Die Stationäre Bewegung einer freien Flüssigkeitsoberfläche im Elektrischen Feld
Authors: Hermans J. J. 
Published: September 2010

The double layer at the boundary of two phases may result from orientation of dipoles and from an electric charge. The potential difference which results from this charge is partly due to a “diffuse” layer; the corresponding “electrokinetic” potential leads to the “electrokinetic” phenomena, such as cataphoresis. Since the cataphoresis of gas bubbles in water is directed towards the anode, it is generally assumed that the charge of the surface is negative with respect to the bulk of the water.

As regards the total potential difference, neither its magnitude nor its sign are known. From theoretical considerations Verwey concludes that its negative side is directed inwards, i.e., opposite to the surface charge.

In this paper a new effect is studied: the electrophoresis of the surface. Although it is similar in nature to the electrosmosis in a capillary, it is to be distinguished from the latter, since the motion of the liquid is accompanied by a motion of the boundary itself. To avoid confusion, the motion of suspended particles in an electric field is called cataphoresis.

The surprising fact is established that the electrophoresis of the surface takes place in a direction opposite to that of the cataphoresis of gas bubbles. This would mean that the sign of the surface charge is the same as that of the total potential difference calculated by Verwey.

The electrophoresis results from an electric field parallel to the surface. In § 4‐9 experiments are described, in which the external field is logarithmic, while in § 10 a homogeneous field is applied. The velocity of the surface is determined with the aid of a powder floating on it. It takes about a minute for the streaming to become stationary. It is shown in § 4 that this stationary velocity is independent of the nature of the powder used and proportional to the field strength. It is, moreover, independent of the depth of the vessel; its value for distilled water is 1710‐4 cm/sec per V/cm, the experimental error ± 10%. In § 5 the velocity at different points of the surface is examined; that below the surface could be studied with the aid of a suspension.

§ 6 gives the results for some electrolytes. The sign of the velocity is reversed at a concentration of about 10‐3 g Eq./1. Experiments with monolayers (§ 7) show, that the velocity is increased if the molecular area approaches its saturation value of about 20 Å2. It is further found in § 8 that the surface of organic liquids shows a similar electrophoresis, while in § 9 the influence of internal friction is studied.

In order to simplify the calculations as much as possible, the theory is developed for homogeneous fields. In § 11 the electrosmosis between two solid planes is considered; § 12 gives the theory for the free surface. It is shown later on (§ 15), that the results obtained also apply to non‐homogeneous fields if no compensating streaming is to be accounted for. The application of the theory to the experiments described leads to a value of 115 mV. for the electrokinetic potential of the surface (§ 13). It is further shown in § 14, that the time required for the streaming to obtain its stationary character is of the right order of magnitude.

The theory for the flow in a rectangular vessel is developed in § 16. This theory with the experimental results of § 10 leads to an electrokinetic potential of the surface amounting to 150 mV. In view of the difficulties encountered in both the experiments and their interpretation, this result is in fairly good agreement with the value of 115 mV found in § 13. Since the experiments in the rectangular vessel are less reliable, the value of 115 mV is to be considered as the more probable one.

Finally, § 17 gives the derivation of formulae used in § 3 for the logarithmic field in the cylindrical vessel and the field strength in the centre of this vessel.