Section III, 1917 [61] Trans. R.S.C. 



The Buoyancy of Frazil Crystals in Water. 



By H. T. Barnes, D.Sc, F.R.S.C. 

 McGill University, Montreal. 



(Read May Meeting, 1917.) 



For many years the question of the buoyancy of frazil ice crystals 

 in water has been under discussion. Many practical observers of 

 ice conditions in our northern rivers have maintained that these fine 

 needle crystals are denser than water, and hence tend to sink to the 

 bottom. No evidence, however, is at hand to show that ice formed 

 under atmospheric pressure is any denser than normal, and therefore 

 these crystals would all have a tendency to rise. 



It now appears quite clear why very small ice crystals such as 

 frazil appear to have little buoyancy, and, therefore, be easily carried 

 about in the water by the various currents. A body moving through 

 a fluid is subject to a viscous resistance which retards the motion. 

 Under the influence of the gravity pull, a body falling or rising through 

 water will acquire a constant velocity called the terminal velocity 

 which represents the equilibrium between the gravitation force and 

 the viscous resistance. Since the gravitating force is a volume effect 

 while the viscous drag is a surface effect it follows that the former 

 decreases more rapidly than the latter as the diameter of the body 

 decreases. 



Stokes^ has worked out the expression for the terminal velocity 

 of small spherical drops of water falling freely in air and has shown 

 that fog particles may thus remain suspended in air for long periods 

 when they are very small. 



The viscous drag on a small sphere of radius r is a force given by 

 the expression. 



f = 6 X II r V 

 where (i = coefficient of viscosity 

 V = terminal velocity of the sphere. 



Suppose a sphere of density a falls under gravity in a fluid, of 

 density p the force pulling it down \s i nr^ {o — p) g. Hence when 

 the viscous drag balances the downward pull 6 n fi r V = -^tc V^ (o — p)g 



from which F = § the expression generally used. 



iG. G. Stoke's Collected Works, Vol. 3, p. 59 (1901). 



