A study of mass transfer in electropolishing of copper

Electrochimica Acta, 1971,Vol. 16,pp. 1477to 1487.Persamon m.

A STUDY

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OF MASS TRANSFER IN ELECTROPOLISHING OF COPPER* M. G. FOUAD, F. N. ZEIN and M. I. ISMAIL Chemical Engineering Department, Faculty of Engineering, University of Alexandria, Egypt, U.A.R.

Abstract-Limiting current was measured for the anodic polishing of vertical copper electrodes in u-H~PO~ acid using: (a) a cell with diaphragm where the effect of Ha evolved at the cathode on the rate of mass transfer at the anode is eliminated. A general correlation of the data may be represented by the equation Nu = 0.72 (ScGr)“.‘3, where Nu is the Nusselt number, SC the Schmidt number and Gr the Grasshof number. The experimental range used in the correlation was 6.49 x lO*l < ScGr < 2.9 x 1014; (b) a cell without diaphragm, where the effect of H, evolved at the cathode on the anodic limiting current and the rate of mass transfer was studied. It was found that H, evolved at the cathode increases the rate of mass transfer and the anodic limiting current by a value ranging from 2.8-28.4x depending on the operating conditions. The effect of initial roughness on the rate of mass transfer and limiting current was also studied; it was found that surface roughness (within the limits studied) has no substantial effect. R&sum&On a ttudie le courant limite dans le polissage anodique d’electrodes en cuivre verticales dans des solutions d’acide o-phosphorique. Deux types de cellules ont et&utilis& (a) Une cellule avec diaphragme oti l’intluence dei’hydrogkne d&gage ?t la cathode Ctait elimine. Dans le domaine etudit (6,49 x IOL1< ScGr < 2,9 x lo’*) les resultats peuvent &re representc5spar la correlation Nu = 0,72 (ScGr) 0s3 oh Nu est le nombre de Nusselt, SC le nombre de Schmidt et Gr le nombre de Grasshof. (b) Une cellule sans diaphragme avec laquelle on a Ctuditl’influencedel’hydrogene d&gage & la cathode sur le courant limite anodique. L’hydro&ne d&gage a la cathode augmente la vistesse du transport de mat&e de 2,8 & 28,4% selon les conditions. On a aussi 6tudiCl’influence de la rugositt initiale. Dans le domaine Btudie celle-ci n’a pas d’effet appreciable sur la vitesse du transport de matiere. Zusammenfassung-Es wurden die Grenzstrijme beim anodischen Polieren von sekrechten Kupferelektroden in OrthophosphorsPure gemessen. Dabei wurden 2 Typen van Zellen verwendet (a) Zelle mit Diaphragma, bei der kein Einiluss des an der Kathode entwickelten Wasserstoffs aufden Stofftransport vorhanden awr. Die Ergebnisse konnen durch die Korrelation Nu = 0,72 (ScGr)“*Ba dargestellt werden, wobei Nu die Nusselt’sche, SC die Schmidt’sche turd Gr die Grasshof’sche Zahl bedeutet. Der untersuchte Bereich war 6,49 x 1Ol1 < ScGr < 2,9 x 1014. (b) Zellemit Diaphragma, wobei der Einfluss des an der Kathode entwickelten Wasserstoffs auf den anodischen Grenzstrom untersucht wurde. Es wurde gefunden, dass der Wasserstoff die Geschwindigkeit des Stofftransports urn 2,8 bis 28,4 oA vergriissert, je nach den Arbeitsbedingungen. Es wurde such der Einfhrss der Initialrauhigkeit untersucht. Im untersuchten Bereich hatte letztere keinen wesentlichen Einlluss auf die Geschwindigkeit des Stofftransports. INTRODUCTION

THE OBJECT of this investigation was to make a quantitative study of the electropolishing of metals using large electrodes. Electropolishing of metals usually takes place at current which is determined by the physical properties of the polishing solution, the initial roughness of the electrode and geometric and hydrodynamic factors. As polishing solutions are usually acidic the cathodic reaction results in evolution of Ha, which reaches the anode and affect the rate of mass transfer_ In this work an attempt was made to study the effect of this hydrogen on the enodic limiting current and the rate of mass transfer. EXPERIMENTAL for

The apparatus consisted essentially measuring the total current and

TECHNIQUE of an electrolytic anode potential.

* Manuscript received 28 November 1969. 1477

cell and auxiliary

The electrodes

equipment

(anode

and

M.

1478

G. FOUAD, F. N. ZEIN and M. I. ISMAXL

cathode) were vertical electrodes of electrolytic copper plates 5-cm wide, 60-cm high and 3-mm thick, fitting exactly into the rectangular Plexiglass electrolytic cell, so that the whole cross-section of the cell was filled with the electrode. The cell design allowed adoption of cathode-anode distances of 5, 10, 15 and 20 cm_ The height of the electrodes was varied from 10 to 55 cm. The anodic limiting currents were measured by determining the current/voltage curve obtained by increasing the voltage applied to the cell stepwise. About 20-30 64 60 56 52 48 44 40 36 32 28 24 20 16

o

Cell

with

diaphragm

12

x

Cell

without

dio

8 4 0

0

100

300 Anode

500 polarization

700

900

I100

1300

. mV

1. Typical current/potential curves obtained during ekctropolishing. ElectroIyte height 50 cm; electrode spacing 5 cm; 14 M H,PO,; 30°C.

FIG.

points were taken for each curve. Figure 1 shows a typical current/potential curve. In order to ensure steady state conditions an interval of 1 min was allowed at each step before the current corresponding to a given voltage was read. The anode potential was measured against a reference calomel electrode. The end of the capillary connecting the reference electrode to the cell was located at mid-height of the anode. The capillary was in intimate contact to the surface of the anode. Before each run, smooth electrodes were prepared by polishing them with emery papers, rinsing in distilled water, washing with alcohol then acetone and finally drying before dipping in the cell. The solution was aqueous o-H,PO, of various concentrations ranging from 6 to 14 M. A new solution was used for each experiment. C.P. chemicals were used for preparation of all solutions. For each set of experimenta conditions the determination of the current/voltage curve was repeated two to three times with freshly prepared electrodes and solution.

Mass transfer in electropolishing of copper

1479

A synthetic fibre diaphragm was introduced between electrodes to prevent the H, evolved at the cathode from reaching the anode. To study the effect of H, evolved at the cathode on the rate of mass transfer at the anode, a cell without diaphragm was used. RESULTS

(a) Cell with diaphragm The results of the anodic limiting current measurements using a smooth anode are summarized in Table 1. Figure 2 shows the dependence of the limiting current density on electrode height. The currents are mean values averaged over the whole electrode surface. The last three coIumns in Table 1 show the dimensionless groups

20

30

Electrode

Concentration

height

40

5055

,h , cm

FIG. 2. Effect of electrode height on limiting cd, of electrolyte, &Pod: l ,14M; x,12M; 0,lOM; A,6M.

q l,SM;

commonly employed in natural convection problems, Nusselt number Nu, Schmidt number SC and Grasshof number Gr, defined by the relations

SC =

;,

Gr

@(pi

=

Pi@

PO) .

The meaning of the symbols is as folows: K,, mass transfer coefficient, cm/s, f, transference number, X,, fiIm factor = unity, z, valency of cation = 2, F, faraday, 96,500 C, ci, concentration at interface, of Cu,(PO,),, g-ion Cu/cm3, D, diffusion coefficient of Cu2+ in H,PO,, cma/s, .u, average dynamic viscosity in poise, g/cm.s, p, average density, g/cmS,

33.0 39.6 50.7 53.8 58.0 32.2 41.6 50.6 52.9

14 12 10 8 6

14 12 10 8 6

14 12 10 8 6

14 12 10 8

30

40

50

55

37.1 42.3 53.1 56.0 65.8

39.8 50.3 57.3 61.1 72.7

43.5 61.0 66.5 62.2 81.0

14 12 10 8 6

20

56.7 76.5 75.5 96.0 86.5

14 12 10 8 6

Limiting current density mA/cmD

10

Electrode height cm

Concentration of WO, M

1,735 1640 1,840 l-925

1.780 1.560 1.850 l-980 2,380

2000 I.666 1.935 2*040 2700

2.140 1,980 2.090 2.222 2.980

2.340 2,410 2.240 2.265 3.320

3.055 3.015 2.750 3.490 3.545

MEiS transfer coefficient x10* cm/s

9,63 13-05 14.22 14.22 12.63 9.63 13.05 14.22 14.22

2,519 2.210 1.767 1,330

9.63 13.05 14.22 14.22 12.63

9.63 13.05 14.22 14.22 12.63

9.63 13.05 14.22 14.22 12.63

9-63 13.05 14.22 14.22 12.63

ci x 10’ g-ion/cma

2.519 2.210 1.767 1.330 @879

2.519 2.210 1.767 1.330 0.879

2.519 2.210 1,767 1.330 0,879

2.519 2.210 1.767 1.330 O-879

2,519 2.210 1.767 1.330 0.879

CP

Average viscosity

1.554 I.513 1.450 1,390

1,554 1.513 1.450 1.390 1,300

1.554 I.513 1.450 1,390 1a300

1.300

1.554 1.513 1.450 1.390

1.554 1,513 1.450 1,390

Average densit g/cm r

TABLE 1. CELL WITH DIAPHRAGM. ELECTRODE SPACING 5 cm. 30°C

1.615 1.595 1,540 1.480

1,615 I.595 1,540 1.480 1,380

1.615 1,595 1a540 1a480 1.380

1.615 1.595 I.540 1.480 1.380

a615 a595 a540 a480 ,380

l-615 I.595 1.540 1*480 1-380

g/Pm’

0.122 0.165 0.180 0.180

0.122 O-165 0.180 0.180 0.160

0,122 0.165 0.180 0,180 0.160

0.122 0.165 0.180 0.180 0.160

0,122 0.165 0*180 0.180 0.160

0,122 0.165 0,180 0.180 0.160

2.25 2.03 1.69 1.33

2.25 2.03 I.69 l-33 0.94

2.25 2.03 1.69 1.33 0.94

2.25 2.03 I.69 1.33 0.94

2.25 2.03 1.69 1.33 0.94

2.25 2.03 1.69 1.33 0.94

SC x10-8

PO

g/cm’

pi -

1320 1266 1400 1470

1233 1096 1280 1353 1650

1106 938 1074 1133 1500

890 833 870 928 1240

648 673 671 627 920

423 423 382 484 491

Nu

ScGr

10.8000 15.8500 21*8000 29.0000

8.1200 11.9200 16.3500 21.8000 29.3000

4*1500 61100 8.3700 11*1300 15@000

1.7500 2.5800 3.5400 4.7000 6.3200

0.5200 0.7640 O-6120 l-3900 1.8700

0.0649 o-0955 0.1318 0.1740 o-2340

x 10-18

1481

Mass transfer in electropolishing of copper

g, gravitational

acceleration, cm/sa,

pi, p,,, density of solution at interface and Y,

f

=

in the bulk, respectively, g/cm3,

kinematic viscosity, cmz/s,

h, electrode height, cm, I,, limiting current density, A/cm2. The physical properties of the solutions used in computations of Nu, SC and Gr are shown in Table 1. The viscosities were measured with an Ostwald viscometer and densities were measured with a pycnometer. The value of the diffusion coefficient of Cua+ adopted for calculation in this work is taken as the average of the theoretical and experimental values. l The average viscosities and densities in Table 1 were evaluated as the arithmetic mean composition between bulk solution and anode/ solution interface. The interficial concentrations,* densities, and viscosities were measured at 30°C for the saturated solution of Cus(PO& in the aqueous phosphoric acid used in the polishing bath. The saturated solution of Cu,(PO& in the different concentrations of o-HsP04 was prepared by dissolving solid Cu3(PO& in the particular concentration of H,PO, at an elevated temperature; the solution thus obtained was allowed to cool to 30°C and kept at this temperature long enough to ensure that equilibrium was reached. Cu2+ was determined in o-HgP04 acid by iodometry. Figure 3 is a log/log plot of Nu USScGr. Within the range studied, 6.49 x 101’ < ScGr ( 2.9 x IO’*, the results can be represented by the relation NU = 0.72 (SCG~)~~~. Statistical analysis of the data in Table 1 led to Nu = O-725 (SCG~)O’~~,with the 95 % confidence limit f0.015 for the exponent.

3 30 3-20 3 IO s

300

_o m

290 2 80 2 70 260 250 II 8

12-o

122

12.4

12-6

12-e

13 0

13.2

13-4

13-6

13.8

14.0

14.4

14-2

14-6

log ScGr FIG. 3. General correlation of natural convection data. Electrode spacing 5 cm; 30°C. Concentration of electrolyte, M,PO,: 0, 14 M; x , 12 M; 0, 10 M; A,6M.

0,

8 M;

Limiting currents calculated from the above equation are nearly in agreement with those calculated from the theoretical finding of 0strach,2 Nu = 0.67 (SCG~)~~~. The exponent 0.23 reveals that the flow of the hydrodynamic boundary layer is laminar. The importance of the above equation in electropolishing is that it makes it possible to predict the polishing current (limiting current) from the physical properties of the polishing solution and the geometry of the electrode. * C was taken as equal to the saturation concentrations of Cu*+ determined experimentally.

1482

M. TABLE

G.

FOUAD,

F.

2. EFFECT OF INITIAL

N.

and M.

ZEIN

I. ISMAIL

SURFACE ROUGHNESS CURRENT ELECTRODE

CELL WITHOUT DIAPHRAGM ELECTRODE HEIGHT 8 cm

ON THE LIMITING

w~c~tvci 3.5 cm 30°C

Initial surface roughness, peak-to-valley height mm

Diffusion layer thickness mm

14 14 14 14 14 14

Smooth 0.04 0.08 0.12 0.16 0.23

0.243 0.243 0.243 0.243 0.243 0.243

55 55 55 55 55 55

12 12 12 12 12 12

Smooth O-04 0.08 o-12 0.16 O-23

0.241 0.241 O-241 0.241 0.241 O-241

75 75 75 75 75 75

10 10 10 10 10 10

Smooth 0.04 0.08 0.12 0.16 O-23

0.233 0.233 0.233 0.233 0.233 o-233

85 85 85 85 85 85

: 8 8

Smooth 0.04 0.08 O-12

O-198 O-198 O-198

100 loo 100

:

0.23 0.16

O-198 0.198

100

6

Smooth

0.160

110

6”

0.08 0.04

O-160 0.160

110

z 6

0.16 0.12 0.23

o-153 0.153 0.153

115 115

Concentration of &PC’, M

Average limiting current density mA/cms

E#ect of initial roughness. Table 2 shows the effect of initial roughness of the anode on the limiting current. Six electrodes having different grades of artificial roughness were used. The roughness studied was horizontal parallel grooves of triangular profile.3 The results show that the limiting current (based on the projected area) is not affected by the initial roughness for most of the cases studied. This is explained by the fact that the diffusion layer thickness shown in Table 2 and calculated by

8N =I

zFc$ L

is larger than the maximum height of the protrusion, ie the electrode behaves as a smooth electrode.3 Accordingly, the equation iVu = O-725 (SCG~)~~~ is valid for rough electrodes (within the limits studied here). In practice, the roughness encountered lies mostly within the range used in this investigation.

Mass transfer in ekctropolishing of copper

1483

In the case of dilute polishing solutions, eg 6 M HsPOo, deviation from smooth electrode behaviour takes place, especially for electrodes of high degree of roughness (see Table 2). The limiting current and the rate of mass transfer increase by about 4.5% over that of a smooth electrode for electrodes of O-12, 0.16, 0.23 mm protrusion height. In these cases, the height of the peaks is larger than the diffusionlayer thickness. This results in an increase in the effective cross-sectional area for diffusion, with a consequent increase in the rate of mass transfer and limiting current. (b) Cell without diaphragm In absence of a diaphragm between the cathode and anode, Hz gas evolved at the cathode reaches the anode along with the displaced solution* and results in an increase in the rate of mass transfer and limiting current. Tables 3-6 show the extent of this increase under different conditions ; it ranges from 2.8 to 28.4 %. TABLE 3. CELL WITHOUT DIAPHRAGM. ELE~RODE SPACING SCIXI.30°C. Increase in mass transfer due to gas stirring at anode %

Concentration of &PO, M

Limiting current density mA/cma

Mass transfer coefficient x 104 cm/s

& gas discharge velocity x 103 cm8/cm9.s

14 12 10 6

71.0 90-o 94-5 120-o 108-O

3.825 3.545 3 -440 4-365 4-420

9-1s 11.60 12-22 15-50 13-93

107.0 74.5 96-O 121.4 122.5

5-65 7.97 10.30 16-20 20-45

25-4 17.7 25-O 25-o 24.6

20

14 12 10 8 6

52.0 73-o 80.0 75-o 99-o

2*800 2-875 2.915 2-725 4.060

9-70 9-41 10-33 9.66 12.78

127.2 132-S 136.3 129-3 205-5

S-30 12.90 16-98 20-22 37.60

19.5 19.7 20.3 20.5 22-2

30

14 12 10 8 6

46-O 58-O 67.0 71-o 85.0

2.480 2.285 2440 2.585 3.490

5-93

7-48 8-65 9.15 10.98

138-O 128-O 147-o 150-O 210-o

11-00 15.42 21-30 28-75 48.50

15-6 15.3 16-9 16-l 17.0

40

14 12 ,lO 8 6

42.0 48-O 60-O 64-O 75.0

2-260 l-890 2-182 2-330 3-080

s-41 6-20 7.74 8-25 9-66

147.0 126 0 139.5 162-O 232-O

1340 17.08 25.40 34.60 55.50

13.2 13.5 13-o 14-3 15.5

50

14 12 10 8 6

37.0 44-O 55.0 59.0 65-O

2.000 1.733 2GOl 2-148 2-665

4-77 6-67 7-10 7-60 8-38

150-o 121.5 117-o 131.3 199.5

14.75 19.50 29 -20 39.80 61.70

12-l 11.1 8.5 9.7 12-o

55

14 12 10 8

35-o 45-o 55.0 58-O

l-885 l-770 2GoI 2.110

4.51 5-80 7.10 7.48

115-o 103-3 122.0 142-O

15-35 22GO 32-00 42.90

Electrode height cm 10

8

ANu

Re

8.7 S&2 8.7 9.6

M.

1484

G.

FOUAD, F. N. ZEIN and M. L ISMAIL

TABLE 4. CELL wrrrrowr DUwm.4oM. ELECTRODE SPACING 10 cm. 30°C

Electrode height cm

Concentration of HsFO~ M

Limiting current density mA/cmz

Mass transfer coefficient x 10’ cm/s

J& gas discharge velocity x10’ cma/cm2.s

ANu

Re

Increase in mass transfer due to gas stirring at anode %

10

14 12 10 8 6

72-O 92.2 94.0 115-o 126.0

3.880 3-630 3.420 4.190 5.160

9-30 11.90 12.12 14.82 16-25

108.2 102-5 96-O 120.2 141.4

5-72 8-15 9.95 15.50 24.95

25.2 25-O 25.3 26.1 24.5

20

14 12 10 z

50-o 75-o 80-O 75-s 100-O

2.690 2.950 2.915 2.750 4.100

6.45 9.67 10.33 9.73 12.90

127.2 138.1 139.0 131-3 207-S

7.96 13.30 16-98 2040 38-00

20.5 20.0 20.8 20.8 22.2

14 12 10 8 6

45.0 56-O 65.0 64-O 85-O

2.420 2.210 2.365 2-335 3.480

5.80 7.20 8.38 8.25 1O-98

131-5 152.8 133-5 148.5 224-O

10.75 1490 20.70 25.95 48.40

15*1 19.3

40

14 12 10 8 6

40.0 47-o 58.0 63.0 76.0

2.155 l-850 2.115 2-295 3.120

5-15 6.06 7.47 8.12 9.80

137.8 128.0 129-3 1644-o 216-5

12.78 16.70 2460 3400 5615

13.0 14-l 12-4 14-8 14.3

50

14 12 10 8 6

36-O 46-O 54.4 57-o 65-O

I-940 1.810 1.980 Z-075 2.665

464 592 7.01 7.35 8.45

142-2 110.5 111-l 134.0 214-O

14.35 20-40 28.85 38.50 61.60

11-8 9.5 8.8 10.3 12.9

55

14 12 10 8

36-O 44-o 53.4 59.0

I-940 l-733 l-940 2-150

464 5-67 688 7-60

148-O 137-o 102.8 183.5

15.80 21-50 31.1 43 -70

11-l 11.4 7.5 12.5

30

15.9

18-O 18.3

TABLE 5. CELL WI-I-HOUT DIAPHRAGM. ELECTRODE SPACING 15cm. 30°C

Concentration of KJ’O, M

Limiting current density mA/cmz

Mass transfer coefficient x10’ cm/s

Hz gas discharge velocity x103 cmS/cm”.s

14 12 IO :

72.8 92-8 93-3 119-o 119.0

3.920 3.650 3.400 4-340 4.870

9.40 1 l-95 12-02 15-35 15.35

110-O 103-o 95-o 121.0 131-o

S-80 8-20 9.90 16.05 22-60

25.3 25-l 25-2 25-2 24.0

20

14 12 10 8 6

50.5 76-O 80.0 79-o 102.0

2.720 2-995 2-915 2.880 4.180

6.50 9.80 1O-32 1o-20 13.15

125-8 141-4 166.3 140-5 128-O

8.05 13-45 16-98 21.35 38.80

19.9 20-3 24.8 21.3 24.4

30

14 12 10

46-O 57-o 66-O 74-o 86-O

2-480 2-242 2.402 2-695 3-520

5-94 7-35 8-50 9-55 11.10

131.5 129-5 135-o 165.0 222-o

1100 15-16 21-00 3000 4900

14-7 15.8 15-6 17.2 17-8

Electrode height cm

10

:

ANu

Re

Increase in mass transfer due to gas stirring at anode %

Mass transfer in eiectropoiishing of copper

1485

Table 5 (con&Y) Concentration Electrode of height HJQ cm M

Limiting current density mA/cma

Mass transfer coefficient x 100 cm/s

Ha gas discharge velocity x 10’ cm’/cm’.s

ANu

Re

Increase in mass transfer due to gas stirring at anode %

40

14 12 10 8 6

41.0 48-O 61.0 63-O 76-O

2-210 l-890 2.220 2.295 3.115

5.29 6.20 7.86 8.12 9.80

150-O 150-3 157.8 159-5 205-O

13.10 17.10 25.80 34xlO 56.15

13-9 16.5 16.5 14.3 13-4

50

14 12 10 8 6

38.0 44.0 57-o 59.0 64.0

2.045 I.730 2.080 2-150 2.625

4.90 4.67 7.55 760 8.25

150-O 108-O 123.7 146.5 199.5

15-15 19.50 30-20 39.85 60-70

11-8 9.7 9.4 10.9 12.3

55

14 12 10 8

37.0 45-o 54.0 58.0

1 a990 1.970 l-970 2.115

4.77 5.80 6.96 7.48

41-l 176.5 136-O 164-o

16.20 22-W 31-50 43-W

2-8 14.8 9-9 11-3

TABLE 6. CELL WITHOUT DIAPHRAGM ELECTRODE SPACING 20cm. 30°C

Electrode height cm

Concentration of I&IQ M

Limiting current density mA/cm*

Mass transfer coefficient x10’ cm/s

Ha gas discharge velocity x 103 cmalcmB.s

10

14 :z 8 6

72.9 96-O 95.0 123.0 131-o

3.920 3.780 3.460 4.480 5.360

20

14 12 10 8 6

52.0 78.0 81-O 81-O 104

30

14 12 10 8 6

40

Increase in mass transfer due to gas stirring at anode %

ANu

Re

9-40 12.35 12.25 15.90 16.95

110-o 107.0 96.0 131-o 165.2

5-80 S-50 1 O-05 1660 24.85

25.3 25.2 25-O 26.7 28-4

2-800 3.070 2-950 2.950 4.260

6.85 10.05 lo-44 1 O-44 13.45

133.3 142.5 141-2 139.2 228-O

S-30 13.80 17-20 2190 39.60

20.2 19.9 20-9 203 23 -8

46.5 58-O 67.0 76-O 87.0

2-500 2.285 2440 2-765 3.565

6-W 7.50 8.65 9.80 1 l-20

140-5 124.5 147.0 171-o 222-o

11.12 1544 21.30 30-80 49.60

15-7 14-9 16.9 17.5 17-6

14 12 10 8 6

42.0 49.0 61.0 65-O 77-o

2-260 l-930 2-220 2-365 3.160

5-42 6.32 7.89 8.40 9.95

171.0 141.3 139-5 157-S 205.0

13.40 17.40 25.80 35.10 37.00

15-3 15.0 12.8 13.6 13.3

50

14 12 10 8 6

39.0 45-o 58-O 62.0 65.0

2.100 l-772 2-110 2.260 2-660

5.05 5.80 7.50 8-00 8.40

168.5 160.5 139-O 169-O 199.5

15.55 19.93 30.70 41.85 61-60

13.0 14.8 10.5 12.1 12-l

55

14 12 10 8

36-O 44-O 56-O 59-o

1.940 l-731 2xl40 2-145

4.65 5.68 7.25 7.60

135.5 118-S 158.3 192-O

15.80 21-50 32-60 43-70

10-l 1Z 13.3

M. G. FOUAD,F. N.

1486

ZEIN

and

M.

I. ISMAIL

Figure 4 shows the dependence of the increase in the rate of mass transfer (expressed as A Nu, where A Nu = NU cell without diaphragm - Nu,,,, with diepw~& On

b

5

IO

15 20

25

30

35

40

45

50

55 60

65

70

ffe

no. 4.

Effect of hydrogen evolved at cathode on the rate of mass transfer at anode. El&rode spacing 5 cm; electrode height 10-55 cm; 30°C. Concentration of electrolyte, HSPOI: 1, 14 M; 2, 12 M; 3, 10M; 4, 8 M; 5,

6, M.

the gas discharge velocity, height of the electrode and the physical properties of the soIution, these variables can be combined in a modified Reynolds number;

Re

--, p0J-f -

P

where p,, is the density of the solution, g/cm 3, Vthe gas discharge velocity, cms/cmas at the limiting current, H the electrode height, cm, and ,X the viscosity of the solution,

g/ems . With increase of Reynolds number, the increase of the rate of mass transfer initially increases, reaches a maximum and then decreases. This decrease can be explained by the fact that as the height of the electrode increases, the action of the gasdisplaced solution at the anode is confined to the upper part of the electrode. This may be attributed to the possibility that the stream of the gas-displaced solution is unable to go deeper due to the increased solution resistance.4 Figure 5 shows the effect of distance between the electrodes on the incremental increase in the rate of mass transfer due to Hz discharge. At small electrode spacing, the effect of hydrogen in increasing the limiting curent at the anode becomes more pronounced. It is worth mentioning that the electropolishing in both types of cell resulted in a highly polished anode surface. In practice it is recommended, therefore, to use a cell

1487

Mass transfer in electropolishingof copper

230

210

I30 I80

I60 150

130 120 IO 100

2

4

8

JO

14

16

20

22

26

.Qe

5. Effect of electrode spacing on rate of mass transfer. Concentration of electrolyte, HBP04, 12 M; 30°C. Electrode spacing 0, 20 cm; x, 15 cm; 0, 10 cm; 0, 5 cm. without diaphragm in electropolishing processes as this will increase electropolishing without affecting the quality of the polished surface. AcknowCec&ement-We

the rate of

wish to express our thanks to Prof. N. Ibl for valuable discussions.

REFERENCES 1. N. IBL, in Advances in Electrochemistry and Electrochemical Engineering, ed. P. DELAHAY and C. W. TOBIAS, Vol. 2, p. 108. Interscience, New York (1962). 2. S. OSTRACH, Nat. Advisory Comm. Aeronaut. Tech. Notes, No. 2635 (1952). 3. M. G. FOUAI) and A. A. ZATOUT, Electrochim. Acca 14, 909 (1969). 4. G. H. SEDAHMED, Thesis, University of Alexandria (1969).