416 -2- 



Bubble, the photographs show a steel ball, i inch diameter, soldered at the lower end of a vertical* 

 rod invnersed in the liquid; this arrangement was used to find the scale of the photographs and to 

 give a reference mark from which the vertical displacement of the bubble could be measured. 



In the original photographs, a region of turbulence is clearly shown behind the large bubble. 

 This is due no doubt to some anisotropic optical property of nitrobenzene when subjected to viscous 

 stresses. That such stresses exist could be inferred from the fact that the largest of the small 

 bubbles in the wake of the large one is not spherical and is rapidly changing in shape. This bubble 

 has a diaineter of about 6 mm. still smaller bubbles are less distorted and one of diameter about 

 2 mm., seen to the left side of the 6 mm. bubble Ts distorted so that its length/diameter ratio Is 

 about 1.1. 



The rate of shear which might be expected to produce a distortion of this amount has been 

 calculated i. in the field of flow represented by the equaticns 



u = Cx, v = -Cy, w = o (l.l) 



an air-buDble of mean radius a would be pulled out so that 



L - B 2C M3 , , 



i-Tj - ^r- (1-2) 



where L and B are the length and Breadth of the bubble and /^ and T the viscosity and the surface 

 tension of the liquid. For nitrobenzene, M = 0.018 Ixjises, T = U3.9 dynes/cm., so that for the 

 2 rm. bubbles, a = o.i cm., l'/B = l.l and (l - B)/(l + B) = 0.05. giving 



0.05 X 43.9 , , 



= 6.1 X 10' sec"' 



'^ " 2 X 0.018 X 0.1 



The rate ■ of dissipation of energy per c.c. in the flow represented By equation (i.i) is 



.=#)' ■m')- ' 



fJji = 1.3U X 10 ergs/c.c./sec. 



If the rate- of dissipation were constant through the wake and if wake extends over the wnole 

 of the region which appears disturbed in Figure i, mmely through a diaireter of 5.9 cm., the total 

 rate of dissipation in the wake is 



1.34 X 10 X (volume of wake) 

 1.3" X 10" X JI (5.9)^ X 3.8 



= l.u X 10' ergs/sec. 



The total rate of dissipation would be known if the drag co-efficient, c. of the large bubble 

 were known. since the density p of nitrobenzene is 1.2 gm/c.c. whilst the velocity of rise, u, of 

 the large buBBle in this experiment was 36.7 cm/sec. and its maximum transvt^rse dimension, 2A, was 

 5.1 cm., the total rate of dissipation was 



C^ f t p U^ 7T A^ X u 



ii X 1.20 X 36.73 X7T xf-j- ) [ 



6.1 X 10 Cp ergs/sec. 



Since Cr, is of the order 1.0 (see Table I) it will be seen that the rate of dissipation which 

 would distort the bubbles By the observed amount is of the same order ;s that deduced from the rate 

 of rise. 



For 



i G. I. Taylor "Formation of Emulsions in definaBle fields f flow" 

 Proc. Roy. SOC. Vol. 1U6 p. 501, (l93«) 



