barnea 1976

On the Effective Viscosity of Liquid-Liquid Dispersions

E. Barnes* and J. Mizrahi

/M/ hstitute for Research and Development, POB 3 73, Hsifa, lsrael

An experimental study on the effective viscosity of relatively coarse and unstable liquid-liquid dispersions is reported. Such dispersions are of importance in processes in which two immiscible liquid phases are agitated and pumped to induce mass and/or heat transfer. The effects of the viscosities of the dispersed and continuous phases, the volumetric concentration of the dispersed phase, and surface active impurities have been studied. The experimental results are in general agreement with a theoretically based extension of a previous correlation for the effective viscosity of solid-liquid suspensions. The technique described can be conve- niently used for the quantitative evaluation of the effects of surface active contaminants by means of interfacial effective viscosity measurement.

Introduction Many experimental studies have been published pertain-

ing to the effective viscosity of suspensions of spherical solid particles and of emulsions; however, no data are available, to the best of our knowledge, concerning the effective viscosity of liquid-liquid dispersions.

In this context, the term dispersions (unlike emulsions) is meant to designate inherently unstable liquid-liquid systems in which, due to the relatively high coalescence rate, the primary break is completed within a relatively short time. Such dispersions are generally prepared inten- tionally in order to transfer mass and/or heat between two immiscible liquid phases, and they must be inherently unstable, since relatively fast separation of the dispersions produced presents a practical constraint. Such dispersions, produced by mechanical mixing, are generally character- ized by a relatively large mean drop diameter (in the range of 50-600 p while emulsions are in the range of 1-10 p). This is an indirect consequence of their relatively high coalescence, since the mean drop diameter produced by a mixer is a result of a dynamic equilibrium between droplet break-up and recoalescence processes.

In solvent extraction and direct-contact heat transfer processes, dispersions are agitated, pumped, flow through pipes and conduits etc., and the rheological properties of such dispersions are therefore of importance. Moreover, as will be shown, valuable quantitative information may be obtained about the degree of purity of the system and the presence of surfactants by measurements of the dispersions effective viscosity. Such a quantitative index may allow one to define the state of contamination of a liquid- liquid system and/or to correlate it with other dispersion bulk properties.

Theoretical Aspects Einstein (1906, 1911) was the first to present a theoreti-

cal analysis of the effective viscosity of suspensions pertaining to the limiting conditions of spherical solid particles at infinite dilution:

Einsteins asymptotic solution was extended by Taylor (1932) to include spherical fluid particles, while retaining the limitation of infinite dilution:

b = 1 + 2 m [ -1 2/511c + Pd = PC P c + P d

0.4 + P d / P c 1 + P d / P c

1 + 2 . 4 ] (@--+O) (2) The increase in viscosity expressed by eq 1 is due to the distortion of the field of laminar shear flow in the vicinity of each particle, which has the effect of increasing the velocity gradient in its immediate neighborhood. Taylors extension (eq 2) accounts for the effect of internal circulation within the fluid drops due to transmission of the tangential and normal stresses across the interface between the continuous and the dispersed phases. These result in a reduc- tion of the magnitude of the distortion of the flow pattern outside the drops. Equation 2 is reduced back to eq 1 if the dispersed phase viscosity is very large compared to that of the continuous phase, i.e., p d / P c - m .

The left-hand term reaches a lower limiting value given by eq 3 for the case where the dispersed phase viscosity is negligible compared to that of the continuous phase:

= 1 + 9 (/Ld//Lc - 0; 9 - 0 ) (3) The presence of surfactants in the system tends to retard the internal recirculation, since the motion of the interface creates a concentration gradient of surfactants on the interface and, consequently, a gradient of interfacial tension. Taylors equation was further extended by Oldroyd (1953, 1955) to include the case of droplets with partial internal circulation:

PC

where d is the droplet diameter, { is the two-dimensional shear viscosity of the film, and is the area viscosity of the film, i.e. the two-dimensional analogue of the bulk viscosity.

As the term: , s = S [ ( 2 t + 3a) ]

has the dimensions of viscosity, it may be called the effective surface viscosity or the interfacial retardation viscosity, P ~ .

120 Ind. Eng. Chem., Fundam., Vol. 15, No. 2, 1976

In eq 6, w s is added to gd; therefore one may substitute Pd*, the effective viscosity of the dispersed phase for the sum (pd + w S ) , for the sake of simplicity:

Oldroyds approach is similar to that used by Boussinesq (1913) in order to extend the Hadamard (1911, 1912)- Rybczinsky (1911) equation for the terminal velocity of fluid spheres in an immiscible fluid, to include cases of partial internal recirculation.

Equations 6 and 7 may also be derived using the Levich (1964)-Newman (1967) approach with a different interpretation for ws:

where y is the interfacial tension, r is the surface concentration of surfactants, and K is the retardation constant.

The different approaches result in the same equation, but each has a different physical meaning for ls. The exact interpretation of ps has, however, no practical importance, since some of the factors involved in either eq 5 or 8 may not be measured directly.

Equations 2 and 7 have been experimentally corrobo- rated by Nawab and Mason (1958) in an extensive experimental program with dilute emulsions. Some of the liquid- liquid systems studied by these authors fitted closely eq 2, while others deviated from it; the latter results could be fitted to the general form of eq 7 using empirical values of ps . It can thus be seen that eq 7 is a valid extension of eq 1 for dilute emulsions which accounts for the slip velocity on the liquid-liquid interface resulting from either full or partial internal circulation inside the drops.

The extension of eq 1 to higher suspension concentrations presents a significantly greater problem. Numerous attempts at such a theoretical extension have been published, most of them falling within one of the two following categories. (a) The first is the evaluation of the contribu- tion of reflections of higher order, using the reflection technique. According to this technique Einsteins solution, represented by eq 1, could be derived taking into consideration only the first reflection. More elaborated models lead to a power series:

!!9 = 1 + K19 + K&J + K3a3 + - - - (9) in which K1 equals 2.5 for spherical particles with no-slip condition. (b) The second approach is the use of cell models, according to which the suspension is replaced by a rep- resentative particle confined in a statistically representa- tive cell (usually spherical), the ratio of the particle volume to the cell volume being equal to 9. Cell models have been extended to account for either full or partial internal circulation within the drops, e.g., by Yaron (1971). However, mathematical derivations obtained by cell models do not reduce to Einsteins limiting equation as 9 approaches zero (Happel, 1957).

A theoretically based exponential function has been de- veloped by Vand (1948):

PC

~ = e x p [ 2.59 . ] PC 1 - 0.6099 (10)

Mooney (1948) has shown that his semitheoretical correlation could successfully be used to correlate separate experimental data from various sources, using values of K varying between 0.75 and 1.5.

The empirical picture was not clear, since the plot of w4/pC vs. a, obtained by various authors for suspensions of spherical solid particles for various solid-liquid systems and with various measuring techniques, did not result in a unique curve. This implies either that the effective viscosity is not a unique function of 9 (as predicted theoretically) or that various sets of experimental results include rather large errors due to non-Newtonian effects, surface roughness, deviation from sphericity, etc.

Thomas (1965) has shown that a much more coherent, experimental picture may be obtained by recalculation of data of 16 sources, eliminating several sources of error and smoothing secondary effects, the scattering being reduced to reasonable limits of f 7 % at 9 = 0.2 and f13% at 9 = 0.5.

Barnea and Mizrahi (1973) have shown that the averaged experimental data of Thomas yield a straight line when re- plotted as l/ln ( ~ ~ / p ~ ) vs. 1/9 implying, for the exponential correlation:

From the slope and intercept, K1 and K2 have been calculated to be respectively 2.66 f 0.20 and 1.00 f 0.03. Taking into account the theoretically based equations due to Vand and Mooney, the experimental picture of solid-liquid suspensions may be reasonably represented by eq 13, which reduces Einsteins equation (eq 1) as 9 approaches zero:

= exp [ -1 2.5@ PC 1 - @

If it may be assumed that there is no interference between the effects of particle interactions and internal circulation, eq 7 may be extended to liquid-liquid dispersions of significant concentrations, by analogy to eq 13.

A somewhat similar exponential equation which did not include retardation effects was suggested by Leviton and Leighton (1936) as an extension to Taylors equation (eq 2);

- = exp [ 2.5(04 Pdi(c) (@ + @/3 + QLL;J)] (15) PC 1 + Pd/Pc

Leviton and Leighton support eq 15 by their own experimental results. Numerical comparison of eq 14 and 15 re- veals a reasonable agreement in the range of 9 between 0 and 0.5.

Equation 14 implies that: a plot of (In ( ~ ~ / ~ c ) vs. @/(l - 9)) should result in a straight line with a slope between or equal to 1.0-2.5; an increase of &/!.Lc should result in an increase of the straight line slope; and the presence of surfactants should increase the slope. These predictions were confirmed in the experimental study presently reported.

Experimental Section Previous experimental studies of effective viscosities

of two-phase systems have been using suspensions of solid particles of the same specific gravity as the liquid phase, or

Ind. Eng. Chem., Fundam., Vol. 15. No. 2, 1976 121

Table I. Physical Properties of the Phases Used at 20 C Viscosity, Density,

Phase Produced by Grade Saturated with CP g/cm3 Glycerine 76% Glycerine 82.5% Glycerine 89% Toluene M oil M oil Ethylene glycol Ethylene glycol Water Water Tetradecane Silicone oil

Frutarom (Israel) Frutarom (Israel) Frutarom (Israel) Frutarom (Israel) Paz (Israel) Paz (Israel) Merck Merck -

- Fluka Union Carbide

n

CP CP CP CP Tech. Tech. Pro- Analysi Distilled Distilled Tech. Tech.

Figure 1. The experimental apparatus.

very small particles in a relatively viscous liquid phase or stabilized emulsions. The relative stability of the suspension is a common feature to nearly all previously reported experiments. A viscometer for coarse, fast settling suspensions (of the rotational concentric cylinder type, with pro- vision for recirculation of the suspension), which has been described by Clarke (1967), could not be applied to coales- cing dispersions.

A Brookfield Model LVT viscometer, immersed in a 2-1. beaker (equipped with baffles and a mixing impeller-Fig- ure 1) was used for the present experiments. The technique used was to introduce both liquid phases into the beaker in the desired proportions (but constant total volume in order to retain constant immersion depth) and to produce a dispersion by mixing. The mixing was then stopped and several measurements were taken after 15 s; the dispersion was then remixed and the effective viscosity was remeasured, a t least three times and with at least two different levels of shear rate. The results of measurements with different shear rates (usually a factor of 2 in shear rate still enabled accurate reading) had revealed a Newtonian behavior; in the range investigated (0 < @:S 0.33; shear rate being var- ied by a factor of 2), deviation being not significantly greater than the overall accuracy of the measurement which was f 2 % . The results plotted in the figures are always the mean of the actual measurements.

Since the liquid rotational movement may interfere with the measurement, preliminary tests were conducted to evaluate this effect using single-phase systems. Thus, the

Toluene Toluene Toluene Glycerine solutions Water Ethylene glycol M oil Tetradecane M oil Silicone oil Ethylene glycol Water

40.0 82.8

202 0.63

30.0 31.0 21.8 21.7

1.055 1.025 2.39

402

1.198 1.216 1.233 0.867 0.868 0.870 1.146 1.114 1.00 1.00 0.762 -

viscosity of three glycerine-water solutions of known concentrations and viscosities (from literature sources) was measured by: (a) an Ostwald viscometer; (b) the Brookfield viscometer in conventional application as recommended by the manufacturer; and (c) the Brookfield viscometer in the setup described in Figure 1 and following the above described procedure.

I t was established that 10-15 s after mixing was stopped was sufficient time to eliminate this interference, with a negligible error in the viscosity reading. Measurements taken by method (c) 15 s after mixing was stopped were in good agreement with the results of methods (a) and (b) and the literature values.

The precise temperature was measured during each experiment. A graph of the viscosity of the continuous phase (saturated with the dispersed phase) vs. the temperature, in the range of 15-25 OC, was prepared for each phase system.

The ratio of the measured effective viscosity to the continuous phase viscosity a t the experimental temperature (taken from the graph) was used as an index. Since the setup was not insulated and the temperature kept at 20 f 2 C, the dispersed/continuous phase viscosity ratio may fluctuate somewhat within each set of experiments, con- tributing to the overall error.

The measured viscosities and densities of all the mutual- ly saturated phases used are given in Table I. The viscosity of all continuous phases and part of the dispersed phases was measured with the Brookfield setup following the very same procedure as for measurements of effective viscosities of dispersion. The viscosity of dispersed phases of relatively low viscosity (less than 15 cP) was measured with an Ostwald viscometer.

I t was originally intended to prepare phase systems with very small phase density differences so that separation of the unstabilized system would be slow. It was found, however, that in very pure systems (i.e., systems of low w S ) , separation occurred within few seconds, even when the density difference was less than 0.005 g/cm3. Moreover, it was found that for such very pure systems, where the viscosity ratio is high, it is generally very difficult to disperse the less viscous phase in the more viscous. Work with very pure liquid-liquid system was therefore considered unpractical. Another operational constraint was imposed by the fact that the Brookfield LVT model could not measure viscosities lower than 15 CP with reasonable precision, this dictat- ing that the viscosity of the continuous phase should be higher than this value.

The dispersion concentration range posed a further constraint and was limited to @ less than 0.33 for the following reasons. As was mentioned above, the natural tendency of systems with a high viscosity ratio is generally to keep the less-viscous phase as the continuous one. Spontaneous


* / I F *

Figure 5. Experimental results obtained with the system ethylene glycol-M oil.

*/l+

Figure 2. Experimental results obtained with the system water- silicone oil.

I I I 1

01 03 04 05

Figure 6. Experimental results obtained with the system water-M oil.

+/Fa Figure 3. Experimental results obtained with the system tetradecane-ethylene glycol: 0, untreated tetradecane; 0, tetradecane treated with active carbon.

15

I I 01 02 03 04 05

+/ lW

Figure 4. Experimental results obtained with the system M oil- ethylene glycol.

phase inversion took place in many cases, whenever the dispersed phase concentration was raised above 40-50%. In other cases, irregular and nonreproducible results, as well as non Newtonian effects, were obtained with dispersed phase concentration exceeding 30-50%. The reasons for these anomalies may be: the coalescence rate of such concentrated dispersions is relatively high, resulting in relatively large droplets (of diameter exceeding 1 mm) and fast separation; the formation of multiple dispersions, Le., the presence of continuous phase droplets within the dispersed phase drops; and formation of a dispersed phase film on the viscometer, etc. This phenomenon is demonstrated in Figure 2 in which the experimental results for the water- silicone oil (water dispersed) system are given. The plot of In (p$ /pc) vs. (@/l - @) results in a fairly straight line, as is predicted by eq 14, up to a concentration of about @ = 0.315, while beyond this concentration, an inconsistent picture is obtained. The straight line has a slope of 2.28, Le., much closer to the slope of 2.5 predicted for solid spheres than to the slope of 1.003 expected for a system with a pd/pc ratio of 0.00255 with full internal circulation, corre- sponding to an interfacial retardation viscosity of 2338 cP.

q1-+ Figure 7. Experimental results obtained with the system toluene- glycerine solutions of various concentrations, with and without the addition of 8 ppm of AHP-12 surfactant. Original phases: i. , 89% glycerine; 0, 82.5% glycerine; 0, 76% glycerine. With 8 ppm AHP- 12: a, 89% glycerine; 0 , 8 2 . 5 % glycerine; ., 76% glycerine.

In each of the 1 2 different sets of data collected, the effective viscosity of the dispersion was measured as a function of the dispersed phase volume fraction, which was var- ied from 0 to 0.33. The sets were different in either one or more of the following parameters: phase system-the ratio of continuous to dispersed phase viscosities in the liquid pairs investigated ranged from 0.7 to 390; continuous phase viscosity, at apparently the same level of surface active contamination; level of surface active contamination (calculated pLs ranged from 29 to infinity).

All the experimental results are shown in Figures 2-7 as plots of In (pm/pc) vs. (@/I - a). Figures 2-6 indicate the asymptotic solutions for solid spheres (eq 14) and full recirculation (eq 15 with ps = 0, i.e., pd* = pd), while Figure 7 indicates the asymtotic solutions for solid spheres (slope 2.5) and for bd*/pc = 0 (slope 1.0).

Ind. Eng. Chern., Fundarn., Vol. 15, No. 2, 1976 123

Table 11. Experimental Results at 20 C

p d Fig- Continuous (measd ),

Expt ure Dispersed phase phase CP

1 2

3

4

5 6 7

8

9

10

11

12

2 3

3

4

5 6 7

7

7

7

7

7

Water Tetradecane

Tetradecane treated by active carbon

M oil

Ethylene glycol Water Toluene

Toluene

Toluene

Toluene + 8 ppm

Toluene + 8 ppm

Toluene + 8 ppm

AHP- 12

AHP-12

AHP-12

Silicone oil Ethylene

glycol Ethylene

glycol

Ethylene glycol

M oil M oil 89%

82.5%

76%

89%

82.5%

76%

Glycerine

Glycerine

Glycerine

Glycerine

Glycerine

Glycerine

1.025 2.39

2.39

31.0

21.8 1.055 0.63

0.63

0.63

0.63

0.63

0.63

Discussion

I t can be seen that the anticipated straight lines were obtained for the 12 different phase systems, for dispersed phase concentration lower than 0.33. The measured slopes of the obtained straight lines ranged from 1.32 to 2.52, that is within the expected range of 1.0-2.5 (Table 11).

Einsteins asymptotic solution for dilute suspensions is not dependent on the particle size. However, in cases of concentrated suspensions, large particles and wide particle size distribution deviations from this ideal picture are en- countered. In addition, drop-size effect is anticipated for liquid-liquid systems containing surfactants as indicated by eq 4.

The fact that the experimental results for the range of dispersed phase concentrations 0-0.33 fits fairly straight lines and no consistent trend of change of the slope with in- creased concentration is indicated implies a rather mild drop size effect in the range investigated in the present study. Although the phase systems studied included such systems with p c / p d ratios as high as 390, in which a fully de- veloped internal circulation pattern was expected with a predicted slope less than 1.03, this lower limit was not reached experimentally.

As was explained above, the technique used was not ade- quate for very pure systems due to problems of phase continuity and extremely fast coalescence. The lowest value of calculated ps obtained was thus 29 cP, limiting the internal recirculation pattern and consequently the minimum ob- tainable slope.

In a single experiment, the experimental slope obtained was 2.52, i.e., slightly higher than the upper predicted limit of 2.5. However, it should be noted that by actually plotting Thomas averaged corrected experimental data for solid spherical particles, a slope of 2.66 & 0.20 was obtained. The value of 2.5 was adopted in eq 13 and 14 since it falls within the margin of error, reduces the empirical correlation to Einsteins limiting solution for - 0, and is in better agreement with Vands theoretical derivation.

Figure 7 shows the increase of the slope with increasing ( p d / & ) and with the addition of surfactant. The surfactant used belongs to a family of dialkyl dihydrogen hypophos-

Slope of In ( p / p s ) Predicted

V C vs. slope with pd* YS

CP (measd) culation CP CP (measd), (@/l - a) full recir- (calcd), (calcd),

- 402

21.7

21.7

21.8

31.0 30.0

202

82.9

40.0

202

82.8

40.0

2.28 2.31

2.10

2.10

2.06 2.52 1.32

1.61

1.89

1.82

2.07

2.24

1.004 1.15

1.15

1.88

1.62 1.05 1.005

1.011

1.023

1.005

1.011

1.023

2339 149.6

59.7

60.0

74.7

54.8

56.5

58.3

243.6

205.6

190.8

W

2338 147.2

57.3

29.0

52.9

54.2

55.9

57.7

243.0

205.0

190.2

W

phates (AHP-12), produced by Chemicals and Phosphates Ltd., Israel. For each of the three systems, the slope was in- creased by the addition of 8 ppm of AHP-12 to the toluene phase. The slope increases also with the dispersed-continuous phase viscosity ratio for each of these two families of lines (both uncontaminated and contaminated by AHP- 12). It was attempted to bring the slope in all three systems to the predicted upper limit of 2.5 by further addition of AHP-12; however, no significant and consistent changes of the slope were obtained, possibly since the critical micelle concentration was already reached in the first addition, as was also indicated by interfacial tension measurements. A clear indication of the effect of surfactants is also shown in Figure 3, where the slope obtained for the systems of tetradecane dispersed in ethylene glycol was significantly low- ered by treating the system with active carbon, on which the surfactants were partially absorbed.

The experimental results thus corroborate the general validity of eq 14. The various values of ps calculated from eq 14 for the various systems are given in Table 11. I t should be noted that ps values calculated for experiments 7-9 (toluene dispersed in aqueous solutions of glycerine of various concentrations) are close, supporting the assump- tion that the values of ps calculated by such methods are truly characteristic of the degree of purity of a liquid-liquid system. It is significant also that different values of ps have been obtained for the M oil-ethylene glycol system, when phase continuity was inversed (experiments 4 and 5).

pS, whether interpreted by either eq 5 or 8, is actually a measure of the slip of the liquid-liquid interface and may result from a combination of various effects. An infinite value of !Ad* indicates no-slip conditions, while a zero value of pd* indicates total slip.

The fact that phase continuity effects ps may be explained by either the different mean drop diameter (if eq 5 is adopted-no measurements of the mean drop diameter were made) or by the difference in the retardation constant (if eq 8 is adopted). Whatever the interpretation, the most important point is that ps appears to be an easily obtained, quanti tat ive measure of the degree of purity of a practical liquid-liquid system; surface-active agents may have pro- nounced effects even when present in quantities below the


limit of detectability by chemical analysis. Their effects on liquid-liquid coalescence are well known (Barnea, 1972). pLs thus represents a criterion by means of which comparison of results pertaining to various effects in liquid-liquid systems may be rendered easier for analysis. For instance, Rodger et al. (1956) measured the specific area obtained in liquid-liquid mixing and report changes that could not be accounted for by any bulk physical property and not even by interfacial tension measurements. These authors were thus forced to include in their correlation a standardized settling t ime, which is in fact another very sensitive measure contamination. However, such settling time was arbi- trarily defined while p, is a property with a definite quantitative value. The present experiments indicate a clear qual- itative dependence of the settling time on p,, though settling times were not systematically measured.

Finally, it should be pointed out that the experimental results obtained in this study are generally smoother and more consistent t h m most experimental results published with solid spherical particles. This is probably due to the fact that secondary effects such as surface roughness, deviation from sphericity, etc., are eliminated or reduced in liquid-liquid systems.

Acknowledgment This paper is published by permission of the Managing

Director of IMI Institute for Research and Development. Mr. A. Shpak assisted in the execution of the experimental work.

Nomenclature K = retardation constant (eq 8)

y = interfacial tension r = surface concentration of surfactant @ = volumetric concentration of dispersed phase pc = continuous phase viscosity Pd = dispersed phase viscosity pd* =dispersed phase effective viscosity p, = effective interfacial viscosity p4 = effective viscosity of a dispersion of concentration @ u = area viscosity of the interface .t = two-dimensional shear viscosity of the interface

Literature Cited Barnea, E., Mizrahi, J., Chem. Eng. J., 5, 171 (1973). Barnea, E., D.Sc. Thesis (in Hebrew), Technion. Israel Institute of Technolo-

Boussinesq, J., C. R. Acad. Sci., 156, 1124 (1913). Clarke, B., Trans. lnst. Chem. Eng.. 45, T 251 (1967). Einstein, A., Ann. Phys., 19, 286 (1906). Einstein, A., Ann. Phys., 34, 591 (1911). Happel, J , J. Appl. Phys., 28, 1288 (1957). Hadamard, J. S.. C. R. Acad. Sci., 152, 1835 (1911). Hadamard, J. S., C. R. Acad. Sci., 154, 109 (1912). Levich, V. G.. --Physiochemical Hydrodynamics, Prentice-Hall, 1964. Leviton, A., Leighton, A,. J. Phys. Chem., 40, 71 (1936). Mooney, M., J. Colloid Sci., 6 , 162 (1948). Newman. J., Chem. Eng. Sci.. 22, 83 (1967). Nawab, M. A., Mason, S. G., Trans. Faraday SOC., 54, 1712 (1958). Oldroyd, J. G.. Proc. Roy. SOC., Ser. A, 218, 122 (1953). Oldroyd, J. G., Proc. Roy. SOC., Ser. A, 232, 567 (1955). Rybczinsky, W., Bull. Acad. 8ci. Cracovie, Ser. A, 40 (191 1). Rodger, W. A., Trice, V. G., Jr.. Rushton. J. H.. Chem. Eng. Prog., 52, 515

Taylor, G. I., Proc. Roy. SOC., Ser. A, 138, 41 (1932). Thomas, D. G.. J. Colloid Sci., 20, 267 (1965). Vand, V.. J. Phys. Colloid Chem., 52, 2 17 (1 948). Yaron, I., DSc. Thesis (in Hebrew), Technion, Israel Institute of Technology,

gy, Haifa, Israel, 1972.

(1956).

Haifa, Israel. 1971.

Received for review May 19, 1975 Accepted January 30, 1976

Upstream Penetration of an Enclosed Counterflowing Jet

William D. Morgan and Brian J. Brinkworth

Depadment of Mechanical Engineering, University College, Cardiff, Cardiff CF 7 IXP, United Kingdom

Gordon V. Evans

lndustrial Physics Group, Atomic Energy Research Establishment, Harwell, Oxon. OX 1 1 ORA, United Kingdom

It is shown that the upstream penetration, expressed in pipe diameters, of a turbulent jet into a counterflowing turbulent pipe flow is a function only of the ratio Zo f the momentum fluxes in the jet and the main stream flow. For low jet momentum, the relative penetration is proportional to Z*. There follows a transition, in the vicinity of Z = 1, to a high jet-momentum regime in which the relative penetration is proportional to Z16.

Introduction

For successful operation of the constant injection-rate method of flow-rate determination (Hutton and Spencer, 19601, there must be a substantially uniform distribution of tracer within the flow at the sampling point. When the tracer is mixed with the flow by natural turbulence, it is found that the downstream distance a t which satisfactory distributions are obtained is inconveniently large, of the order of 100-150 pipe diameters (Evans, 1967; Clayton et

al., 1968). Methods of reducing this mixing distance, such as the use of vortex generators (Evans, 1968) and high velocity jets (Clayton and Spackman, 1969) have been used but their effects on the mixing distance have not been ex- amined systematically.

Studies are currently in hand of the behavior of jets of tracer injected with high velocity against the flow and of the reductions in mixing distance that are achieved by this. In the course of this work, certain characteristics of the tracer plume upstream of the injection point have been es-

Ind. Eng. Chem., Fundam., Vol. 15, No. 2, 1976 125

barnea 1976

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