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XIX. On the Friction in Free Surfaces of Liquids. 

 By A. Oberbeck*. 



1. TN his fine investigations on liquids which are with- 

 JL drawn from the influence of gravity, Plateau f discusses 

 the question why only a few liquids are suitable for the pro- 

 duction of thin films, while most of them are totally unsuited 

 for that purpose. According to his view, two properties of 

 liquids play an essential part therein — the tension and the 

 viscosity of their surfaces. The investigation of this second 

 property is the aim of the present memoir. 



As is well known, what is designated as the viscosity of a 

 liquid is its deviation from the state of perfect fluidity, and 

 manifests itself by a frictional resistance exerted by different 

 quickly moving neighbouring parts of the liquid upon one 

 another. From experiments which are subsequently to be 

 more fully communicated, Plateau inferred that the amount 

 of this frictional resistance varies according as the motion of 

 the parts takes place in the interior or in the nearest vicinity 

 of the free surface of the liquid ; so that we have to distin- 

 guish an internal and a superficial viscosity. As the hydro- 

 dynamic differential equations with respect to the friction are 

 at present in excellent accordance with all the known facts, 

 and in them the friction has for its expression a single cha- 

 racteristic constant for each liquid (the friction-coefficient), 

 the phenomenon discovered by Plateau might also be expressed 

 in the following form: — The friction-coefficient is indeed a 

 constant in the interior of a liquid; but at very small distances 

 from the free surface it is a function of the distance from the 

 free surface. 



All the experiments which have been made upon free liquid 

 surfaces teach that the liquid parts in them are in essentially 

 different conditions from those in the interior; hence it would 

 be quite conceivable that their mutual friction also is different. 

 But it has been held necessary (by Poisson) to assume that 

 the density rapidly changes very near the free surface. 

 Although hitherto neither an experimental proof of this has 

 been produced, nor even theoretically is there any occasion to 

 designate this assumption as a necessary one, yet a variation 

 of the friction-coefficient would include it as a self-evident 

 consequence. 



The friction of two different liquids against each other is 



* Translated from Wiedemann's Annalen, 1880, No. 12, pp. 634-652. 

 t Plateau, Mem. de I 1 Acad, de Belgique, 1868, xxxvii. pp. 1-102 ; Poe-g-. 

 Ann. cxli. pp. 44-58(1870). 



