However, for droplets film boiling on rough surfaces and for film boiling on rough immersed surfaces, the contact is quasicontinuous (fluctuating about a mean) and a physical model is less clear. The foregoing observations suggest three parameters which are important in liquid-solid contact at stable film boilins temperatures: the subcooling. parameter
[E (sL)l;
- .
the- ratio of (maximum surface roughness) to
.
-
. _
k L
Nu = Nusselt number, h L / k Pr = Prandtl number, c p p / k q = local heat flux t = temperature
GREEKSYMBOLS a
6
(gas laver thickness): and a Biot modulus based on mean , ,
E
roughness element characteristic geometry
,u
‘51.
~ L .
‘The first
l
-
1
two regulate interface stability and onset of contact due to “tickling” ; the third determines surface temperature relative to heating element “bulk” temperature in the presence of time-dependent phenomena a t the solid surface-i.e., local surface cooling. I t should be possible to express a n effective area ratio and resulting Nusselt number ratio in terms of these parameters to permit comparison of contact and zero contact cases. I t may become desirable to control heat flow by controlling liquid-solid contact in the stable film boiling regime. If so, there appear to be a t least three methods available for development : application of external pressure fields; suction through heating elements; and use of electrostatic field. The first has been tentatively explored by DiCico and Schoenhals (4) who shobved that pressure pulsations enhance heat flow. The second has been developed by Weyner and Bankoff (7). The third has been used by Markels and Durfee (6) in pool boiling and by the present author in droplet film boiling. I n all these cases, it will be necessary to learn to avoid the destructive instabilities described above if stable operation is to be achieved a t high surface temperatures.
Nomenclature
A
= surface area = specific heat a t constant pressure = heat transfer coefficient
cp h
= thermal conductivity = characteristic length
T
= = = = =
thermal diffusivity vapor layer thickness roughness element characteristic dimension time dynamic viscosity
SUBSCRIPTS 1
= contact = liquid-solid interface = liquid
o
=
c
i
steady state
= total
literature Cited (1) Bankoff, S. G., Mehra, V. S., IND.ENG.CHEM. FUNDAMENTALS 1. 38 11962).
( 2 ) ’Berenson,‘ P., Mass. Inst. Technology, Cambridge, Mass., Tech. Rept. 17 (1960). (3) Bradfield, W. S., Proceedings of Symposium on Two-Phase Flow, University of Exeter, Vol. 11, p. A301, June 1965. (4) DiCicco, D. A., Schoenhals, R. J., J . Heat Transfer C86, No. 3,
457 (1964). ( 5 ) Bradfield, \V. S., Barkdoll, R. O., Byrne, J. T., Convair Scientific Research Lab., San Diego, Calif., Research Note 35 (1960). (bj-Markels, M., Jr., Durfee, R. L., A.I.Ch.E.J. 10, 106-9 (January 1964). (7) Wayner, P. C., Jr., Bankoff, S. G., Ibid., 11, 59-64 (January 1965). ( 8 ) Westwater, J. W., Hosler, E. R., ARSJ 10, 553-8, (April 1962). ( 9 ) Zi& S. M., Wright, R. W., Morse, A. F., et al., Research Lab., Ramo-Wooldridge Corp., Camoga Park, Calif., Rept. RWC-RL-167 (1960). (10) Zuher, N., Tribus, M., Dept. Engineering, University of California, Los Angeles, Rept. 58-5 (1958). RECEIVED for review August 5, 1965 ACCEPTEDDecember 1, 1965 Work supported by the National Science Foundation under Grant G20191.
DIELECTROPHORETIC PROCESS FOR LIQUID-LIQUID MIXING [ B R U C E 0 . HLOLLAND Central Research Laboratories, Broken H i l l Proprietary Co., Ltd., Shortland 2N, N.S. W., Australia
OLLOWING
the publication of a paper by Cropper and
FSeelig (2) describing mixing with an electrostatic field, but also influenced by the earlier work of Swinkels and Sullivan (6) on the movements of molecules in nonuniform electric fields, experiments were designed to evaluate the factors controlling the mixing of miscible polar and nonpolar liquids under the influence of high-intensity, pulsating, nonuniform electric fields. The apparatus used in these experiments was basically similar to that described by Cropper and Seelig ( Z ) , but with variations in the specifications and arrangement of the various components. This apparatus is not described in detail here, but the essential circuitry is shown in Figure 1. Major variations from the techniques used previously were the use of reaction cells of varying shapes and dimensions to 204
I&EC FUNDAMENTALS
investigate the effects of cell geometry, and the adoption of a modified Schlieren technique (7) to detect and record liquid movements and changes in density. Experimental Procedure
Suitable volumes of the two liquids were introduced separately into the cell, care being taken to avoid mixing, and the electrode spacing was adjusted. A constant potential was applied across the electrodes, and the time for complete mixing, based on the Schlieren pattern, was noted with the aid of a stopwatch. This procedure was repeated a t intervals of 0.5 kv. over a range of applied potentials commencing from 5.0 kv. and continuing until the time for complete mixing was too short to be measured accurately. The upper limit, depending on the particular combination of liquids used and the electrode spacing, was usually between 12 and 16 kv. Each
~~~
~
~~
A liquid-liquid process utilizing high-intensity nonuniform electric fields was critically examined.
An exponential expression relating the time required for complete mixing to the field strength was experimentally derived using various combinations of polar and nonpolar liquids. Parameters in this expression include the dipole moment of the polar phase, interfacial area, electrode separation distance, viscosity, and the respective weights of the polar and nonpolar liquids, Some observations concerning the mixing process are reported.
run \vas made in triplicaie, the order being randomized so as to minimize fortuitous errors. After all measured and other values were converted into hlKS units, the resultant data were plotted, and from the curves thus obtained equations were derived for each combination of experimental conditions.
240v
Curves illustrating ten separate sets of experimental conditions for the system o-dichlorobenzene-cyclohexaneare shown in Figures 2 and 3. Examination of these experimentally derived curves showed that in every case the curve \vas described by an exponential equation of the general form:
F
=c
x
"3
R/ABLE SPEED MOTOR
AUTOTRANJFORM
c ROTARYwr$"
240 v 5
IO-kL
Further detailed mathematical analysis of the data indicated that constant c was a function of the dipole moment and the cell geometry. This constant \vas then expanded into:
x @)-I
c = p(u
This expanded value of c agreed with the experimental data with a confidence level of 0.94. Constant k \vas similarlv expanded into a n expression incorporating the viscosity of the nonpolar liquid and a nonI
I
.
1
I
30
60
Figure 1.
Circuit for dielectrophoretic mixing
I
I
I
1
I
90
/20
150
180
210
TME @ € C O N M )
Figure 2. Relationship between field force and mixing time for system o-dichlorobenzene-cyclohexane Interfacial Area,
sq. M.
8.0 8.0 8.0 8.0
10-4
Spacing,
M. x
10-2
1 .o 1 .o 1.5 1.5
C~H~C~Z, Kg. x
loW3
2.613 2.613 2.613 2.613
C6H12,
Kg. x
7.731 11.609 7.731 11.609 VOL 5
NO. 2
MAY
1966
205
jr,,
(SECONDLT)
Figure 3. Relationship between field force and mixing time for system o-dichlorobenzene-cyclohexane interfacial Area,
sq. M.
10-4
12.5 12.5 12.5 12.5 12.5 12.5
dimensional factor relating the respective weights of the two liquids. This constant ultimately took the form:
where vnp = viscosity (newton x second/sq. meter). The confidence level of this expression, compared with the experimental data, was found to be 0.89. I n the present investigation some 90 experiments were carried out involving combinations of two nonpolar liquids, benzene and cyclohexane, with four polar liquids: acetic acid, nitrobenzene, o-dichlorobenzene, and pyridine. The reaction cells used were of circular, square, and rectangular cross section with cross-sectional areas of 8.0 X lo-' and 12.5 x sq. meter in each shape. The electrode ~
Table I .
Values for Nonpolar and Polar liquids
Density Dielectric constant Dipole moment Viscosity
Nonbolar Liauids Benzene Cyclohexane 0.0000874 0.0000779 2,281 2.025 0 0 0.00645 0.00958
Polar Liquids Acetic Nitro- o-Dichloroacid benzene benzene Density 0.0001409 0.0011987 0.0001306 Dielectric constant 6.15 34.82 9.93 Dipole moment 1 .74 4.22 2.25 Viscosity 0.01115 0.02022 0.01318
206
l&EC FUNDAMENTALS
Pyridine 0.0009787 12.3 2.21 0.000974
Spacing,
M.
10-4 0.5 0.5 1 .o 1 .o 1.5 1.5
CahCb, Kg. x
1.307 2.613 1.307 2.613 1.307 2.613
CE.HIZ, Kg. x
11.609 11.609 15.478 15.478 15.478 15.478
spacings used were 0.5 x lo-*, 1.0 x and 1.5 x meter, but a few experiments were carried out using electrode meter. I n spacings of2.0 x lo+, 2.5 x lop2>and 5.0x the present work no significant differences were found between the effects due to different shapes of reaction cells. The values in MKS units for density, dielectric constant, dipole moment, and viscosity of the liquids used are shown in Table I. The electric current determined for the various systems was, as expected, small, ranging from about 0.001 to 0.05 ma. depending on cell geometry, the field force applied, and the particular system under investigation. Some data for the system o-dichlorobenzene-cyclohexane are presented in Table
11. The power requirements for the two sets of conditions quoted in Table I1 were 4.11 and 1.33 watts per liter, respectively. A comparison was made by mixing o-dichlorobenzene and
Table II.
Data for System o-Dichlorobenzene-Cyclohexane
I Weight of CsHdC12, kg. X Weight of CaH12, kg. X Interfacial area, sq. m. X Electrode spacing, m. X Field force, newtons/sq. m. Current, ma. Pulse width, sec. Pulse interval, sec. Time for complete mixing, sec.
2.316 11.609 8.0
1.5 5.8 0.009 0.75 0.95 115
11 2.316 15.478 12.5 1.5 2.4 0.003 0.75 0.95 125
T h e process described above is considered to be mainly dielectrophoretic, but it is felt that electraDharetic effects cannot be completely disregarded
sufficiently wide area. The viscosity and some other physicochemical properties can also be modified under influence of a high-intensity electric field (7, 4). There is also an indicaiion, a t present not completely confirmed and hence not published, that some thermodynamic properties, such as heat capacity and heat of solution, may be slightly altered under highintensity electric field effects. Although these effects may be small, they should not be completely ignored. Further detailed examination of the mechanisms and processes involved in the turbulence are beino; carried out. and it is expecte a later, Acknot
Tribulc IS "ut: TO J. 0 . xatwmc, now ar me acnoo, 01 Lnemical Engineering, University of New South Wales, and W. G. Kirchner, University of Newcastle, for many stimulating discussions, and for suggestions concerning the evaluation and interpretation of the experimental data. T o Kirchner, in particular, credit is due far the design of the experimental circuitry. T h e permission of the Research Manager of T h e Broken Hill Proprietary Co., Ltd., Central Research Laboratories, to publish this paper is also gratefully acknowledged. Nomenclature
All quantities are expressed in MKS units. = interfacial surface area, sq. m. 6, k = constants a
T h e initial indication of a 1~~ ootential aoolied across the cell was turbulence at the interface, increasing in intensity as the potential was increased. This is illustrated in Figures 4 and 5 . This turbulence was interpreted mainly in terms of dipole orientation, particularly in the polar liquid, and the subsequent movement of these toward areas of high field intensity. It is very probable that the interfacial turbulence is not due to a single mechanism, but is the complex resultant of the effects of several processes. Following- the investigations carried out by Pohl (5),it has become conventional to separate the effects of electrical forces in dielectric fluids into two categories: dielectrophoretic and electrophoretic. Dielectrophoretic effects are those which result from the action of a n applied electric field on dipole molecules constituting the bulk of the fluid, and electrophoretic effects arise from the action of the field on charged particles within the fluid. ~~~~
~
~
~
~
~~
~
~
~~
~
~
~
~~~~
SUBS
