﻿1152 Prof. E. K. Rideal on the Flow of 



a constant orientation of the elementary wave are defined 

 by the same criterion, viz. zero phase-difference between two 

 adjacent wave-lengths. Thus it becomes obvious that one 

 implies the other. 



To ProF. Lorentz and Prof. Ehrenfest the author is very 

 grateful for the discussion of the subject. 



CVIII. On the Flow of Liquids under Capillary Pressure. 

 By Ekic Keightley Rideal *. 



THE rate of penetration of liquids into capillary porous 

 materials, of importance not only in biochemical pro- 

 blems but also in the study of the phenomena of adsorption 

 by materials such as charcoal and substances constituting 

 the membranes of semi-permeable osmometers, has attracted 

 but little attention. Bell and Cameron (Journ. Phys. Chera. 

 x. p. 659 (1906)) showed that in the case of a few liquids 

 the rate of movement of a liquid moving through a hori- 

 zontal capillary was such that the relationship % 2 = kt (where 

 x was the distance traversed in time t) held within the limits 

 of accuracy of the experimental method. Cude and Hulett 

 (J. A. C. S. xlii. p. 391 (1920)), in their study of the rate of 

 penetration of charcoal by water, obtained for the initial 

 period of penetration a similar relationship. Washburn 

 (Phys. Rev. xiii. p. 273 (1921)) has examined the problem 

 in more detail, and deduced for the conditions of horizontal 



flow the equation x 2 = --~— - -rt, where <y is the surface 



tension, rj the viscosity, r the capillary tube radius, and 6 the 

 angle of wetting. The validity of a similar expression was 

 tested experimental^ for liquids moving through capillaries 

 under the influence of their own capillary force as well as a 

 constant large external pressure. For all liquids which wet 

 the tube wall of the material, cos 6 is evidently equal to unity. 

 The same value obtains for liquids which do not wet the tube, 

 since the angles of wetting noted in the literature are pro- 

 bably ficticious, and are due to observations on the alteration 

 in the radius of curvature at some point distant from the 

 point of contact with the tube wall, and not at the contact 

 point itself. Washburn has assumed that Poiseuille's law 

 holds true during the flow after the initial period of turbu- 

 lence has ceased, and has calculated with the aid of this 



* Communicated by the Author. 



