Volume 66A, number 6 PHYSICS LETTERS 26 June 1978

ELECTROHYDRODYNAMICAL TRANSIENT FLOW IN THE LIQUID AROMATICS

ANTHRACENE AND NAPHTHALENE

F. GELSDORF and H. KRAUSE IV. Physikalisches Institut der Universitiit G6ttingen, D-3400 G6ttingen, Germany

Received 14 April 1978

The propagation of electrohydrodynamical flow fronts generated by injection from nickel electrodes is investigated by schlieren optics in naphthalene and highly purified anthracene.

It had been shown in different cases that the appli- cation of electrical voltages in the range of 102-103 V combined with charge injection leads to a convective motion of dielectric liquids [1,2]. Measurements of Krause pointed out [3] that in the case of anthracene bipolar EHD-convection can be observed. Moreover the EHD transient flow was of the laminar type, con- trary to the case of nitrobenzene investigated by Hopfinger and Gosse, where it was turbulent [4].

In the present work the EHD transient is investigated in the aromatic liquids naphthalene and anthracene, wfiich was highly purified by zone melting (received from "Kristallabor des SFB 67 der Universit/it Stutt- gart", W. Germany).

The visualisation of the propagating EHD streamers was done by schlieren optics and the schlieren frames were recorded with a f'tim camera. The measuring cells used consisted of quartz or PTFE (teflon) respectively with plane parallel nickel disc electrodes and electrode separations of 5 mm.

Anthracene. In liquid anthracene EHD convection already begins if voltages in the region of 100 V are applied to the electrodes. Then EHD streamers originate at both, the positive and the negative electrode, indi- cating that highly purified anthracene shows also bi- polar EHD convection as reported by Krause [4] for the analytical grade substance.

After recording the schlieren frames, trajectories of the EHD streamers were obtained from the single pictures of the film. It followed from this evaluation that the propagation velocity of the streamers is nearly

I x [ c m ]

0.2

0.1

~o 300 V

500 V

,,,o 1000 V

. "% " , . r , .

~- ak. aa ~ . . o

/ ' a a A . ' . c ~ o " "°'°"

,yS 0

0.1 0.3 0.5 07 t [s ]

Fig. 1. Trajectories of EHD streamers in anthracene (tempera- ture 233 °C, dashed line for electrode separation, filled out symbols for position of the positive streamer).

constant throughout wide regions of the electrode space (fig. 1). Therefore the flow fronts met one another nearly in the middle between the electrodes.

The dependence of the flow velocity on the applied voltage follows from fig. 2, which shows, that the velo- city of both streamers is proportional to the applied voltage in the observed range. The voltage was varied from 200 V to 1000 V. For voltages lower than 200 V the schlieren frames became poorly defined; above 1000 V the assumption of laminar EHD convection no longer holds in this case.

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Volume 66A, number 6 PHYSICS LETTERS 26 June 1978

v [cm/s] / o

. / / . / /

/ /

o o.1 0.5 1 u [kV] Fig. 2. Dependence of the propagation speed on the applied voltage (temperature 233 °C, filled out symbols for the speed of the positive streamer).

The temperature dependence of the EHD mobility - the latter is defined by the quotient of the mean flow velocity and the average electric field (E = U/d) -

was investigated in the range from the melting temper- ature (216.2 °C) up to 250 °C since the zone refined anthracene may not be heated more than some 10 degrees above the melting temperature to preserve its purity. Nevertheless there is a rather good agreement in the variation with temperature between viscosity and EHD mobility.

Naphthalene. In naphthalene the EHD convection starts, if a voltage higher than 400 V is applied to the electrodes. The schlieren frames then show that the EHD streamer mainly originates at the negative elec- trode and propagates through the electrode spacing in the direction of the counter electrode. At the positive electrode only very weak EHD motion occurs, which may be due to a very weak injection of positive charges. Therefore the EHD convection in this case may be re- garded as a very asymmetric process.

In the same way as in anthracene one obtains trajec- tories of the propagating negative EHD streamer. An example is represented in fig. 3. The deceleration near the counter electrode results from the fact, that this

0.5

0.4

0.3

0.2

0.1

x [cm]

o oo° ,o

/ ,,,/, ,' p

/ A ~ Z ,'

~P~ o 1000 V

~ • 750 V

/ o o12 o14 o16 o.a t N

Fig. 3. Trajectories of EHD streamers in naphthalene (temper- ature 98 °C, dashed line for electrode separation).

electrode is a rigid barrier so that the streamer must turn aside.

The dependence of the flow velocity on the applied voltage was investigated in the range of 500-1000 V, limited by the same arguments as for anthracene. We found, that the velocity is not proportional but almost squarely dependent on the external voltage.

This dependence on the applied voltage was meas- ured for various temperatures. So the temperature de- pendence of the EHD mobility could be obtained. Since this mobility varies proportional to the voltage this evaluation had to be effected for every voltage separately.

We found, that for naphthalene there is also a good agreement in the temperature dependence between viscosity and EHD mobility, indicating, that the flow is mainly controlled by the viscosity of the liquid.

Conclusions. A comparison of the results for the different liquids shows that there is no fundamental difference between unipolar and bipolar EHD convec- tion in the laminar case. The bipolar EHD streamers observed in anthracene before their collision are very similar to those in naphthalene and in both cases the EHD motion is mainly controlled by viscosity.

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Volume 66A, number 6 PHYSICS LETTERS 26 June 1978

The results in the dependence of the flow velocity on the applied voltage may be explained by different injection strengths and not by the type of EHD mo- tion. There are arguments from electrical measure- ments which lead to the conclusion that in liquid naphthalene strong injection exists and therefore a square dependence of the propagation speed on the applied voltage occurs in the laminar case while in anthracene weak injection dominates and therefore the flow velocity is proportional to the applied voltage.

References

[1] J.G. Lacroix, P. Atten and E.J. Hopfinger, J. Fluid Mech. 69 (1975) 539.

[2] P. Atten and J.P. Gosse, J. Chem. Phys. 51 (1969) 2804. [3] H. Krause, Chem. Phys. Lett. 37 (1976) 172. [4] E.J. Hopfinger and J.P. Grosse, Phys. Fluids 14 (1971)

1671.

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