taking the oxygen concentration a t this temperature as 8 ppm. In other words, if this cathode is monitoring oxygen continuously, it will consume 0.23% of the oxygen contained in 1 mL of water in a 1-h period. This is a negligible amount. Practical problems associated with bare metal cathodes are the relatively extensive diffusion field which results in a poor spatial resolution, changes in calibration in liquids having different values of gas diffusivity, and the contamination of their catalytic surfaces by trace contaminants such as proteins or sulfur compounds. Membrane-Covered Cathode. Some of the problems associated with bare cathodes can be solved by using a gaspermeable membrane over the surface of the cathode. By doing this, the contamination of the cathode surface is minimized. In addition, the spatial resolution can be improved and the cathode can be made to give identical calibrations in liquids having different values of gas diffusivity. The analysis of the membrane-covered cathode is similar to that of the bare cathode. A half-spherical, membranecovered cathode is assumed to be immersed in an infinite medium whose undisturbed partial pressure of the gas is PO (Figure 4). The membrane has a thickness of d,, gas diffusivity of D , and gas solubility of S,. Considering the symmetry of the half-sphere, the governing diffusion equations with boundary conditions are

-dP = D o ( ~ , LaP. + - -2)a p at r ar

(rLro+d,)

-

( r - ro - d,) sin

+

dg

DO

X sin d,X

(2

cos

DO

+ h sin d,X)'! +

X cos X d ,

X

Do

X sin d,X)

2

K , = D,S, KO = DOSO s = - -K O d m Km i-0 1- KJKo h= r~ + d m

The current output of the electrode can be obtained from eq 20. Z ( t ) = nFAD,

(E)

r=ro

=nFAD,S,

(14) Steady-state values of partial pressure and the output current of the electrode are from eq 19, 20, and 21, respectively

(ro I r Iro The solution to these equations is as follows (Grunewald, 1971).

+ d,)

(22)

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Ind. Eng. Chern. Fundam., Vol. 17, No. 1, 1978 1.0

r

J

2 .E w

LL

a c3 .L

W

N -

Figure 6. Electrochemical etching apparatus. I

2

I I 1 I 3 4 5 6 R E D U C E D RADIUS r/r,

I

7 'A

I

I

Figure 5. Steady-state partial pressure distribution of a dissolved gas in and out of the membrane for different values of KoIK,.

From eq 22 and 23, the normalized steady-state partial pressure, P,IPo is plotted against the reduced distance from the center of the cathode in Figure 5 for d,/ro = 4.As the ratio of K&, increases, the pressure gradients are shown to be increasingly confined inside the membrane. When the pressure gradients are confined inside the membrane, the output current of the probe is not affected by liquid velocity around the probe. Whether the liquid is stirred or not, the probe will give identical readings a t a given concentration of dissolved gas. Also, the current becomes independent of KO. This means that the probe will give identical calibrations in liquids with different KO.The spatial resolution of the probe is greatly improved compared with that of the bare electrode. The reading of the probe corresponds to the concentration of the dissolved gas right next to the membrane. The condition for the confinement of pressure gradients inside the membrane can be estimated by evaluating the value of s from eq 22 or 23 when steady-state partial pressure a t r = ro d, exceeds 0.99P0

+

-_d m 2 gg (25) Km ro The time required for the electrode to reach within 5% of the steady-state current can be calculated from eq 21 by substituting a numerical value to each variable and performing numerical integration. When the thickness of the membrane is much larger than the radius of cathode, it is deduced from eq 10 that t r = c l -dm2

(26) Dm where c 1 is a constant. Equations 25 and 26 form the basis for designing membrane-covered electrodes. However, they contradict each other in that a thinner membrane is preferred for fast response time while a thicker membrane is better for ensuring that pressure gradients are confined inside the membrane. It is apparent that a decrease in D , is more effective than an increase in dm/rO for improving the probe performance. When the cathode is measuring dissolved oxygen a t 25 "C ( D o = 2 X 10-5 cm2/s, So = 0.056 cm3 of Oz/cm3 atm) the value of Ko/Km is approximately 11 for Teflon, 22 fof polystyrene, and 55 for polypropylene (Modern Plastics Encyclopedia, 1975). In order to satisfy the requirement of eq 24, dmlrOhas to be greater than 9 for Teflon, 4.5 for polystyrene, and 1.8 for polypropylene. Polypropylene is the best in this respect but

CATHODE+

+u e m

~ M B R A N_ftc E HYDRODYWIC BXJNDARY UYER

Figure 7. Concentration profiles of a dissolved gas for different situations (see text for explanations).

the response time becomes longer due to the low D,. As shown in Figure 2c, a shorter recess is enough to retain membrane materials compared with bare metal cathode (Figure 2b). The operation of different membrane-covered cathodes can be compared by using the diagram shown in Figure 6. If the condition in eq 25 is satisfied, the pressure gradients are confined inside the membrane (a in Figure 6) and the electrode current becomes a function of K m only. Under a given partial pressure of the dissolved gas, stirring or gas permeability of the liquid does not affect probe readings. This is the most desirable condition. If the current of the probe changes between liquids having different Ko but with the same partial pressure of the dissolved gas, then the situation will be the same as b in Figure 6. Now, the current becomes a function of both K, and KO.This kind of cathode can still be used to give accurate measurement of concentrations provided that the pressure gradients are confined inside the minimum hydrodynamic boundary layer which can be obtained under different flow conditions used in the experiment. When the pressure gradient extends into the bulk liquid (c in Figure 6), the current output of the probe will change upon stirring of the liquid, and the measurement of concentration becomes difficult. Construction of Probes Several methods exist for making cathodes with tip diameters from 1to 5 pm (Silver, 1965;Whalen, 1967;Bicher, 1970). Among these the method of Silver (1965) is relatively easy to modify to give cathodes suitable for measurement of concentration fluctuations a t the liquid surface. Cathodes of tip diameter 0.2 to 0.6 pm were constructed as follows. Approximately 2 cm of pure platinum wire of 25-pm diameter (Engelhard Industries, Baker Platinum, N.J.) was soldered to a length of 0.3 mm 0.d. copper wire using a conductive paint (G. C. Electronics, Rockford, Ill.). The tip portion of the platinum wire was then etched electrochemically to a fine, long tapered tip of 2-3-pm diameter. The etching of the platinum wire was performed in a simple apparatus shown in Figure 7. It consists of a 50-mL beaker filled with approximately 40 mL of saturated sodium nitrite solution with one or two drops of detergent added. An ac voltage of 1.2

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63

THICK COPE

YIRE

SXLYER WIRE

FIRST

"--CHLORIm DGmSIT

ETCHING TIME, MIN tb)

(a)

(Cl

Figure 8. (a) A typical curve for etching current vs. etching time; (b) the shape of the platinum wire tip after first etching; (c) the shape of the platinum wire tip after second etching.

-CUSS --

CAPILWIY

AC

nxcmsco

0

-

12 V

LOOP

s m WEIGHT

(a) (b) Figure 9. (a) Arrangements for fusing glass onto platinum; (b) fusing procedure.

to 1.3 V was applied between a thick platinum wire (1mm o.d., 3 cm long) and the 25-km platinum wire previously soldered to a copper wire. About 2 mm of the 25-pm platinum wire was immersed in the electrolyte solution. The depth of immersion was controlled by using a micrometer. As etching starts with the switch on, the current decreases slowly at first but faster in the later stages. A typical decrease in current is shown in Figure 8a. When the current had decreased to about 0.5 mA, the etching was stopped by disconnecting the switch. The diameter of the etched portion depends on the etching time: a longer time gives a smaller diameter. If the platinum wire was withdrawn from the electrolyte solution and observed under a microscope, it had the shape shown in Figure 8b. Etching was restarted after withdrawing the platinum wire about 1mm from the solution. This time, the voltage was lowered to about 1.18to 1.20 V. The etching stopped automatically when the meniscus broke. The shape of the tip after the etching was complete is shown in Figure 8c. After etching, the Pt wire was washed thoroughly with distilled water and then with absolute ethanol. A 1.5 mm 0.d. tube of lead glass was drawn down to about 100 km using a

(a) (b) Figure 10. (a) Completed cathode; (b) completed reference electrode (Ag/AgCl).

Nichrome wire heating coil. Reproducible size of glass capillary was obtained by using a weight of 200 g clamped to lower end of the glass tubing to be pulled. Then a hook was made on the end of it (Figure 9). The platinum wire was pushed down inside the glass tubing until the copper was seated against the taper on the inside of the tubing. The glass tubing was then mounted on a micromanipulator point downwards and a small weight (0.05to 0.1 g) was hung on the hook (Figure 9). The capillary was moved by the manipulator into a heating loop of Nichrome wire and observed through a microscope. The Nichrome wire was heated by a carefully regulated ac voltage in the range of 10-20 V until the glass capillary around the fine platinum wire began to melt. As it melted, it was drawn down by the weight and thinned in the process. During the thinning, the body of the glass capillary was raised with the micromanipulator so that heating process caused a progressively thinning layer of glass to melt onto the surface of the platinum. The process was continued until the taper on the extreme tip of the platinum was reached; the taper itself was covered very slowly by reducing heat (Figure 9b). The glass was not allowed to cover the end of the platinum, but was broken off by a sudden raising of the capillary with the manipulator. The broken area was heated gently for a brief moment to ensure smooth finish. At the tip of the platinum a slight recess of glass remained. The copper wire was then soldered to a pin connector as shown in Figure loa. The completed cathode (Figure 10) was tested for electrical continuity between platinum and copper and also for the glass insulation. Its performance as a bare cathode was then assessed in 0.2 M KCl solution and the size of the bare platinum area was calculated in terms of the current it gave per mmHg of oxygen pressure. A thin membrane of 5% polystyrol in carbon tetrachloride was applied to the tip portion of the cathode by dipping and withdrawing slowly. Sometimes, polypropylene, Rhoplex (Rohm Haas Co., Philadelphia, Pa.) and collodion were also used as membrane materials. The electrode was then air-dried point downward a t room temperature for about 4-45 h. The reference electrode, AgJAgC1 was made from a 0.5-mm 0.d. silver wire about 5 cm long. A chloride coat was deposited on the silver surface by making

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I

I

I

I

I

(Cl

P

I

40

(a)

(b)

Figure 11. (a) Arrangements for electrode calibration; (b) apparatus for measuring response time of the cathode; (c) apparatus for measuring concentration a t the surface region of the liquid.

the silver wire +1.5 V against another silver wire (2 mm 0.d.) for approximately 20 s in 0.1 N HC1. The reference electrode was completed by soldering a pin connector to one end of the chlorinated silver wire (Figure lob). The platinum cathode made as described above is sensitive to oxygen in the bias voltage range of 0.60.8 V. This cathode can be made sensitive to hydrogen by palladinizing the free platinum surface following the procedure given by Baumgartl and Lubbers (1972). The procedure is simple but it was not tried since our main purpose was in the measurement of oxygen. Probe Performance a n d D a t a Acquisition The completed cathode was tested for its performance by using a calibration apparatus shown in Figure 11.A mercury battery of 1.35 V was used as a bias voltage source and a 10turn 1 K potentiometer was used as a voltage divider. The current from the electrodes was amplified with a fast response ( ~ Wresponse O better than 0.005 s) current amplifier (Keithley Model 417 Picoammeter, Keithley Instruments, Cleveland, Ohio). A Hewlett-Packard (HP-7402A)oscillographicrecorder was used for signal recording which has a flat response up to 60 Hz. A bias voltage of 0.7 V was used throughodt the experiments. To ensure the confinement of pressure gradient inside the membrane (see eq 25, only those cathodes were selected that gave identical current outputs in air-saturated liquids having different D Ovalues, and that showed no change in current at different speeds of agitation. Liquids used for this purpose cm2/s), 2 M KC1 (DO= 1.8 were: 0.2 M KC1 (Do= 2.1 X X cm2/s), and 30% bovine serum albumin (Do= 1.00 X cm2/s) in 0.2 M KC1 (Goldstick and Fatt, 1970). Well-made cathodes showed a very low nitrogen current. To obtain a calibration curve, gas mixtures with different ratios of oxygen and nitrogen were bubbled into 0.2 M KCl solution and the current outputs were measured when equilibrium was reached. As shown in Figure 12, a linear relationship between current outputs and oxygen composition in the gas mixture was obtained. The response time of the probe was measured by tracing the current response for a step change in dissolved oxygen concentration. This was done by momentarily lowering the cathode from air-saturated solution to nitrogen-saturated solution as shown in Figure l l b . A 95% response time of less than 0.02 s was usually obtained. The temperature depen-

80

la

OXYGEN PARTIAL PRESSURE,

le0

m m Hg

Figure 12. A typical calibration curve of oxygen electrode.

dency of the probes was tested for 20,25, and 30 OC. In this range, the current increased approximately 2.5%IoC on the average. Therefore, temperature control is needed for accurate measurements. The stability of the cathode was estimated by leaving the cathode in air-saturated, unstirred solution of 0.2 M KC1 and monitoring the output for a period of 48 h. The current output was generally constant up to 20 to 40 h depending on individual probes. After this stable period, the current started to increase and the cathode became unstable. This is possibly due to the hydration of the glass insulation around the tip portion or the contamination of the cathode surface. When the probe was used intermittantly, for 30 to 60 min at a time, it was active for more than several weeks. In order to investigate concentration changes inside the diffusion boundary layer adjacent to the gas phase, 0.2 M KC1 solution was first stripped of oxygen by sparging with nitrogen. A stirred vessel, closed except a small opening (Figure 11 c) was employed such that change in bulk concentration of oxygen is negligible during measurements. A micromanipulator (Narishige, Japan) which can be moved in three dimensions in steps as small as 1pm was used. The liquid surface could be made relatively flat by using two counter-rotating stirrers. The degree of waviness of the liquid surface could be measured by placing the cathode a known distance from the liquid surface with the micromanipulator and monitoring the current output. At low agitation speeds or when the two stirrer speeds were matched, the degree of waviness was usually less than about 10 pm. Moisture saturated air was slowly blown over the exposed liquid surface to prevent liquid evaporation. The concentration of the dissolved oxygen inside the diffusion boundary layer was obtained by successively lowering the cathode in predetermined steps. An example of such recordings is shown in Figure 13. It is clearly shown that the concentration at the liquid surface is approximately the saturation value and the concentration profile inside the diffusion boundary layer can be constructed by taking the mean values of fluctuations at different positions of the probe. When the probe is place a t a fixed position from the liquid surface for both the clean liquid and the liquid contaminated with a slight amount of surfactant (100 ppm Tween 20) under identical conditions, the concentration fluctuations are shown to slow down with the added surfactant (Figure 13b). Also, from the observed difference in waveforms, the effect of surfactant can be analyzed with regard to hydrodynamic pa-

Ind. Eng. Chem. Fundam., Vol. 17, No. 1, 1978

65

I

-47 I -I---CDC 6500

-

(DATA ANALYSIS)

y

D I C I T I Z W DATA IN WWIC TAFE

I

CUFlREhT AMPLIFIER

d

10

20 30 %Its, s c

(PI 61&)

I

40

(KEITBLEY 417)

50

Figure 13. (a) Concentration fluctuations of dissolved oxygen in the diffusion boundary layer of the liquid; the positions of the probe from the surface of liquid are indicated; (b) difference in concentration fluctuations between clean liquid and liquid contaminated with surfactant (Tween 20,100 ppm) a t 150 pm blow surface under identical stirring rates.

I 1

-ON-LIM

- -- - OFF-LINL

Figure 14. Data acquisition system.

rameters such as length scale and velocity scale of liquid eddies. From the concentration profiles constructed by the method shown above, the local mass transfer coefficient can be obtained using the following equation.

where ci is the concentration at the interface and cb is the bulk concentration. This equation can be used when the change in the bulk concentration is negligible during the measurement. Numerical calculations of statistical quantities such as the mean value, the variance, the autocorrelation function and the power spectral density function can be performed by using a digital computer. For these calculations, a data acquisition system was set up as shown in Figure 14. The analog signal from the current amplifier is fed to an FM recorder (Model P I 6104, Precision Instrument, Palo Alto, California) to produce a magnetic tape. An analog-to-digital converter (ADC) contained in a hybrid computer (EA1 680, Electronic Associates Inc., West Long Branch, N.J.) was then used for digitization of the analog signal. The digitized data were then analyzed by a large computer (CDC 6500). The analysis of the data will be reported in a separate article.

Conclusions The use of an ultramicro probe of tip size 0.2-0.6 pm was shown to be useful in accurate measurements of concentrations at the surface region of the liquid. This technique adds one more dimension to the study of turbulent mass transfer in addition to conventional methods such as hot film or wire anemometry, interferometry, and holography. With this technique, the investigation of the surface region of the liquid is possible which has been difficult so far. Effects of surfactants in dynamic systems can easily be checked in regard to hydrodynamics and mass transfer resistance. If it is used in conjunction with anemometer probes for measurements of hydrodynamic parameters, experimental measurements are complete as far as interfacial mass transfer is concerned. Many different models can be checked in this way and, above all, an interfacial mass transfer mechanism can be elucidated which can be directly used in improving the performance of existing two-phase contactors or designing new mass transfer devices.

Nomenclature A = surface area of cathode cb = bulk concentration of dissolved gas ci = concentration of dissolved gas a t gas-liquid interface c 1 = constant in eq 26 d, = thickness of membrane d 9 w = distance from the center of cathode where 99% of the bulk concentration is reached D = diffusivity of gas in liquid D, = gas diffusivity in membrane Do = gas diffusivity in bulk liquid F = Faraday constant F(X,t) = function defined under eq 19 h = parameter defined under eq 19 I , = steady-state current output of electrodes I ( t ) = electrode current as a function of time J = massflux k~ = liquid mass transfer coefficient K , = gas permeability in membrane K O = gas permeability in bulk liquid lk = Kolmogoroff's length scale n = number of electrons per mole of gas reduced at cathode surface P = partial pressure of dissolved gas P ( r , t ) = partial pressure of dissolved gas as function of r and t P,(r) = steady-state partial pressure of dissolved gas as function of r r = radial distance from center of cathode ro = radius of cathode s = parameter defined under eq 19 SO = gas solubility in bulk liquid S, = gas solubility in membrane Sc = Schmidtnumber t = time t , = response time of cathode to reach within 5% of the steady-state value u k = Kolmogoroff's velocity scale Greek Letters 6 = thickness of diffusion boundary layer t = rate of energy dissipation v = kinematic viscosity X = dummyvarible Literature Cited Eaumgartl, H., Lubbers, D.W., in "Oxygen Supply", M. Kessler. Ed., pp 130-136, University Park Press, London, 1972. Bicher, H. I., Knisely, M. H., J. Appl. Physiol., 28, 387 (1970). Bungay, H. R., Ill, Huang, M. Y., Sanders, W. M., AlChEJ., 19, 373 (1973).

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Calderbank. P. H.. Moo-Young, M., Chem. Eng. Sci., 16, 39 (1961). Danckwerts, P. V., Ind. Eng. Chem., 43, 1460 (1951). Feder. W., Ann. N.Y. Acad. Sci., 148, 3 (1968). Fortescue, G. E., Pearson, J. R. A., Chem. Eng. Sci., 22, 1163 (1967). Goldstick, T. K., Fatt. I., Chem. Eng. Prog. Symp. Ser., 66, 101 (1970). Grunewald. W., Pfluegers Arch., 322, 109 (1971). Higbie, R., Trans. Am. Inst. Chem. Eng., 31, 365 (1935). Hinze, J. O., "Turbulence", McGraw-Hill, New York, N.Y., 1959. Kolthoff, I. M., Lingane, J. J., "Polarography", Interscience, New York. N.Y., 1952. Larnont, J. C., Scott, D. S., AIChEJ., 16, 513(1970). Masliyah, J. H., Nguen, T. T., Can. J. Chem. Eng., 54, 299 (1976). Modern Plastics Enclyclopedia, 5 1 ( I O A ) , 730 (1974-1975). Scriven, L. E., Chem. Eng. Educ., 2, 150 (1968); 3, 26, 94 (1969). Severinghaus. J. W., Ann. N.Y. Acad. Sci., 148, 115 (1968). Silver, I. A,, Med. Electron. B o / . Eng., 3, 377 (1965).

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Received for review January 21,1977 Accepted August 12, 1977

The authors wish to acknowledge the support of this work by the National Science Foundation through Grant ENG75-09326.

A Procedure for Rapid Degassing of Liquids Hendrick C. Van Ness' and Mlchael M. Abbott' Department of Chemical and Environmental Engineering, Rensselaer Polytechnic Institute, Troy, New York, 12 18 1

A simple glass rectification apparatus proves effective for the rapid degassing of liquids prior to their introduction into a device for vapor/liquid equilibrium measurement by the total-pressure method.

Recent years have seen increasing use of the static method for measurement of vaporlliquid equilibrium data; the work of Gibbs and Van Ness (1972)and of Tomlins and Marsh (1976) are cited as examples. The method requires thorough degassing of the liquids which constitute the system, and unless this is accomplished rapidlydata production is slow. The usual procedures, such as liquid refluxing with periodic vapor withdrawal, alternate freezing and pumping to high vacuum, and vacuum sublimation, all take several days and are tedious. We have developed a batch rectification procedure which is rapid and effective. Degassing is merely the removal of highly volatile components from a relatively nonvolatile liquid; this separation should be easily accomplished by continuous rectification. The only difficulty is that the volatile components are initially present in small amount and must be reduced to near zero concentration. This suggests use of an enriching column operating at almost total reflux, with the enriched volatile components being withdrawn from the top of the column a t a very low rate. Since the amount of overhead product is small, the entire liquid charge is placed initially in the still pot. The apparatus that has evolved from our work is shown in Figure 1. Other designs are surely possible; the present one works well and suits our purposes. I t consists of three main elements: a still pot (A) with thermometer well, a rectifying column (B), and a water-cooled condenser (C). The still pot is a lOOO-mL, round-bottom, single-neck flask connected to an Ace Glass 0-10-mm, high-vacuum, Teflon-plug stopcock with O-ring seals (stopcock 1).The opening terminates in an O-ring joint. The rectifying column is a vacuum-jacketed glass tube with an internal diameter of 2 cm. It is packed over a height of about 50 cm with glass beads, 3-4 mm in diameter. The ends of the column are fitted with O-ring joints of suitable size. The condenser is of the Friedricks type, fitted a t the lower end with an O-ring joint. It is about 5 cm in external diameter and about 20 cm high. The upper opening leads to a vacuum 0019-7874/78/1017-0066$01.00/0

system through a fine capillary, which is the key to successful operation of the apparatus. For our purposes we had the glass blower draw out as fine a capillary as he could. We estimate it to have a minimum diameter of about 0.1 mm and a length of perhaps 0.5 cm. This restriction serves to limit flow of gases and vapor from the top of the column, and unless it is very fine, degassing is accompanied by high loss of liquid from the still pot. The 200-mL reservoir (D) and stopcocks 3 and 4 provide a bypass around the capillary tube, and stopcock 5 opens to the atmosphere. Stopcocks 2,3,4, and 5 are Ace Glass 0-5 mm, high-vacuum, Teflon-plug stopcocks with O-ring seals. Since we degas a variety of organic chemicals, we find it advantageous to use O-rings computed of DuPont's perfluoroelastomer Kalrez, because of its remarkable chemical resistance. During operation the apparatus must of course remain vacuum tight. The O-ring joints placed between the main items of the apparatus allow for easy dismounting of the still pot and the column and also permit interchange of several columns and still pots. The liquid to be degassed is introduced into the still pot through stopcock 1. After connection of the still pot to the column and with cooling water flowing in the condenser, the entire apparatus is evacuated through stopcocks 3 and 4. These stopcocks are then closed, and with stopcock 2 open heat is applied very gradually to the still pot from a heating mantle so as to bring the column into operation at some level below flooding. Boiling in the still pot is not normally a bubbling process, but rather occurs by surface evaporation. For common chemicals such as acetone, benzene, chloroform, and water, the still-pot temperature runs just a few degrees above room temperature. Thus distillation is a vacuum process, and for safety operators are shielded from the apparatus by a protective screen. In applications where the pressure could rise above atmospheric, additional safety precautions would be in order.

0 1978 American Chemical Society