Journal o f Electrostatics, 15 (1984) 351--358 351 Elsevier Science Publishers B.V., Amsterdam -- Printed in The Netherlands

ELECTRIFICATION OF CYCLOHEXANE IN LAMINAR FLOW IN SMALL-DIAMETER METAL PIPES

J.P. GOSSE and A. SOLOFOMBOAHANGY

Laboratoire d 'Electrostatique et de Matdriaux Didlectriques, Centre National de la Recherche Scientifique, Avenue des Martyrs 166 X, 38042 Grenoble Cddex (France)

(Received June 28, 1983; accepted in revised form September 23, 1983)

Summary

Data are given on the density o f charge convected by the laminar f low in capillary tubes o f cyclohexane containing different additives.

We make special note of the experimental results which correspond to a fully develop- ed charge density profile in the output section of the tube, when solutions are either very resistive (> 3 X 1011 f~ m), or rather conductive (< 101° r~ m).

The true zeta potential was 17 mV for cyclohexane and TiAP and 75 mV for cyclo- hexane and Aerosol OT. These values were found independent of the solution con- ductivity.

1. Introduct ion

The electrification of liquids by flow in pipes has for a long time been ob- served and examined, the first s tudy dating from 1893. Since then, several review articles have been published and some of them are given in [ 1--8 ]. They are mainly related to the electrification of hydrocarbons either in tur- bulent flow in metallic or insulating pipes or during filtration through porous materials. Unfortunately, the experimental observations were generally less perfectly explained. So, at the Conference on Electrostatics and Static Elec- trification held in Grenoble in 1977, Bright [9] explained tha t if the electrifi- cation current produced by the liquid flow has to be evaluated for safety reasons, an experimental evaluation is to be preferred to the use of empirical relationships such as that proposed by Koszman and Gavis [10].

However, if some very difficult problems remain, such as the electrifica- t ion of a liquid flowing in an insulating pipe, there exist simple cases for which theoretical formulations can be given. Consider, for example, the elec- trification of a hydrocarbon flowing in a metallic pipe maintained at a con- stant potential with the liquid remaining in the tube for a t ime far longer than the relaxation time of the liquid. Indeed, in that case, the distribution of charge in the double layer in the output section of the tube is the same, whether the liquid is flowing or is at rest. Then, the density of the net

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352

charge convected by the liquid can be related to characteristics of the liquid and the metal--liquid interface (e.g. the zeta potential).

Unfortunately, very few experiments have been performed in laminar flow [11--13]. Our s tudy tries to gain further insight into f low electrification, and to get quantitative information on the influence of parameters such as the resistivity and the nature of the additives on the zeta potential or other double-layer characteristics.

This paper summarizes an experimental s tudy demonstrating how " t rue" values of ~ can be obtained. The variations of the density of convected charges, or o f ~, with the liquid conductivi ty are also investigated, with two different ionic additives in cyclohexane.

2. Electrification by laminar f low

Like other electrokinetic phenomena, f low electrification is due to the existence of a charged double-layer at the liquid-metal interface. According to S tem [4] , this double-layer starts at the closest distance of approach of the ions to the electrode. This distance XA is related to the size of ions in the liquid and for ions of the electrolyte t r i isoamylammonium picrate (TiAP) XA has been evaluated as between 4 and 5 A. In non-polar liquids, the double-layer contains a region where the image-force is strong and determines the charge distribution [14] ; its thickness xs is about 70 A in cyclohexane (er = 2.02). At x = XB the diffuse layer begins and it extends over a rather large distance L D (L D = Debye length). L D is 43 #m in a liquid with a resis- tivity of 3 × 10 .I ~2 m and an ionic mobil i ty of 10 -8 m ~ V -1 s -1.

The classical relation giving the density of charges convected by a laminar flow in a pipe of radius R is

q v = 8 e ~ / R 2

when L D ~ R [15]. ~ is the potential at the distance xs from the metal, at the boundary between the diffuse doublelayer and the region of the image- force. This potential ~ is related to the charge density qs at xB according to

qB = qo [exp(-~/U) - exp(~/U)].

In the region of the image-force (xA < x < xs) , the charge density is given by q = q n e x p ( x s / x ) / e 1 . Thus, at a distance XA from the metal, the charge density qp satisfies

q p = qB e x p ( x B / X A ) / e * . (I)

If XA = 5 A, we get qp = 6.6 × 10 s qB; the charge density increases very strongly in the region of the image-force. Nevertheless, we have demonstrat~ ed [14] that this part o f the double-layer, highly charged but very thin, does not contr ibute significantly to the flow electrification.

Thus, from the density qv of convected charges which can be experi- mentally measured, the potential zeta and the charge density qB at the dis- tance xs from the metal can be deduced; the charge density qA at x -- XA is obtained by using the relation (1).

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3. Experimental

The electrification of cyclohexane doped with t r i isoamylammonium picrate (TiAP) or with sodium ethylhexylsulfosuccinate (Aerosol OT or AOT) has been measured with laminar flow. TiAP and AOT belong to two different types of ionic compounds: TiAP is ionophoric (ionic when solid); AOT is an ionic surfactant, in solution it presents aggregation properties completely different from those of ionophoric solutions [16]. For example, the theory of Fuoss and Kraus [17] on the conductance of electrolyte solu- tions in liquids of low dielectric constant is no longer valid in surfactant solu- tions. The resistivity of TiAP solutions in cyclohexane (CH) remains higher than 4 × 1011 ~2 m, on account of the weak solubility of TiAP in CH. On the other hand, the resistivity of AOT solutions in CH can be lowered down to 5 X 107 ~2 m or less.

The equipment and experimental methods used in this work are similar to those used by Touchard [13]. Essentially, the cyclohexane was blown from a pressure vessel, by nitrogen, through a stainless-steel capillary tube (length: 3 m, internal diameter: 0.35 or 0.5 mm) into an insulated receiving vessel. The potential V of this vessel was measured by means of a Keithley elec- t rometer with a high input resistance (1014 ~2 ). The density qv of convected charges was deduced from the registered curve V(t) through the relation qv = (C/Qv)dV/dt , where C is the capacity of the receiving vessel, the Faraday cage and the electrometer, and where Qv is the liquid f low rate. The resistivi- ty of the studied solutions was measured with a 1621 capacitance measure- ment system (General Radio).

4. Results

Data on the electrification of cyclohexane in laminar flow (102 < Re < 2 × 103) are given in two parts, the first one details results obtained with resistive solutions (CH + TiAP solutions), the second gives results on the rather conductive surfactant solutions (CH + AOT).

Solutions o f TiAP in cyclohexane When the resistivity of the solutions CH + TiAP was higher than 3 X 1011

~2 m, it was observed that the charge densi ty qv of convected charges decreas- ed with t ime during the liquid f low in the capillary tube, and reached a stationary value after a time Tt varying with the Reynolds number and the solution resistivity. With a solution resistivity of about 1012 ~2 m, the stationary value was less than 1/10 of the instantaneous one measured just after the beginning of the liquid flow. This stationary value varied with the Reynolds number, in contradict ion with what is expected from the classical t reatment of electrification in laminar flow. On the other hand, the instan- taneous qv value was independent o f Re and varied with R-2 as theoretically expected.

354

These observations permit ted us to give the following interpretation: In the liquid remaining in the capillary between two experiments, the double layer takes on its equilibrium distribution and that distribution corresponds to the initial charging of the collector vessel. This charge density of convect- ed charges will remain constant until the liquid initially filling the capillary tube has been blown out. In these rather resistive solutions, the double layer cannot fully establish itself at the metal--liquid interface when the liquid is flowing, since the liquid only remains there a short t ime in comparison with the time constant of the liquid. Thus, it is expected that the stationary value of qv decreases with increasing resistivity and Reynolds number.

This interpretation is supported by our experimental s tudy of the dura- tion Tt of the transient o f electrification. It was verified that Tt varies according to Tt = LR2pv/2Re~(eUpK) 1/2 calculated as the t ime spent in the capillary by a liquid particle moving at the distance LD from the metal sur- face. In this expression, L is the tube length, p the liquid resistivity, 77 its viscosity, Pv its volumic mass, U = kT/e the thermal energy and K the ionic mobility. The initial density of convected charges which corresponds to a fully developed charge density profile at the tube exit, is given in Fig. 1 for solutions of various resistivities. With these resistive solutions, the repro- ducibility of the measurements was rather poor and our results are scattered. Nevertheless, qv appears to be independent of the liquid resistivity. Its value 9 or 10 × 10 -~ C m -3 obtained in a capillary with a radius R = 0.5 ram, corre- sponds to ~ = 17 -+ 1 mV independent of the resistivity. The constant value of ~ indicates that the charge densities very near the tube wall (qp) and at a large distance from it (q0) remain proportional.

, ~ C m - ~ clv -

+ -5

10 - - . __.L. ~ . - - . . - - . ~ -e - - - - - + - . ~ --- - - ® ÷

I0 10~o 104~ 1042 ~.m

Fig. 1. Convected charge density qv against the solution resistivity. + TiAP in cyclohexane; ® T i A P and T i A in c y c l o h e x a n e . T u b e rad ius = 0 .5 ram, t u b e l e n g t h ffi 3 m , R e y n o l d s n u m b e r ffi 4 0 0 .

io .6

355

In Fig. 1 we have also given qv values obtained with solutions of TiAP and TiA in cyclohexane. By increased addition o f triisoamylamine (TiA), the resistivity of cyclohexane saturated with TiAP was made to decrease down to about 5 X 10 *° ~2 m. In spite of some scatter in the results, the density of the convected net charge was about the same as with solutions of cyclo- hexane and TiAP.

Solutions of aerosol OT in cyclohexane When the resistivity of these solutions was lower than 10'* ~2 m, no tran-

sient was observed in their electrification, in agreement with our interpreta- t ion of the above-described experiments. From the moment that cyclo- hexane flow started, the voltage of the receiving vessel increased linearly with time. The deduced convected charge density (Fig. 2) was independent of the Reynolds number, and varied with the tube radius according to R-2.

At resistivity values lower than 5 X 101° ~2 m, it was observed that qv was increasing with Re (Fig. 2) and with resistivity (Fig. 3, curve 1). We ex- plain the variation of qv by the neutralization of a part of the convected net charge just when it leaves the capillary. This partial neutralization of the liquid is caused by the antagonistic electric field created by the charged stream leaving the capillary tube. This electric field drags the ions having the same sign as the charged stream back towards the end of the tube, their con- centration being large due to the weak resistivity of the solutions. This dis-

q v

10

_ C~m--3

q

- \ /

108 109

/ / \~,/

/7 / /

Fig. 2. Convected charge density qv against the resistivity of the AOT + CH solution; the Reynolds number corresponding to the symbols are: o 1200; + 800; × 400; • 250. Tube radius = 0.5 mm, tube length = 3 rn.

I I I IIII 1 04o 1 044 (Llxcm)

356

lO

- d

10

d

lO

C,~m -~

® ~ b - - " - - m - -

f I I J l l , , U , , , I , , , , , , , I . . , , , , , I , J . J , l l l J , , I , , I , , . ,

108 109 10 ' ° 10 ̀'4 10 "~2 P (£',.,,m) Fig. 3. C o n v e c t e d charge dens i ty qv against the res is t ivi ty o f t he A O T + CH so lu t ion . R e y n o l d s n u m b e r = 800. T u b e radius ffi 0.5 m m , t u b e l eng th = 3 m. Curve 1 ini t ial sys tem, Curve 2 mod i f i ed ex i t o f the tube .

charge has been proved and we avoided it by setting up at the out let of the capillary tube a small piece of the same tube, insulated from the rest by a thin piece of teflon and electrically connected to the receiving vessel. It was then observed that even at low resistivities (108 ~2 m), the density qv of con- vected charges was independent o f Re, and varied with R -2.

It also appeared (Fig. 3, curve 2) that qv was independent o f the resistivity of the solutions. Its value was 4.5 X 10 -s C m -3 with a capillary radius of 0.5 mm. The related zeta potential was 75 mV.

Sign of the convected charge Cyclohexane (CH) was always positively charged after its passage through

the capillary tube as were solutions of aerosol OT in CH, solutions of tetra- methylphenylene diamine (TMPD) in CH and solutions of TiAP in a mixture of CH and benzene.

Solutions of different concentrations of TiAP in CH were either posi- tively or negatively charged, the reasons for the sign reversal remaining unknown. No change in the chemical composit ion of the solutions was de- tected by UV spect rophotometry or by gas chromatography.

5. Analysis o f data

From our observations, we have deduced some characteristics of the double layer at the metal--cyclohexane interface (Table 1):

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TABLE 1

Characteristics o f the double layer at CH + TiAP and CH + aerosol OT solutions--metal interface

Solution Rcsis- Debye's qv ~ qB XA qp tivity length (R = 0.5 ram)

LD ( a m ) (~m) (C m-') (mV) (C m-') (A) (C m-")

CH + TiAP 1011 24 10 -5 17 5.2 × 10 -4 5 2.3 x 102

CH + AOT 1011 16.3 4.5 × 10 -s 75 2 × 10 -2 14 1.1

Debye 's length and the distance X A of minimum approach have been de- duced f rom the ionic mobilities 1.4 × 10 -8 m 2 V -1 s -1 for TiAP [18] and 6 × 10-gm 2 V -1 s -1 for AOT [19] , bo th in cyclohexane at 20°C.

At a given resistivity, the zeta potent ial and the charge density qs at x = xB are greater for AOT solutions than for TiAP solutions but, at the closest distance of approach XA of the ions to the electrode, the charge density q_p is far higher in solutions o f TiAP in CH than for AOT in CH. This result is in agreement with experimental observations o f the electrical conduct ion of these solutions [ 18, 19] . We cannot explain this result since the parameters determining the charge density at the interface remain unknown.

6. C o n c l u s i o n

We have been able to measure for a large range of resistivities (108---1012 m) the " t r u e " density o f the net charge convected by the laminar flow of

a hydrocarbon in a metallic capillary tube. This t rue density corresponds to an equilibrium charge distr ibution in the double layer, in the ou tpu t section of the tube, identical to the distr ibution wi thout liquid flow. To obtain this value, we have studied the transient o f electrification observed with resistive solutions (~ 3 × 1011 ~ m). At low resistivities (~ 101° ~ m), we have avoid- ed the discharge o f the liquid at its departure f rom the tube, the liquid enter- ing the receiver via a tube o f the same diameter as the capillary, insulated from it and connected to the receiver. Our observations may provide a bet ter understanding of the experimental method proposed by Gibson and Lloyd [7]. In cyclohexane, the solutions o f aerosol OT present a zeta potent ial higher than that of the solutions of TiAP. A similar s tudy extended to differ- ent additives belonging to various chemical families should indicate which of the characteristics of these products determine the zeta potential and the electrification caused by the flow of hydrocarbons through pipes.

358

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