Physics. — "(Jii llu' Theonj of the, Friction of Liquids'. By Pi'of. 

 J. D. VAN DKR Waals Jk. (Comniimirated by Prof. J. D. van 



DKR Waals). 



(Communicated in the meeting of November 30, 1918). 



§ 1. I iilrodudion. The tlieorv of tlie fritMioii of gases has been 

 made the subject of minieroiis reseairlies, the theory of friction of 

 liquids on the other hand has niet with but scant attention. Yet it 

 is clear that the explanation gi\en to account for the friction of 

 gases — viz. that it is brought about in consequence of this that 

 molecules diffusing from one gas layei- to another, at the same time 

 transport an amoujit of momentum from one layer to another — 

 cannot equally apply to the fi'iction of liquids. For the friction of 

 gases increases at higher temperature. For liquids on the other hand 

 the viscosity becomes slighter at higher temperature. Such a beha- 

 viour cannot be accounted for with "friction by means of transport." 



Maxwell calcidated that on the supposition of "friction by means 

 of transport" the coefficient of friction i] should be proportional to 

 \/ T if we assun)e that the molecules are perfectlj' rigid spheres, 

 which do not attract each other. Other assumptions concerning the 

 nature of the molecules (repulsion in inverse ratio with the fifth 

 power of the distance, Maxwkll, or mutually attracting rigid spheres, 

 SuTHKRLAND and Rklvganum) lead to a still more rapid increase of 

 ^l with T. Nor can the thermal expansion of the liquids explain the 

 sign of the coefficient of tenq^erature of >/. For gases i] appears 

 to be independent of the volume. For liquids the expansion will 

 pro-mote an increase of >/ with T, and not a decrease. This has been 

 shown experimentally (except for water, where the reverse takes 

 place), and it is also easy to understand that this is to be expected 

 for friction by means of transport, at least for not associating or 

 dissociating liquids. The expression dei-ived by Maxwell: 



ms 



in which y represents the density, / the mean length of path, .9 the 

 mean velocity, m the mass, and d the diameter of a molecule, will 

 namely have to be corrected for liquids, to: 



