﻿a Problem in Viscosity. 1005 



slab is drawn upwards ; t must adjust itself so that this 

 "condition is fulfilled, i. e. 



e=^m ...... (3) 



It is not easy to measure t accurately while the slab is 

 moving, and of course, if it is stopped, the conditions are 

 changed at once. In practice the liquid layer usually sets, 

 owing to cooling, evaporation, etc., at some little distance 

 about the liquid surface. In our experiments we have used 

 a liquid with a melting-point above room temperature, so 

 that it freezes on the slab a little distance above the surface 

 of the bath; we can then measure the thickness t' of the 

 solid film. If in these conditions the assumptions we have 

 made so far are legitimate, we have from the equation of 

 continuity 



t'v = \ vdx, (4) 



which gives t'^t^^J 2 ^- (5) 



But the assumptions cannot be accurately true, for since 

 the thickness of the layer decreases as the liquid cools and 

 as its viscosity increases, the stream lines cannot be vertical 

 or of constant velocity. We shall consider the effect of this 

 failure of the assumption in III. 



If the surface were a circular cylinder of radius r we 

 should have instead of (1) 



which, using the same assumptions as before, gives in 

 place of (2) 



"=«o + if{^-(t + ,«) 2 log^}. • (7) 



When — is small (7) gives 



v o=h~ * as in (3). 



If is not small we may expect surface tension forces to 



be appreciable. The calculation is then more difficult and 

 we can give no complete solution. The flow would appear 

 to depend on the exact form of the meniscus at the surface 

 of the liquid. But a dimensional argument gives us some 

 information. 



