February 8, 1894] 



NA TURE 



35' 



remembered. If we turn to the coal burnt per hour per 

 square foot of heating surface we find it but 0-298 lbs. in the 

 l^na, and I'D I lbs. in the Ville dc Douvrcs. With regard to 

 evaporation, each square foot of heating surface in the lona's 

 boilers turned 273 lbs. of water into steam per hour; 

 in the Ville de Douvres the corresponding figure was 

 9'02. The feed-water evaporated per lb. of fuel was 9'i5 lbs. 

 in the lona, and 897 lbs. in the Ville de Douvres. Taking 

 carbon values — that is, excluding incombustible ash — and 

 reducing the results to an equivalent of evaporat'on from and 

 at 212 , we find the corresponding figures to be 10*42 lbs. for 

 the lona and 9*94 lbs. for the Ville de J^ouvres, a by no means 

 bad result for the latter vessel's boilers, considering the demand 

 made upon them in other respects. 



Turning to the engines of these two ships, we find that the 

 efficiency of the lona's engines was lyi per cent., whilst the 

 Ville de Douvres' engines had an efficiency of 117 per cent. 

 The weight of steam used in the main engines of the former 

 vessel was 13 '35 lbs. per indicated horse-power per hour, whilst 

 in the Ville de Douvres there were required 2077 lbs. of steam 

 to produce one unit of power. 



The figures we have quoted will be sufficient to give an idea 

 of the scope of the paper. We have not space to go into the 

 discussion upon the various causes of the variations in results ; 

 for these we must refer our readers to the Proceedings of the 

 Institution, where also will be found an account of the long and 

 interesting discussion which followed the reading of the paper. 

 The summer meeting will be held this year in Manchester, 

 at the beginning of August. 



ON THE MOTION OF BUBBLES IN TUBES. 



T^VERY student of physics has observed the motion of bub- 

 "^ bles in tubes. Which of them has not used a big bubble 

 to show the little ones their duty in clearing out the air when 

 filling a barometer tube ? Who has not spent his time and 

 patience in whisking a spirit thermometer to drive a bubble out 

 of the column? ;\Ir. Trouton has recently communicated to the 

 Royal Society the result of some researches on this subject. He 

 has studied the behaviour of big bubbles and of little ones, of 

 bubbles in large and small tubes, of bubbles of air in a liquid, 

 and of one liquid in another, of bubbles in heavy and in light 

 liquids, of bubbles in liquids of various degrees of viscosity and 

 with various degrees of surface tension at their surfaces. From 

 this enumeration it is evident that the number of different mag- 

 nitudes involved is very great, and at the start it seemed almost 

 hopeless to disentangle the effects due to each. The first matter 

 to observe was that, as in other cases of fluid motion, two cases 

 must be distinguished. These are the cases of slow motion and 

 of quick motion. When the motion is slow the viscosity of the 

 liquid causes the flow to be very simple. It entirely stops all 

 whirling and swirling, such as is seen in the water behind a 

 boat. When the motion is quick, on the other hand, the flow 

 is very complicated. Whirls and swirls are set up, and the 

 resistance is increased, owing to the increased energy that has 

 to be communicated to the whirling and swirling liquid for each 

 centimetre that the bubble moves. The slow kind may be de- 

 scribed as viscous flow, and the quick as turbulent flow. The 

 most interesting point observed in connection with the turbu- 

 lent flow was that it was sometimes possible to increase the rate 

 of flow by i/icreasiu^"- the viscosity. Increasing the viscosity 

 of a liquid generally makes it flow more slowly, but in some 

 critical cases the increase of viscosity may produce more effect in 

 decreasing the turbulence than in increasing the viscous resist- 

 ance, and the result is to, on the whole, reduce the combined 

 resistance so that the bubble moves more rapidly in the liquid 

 of greater viscosity. Another matter that was of interest was 

 the question of the size of the bubbles, and how it affected their 

 rate of motion. Very long bubbles moved all at nearly the 

 same rate, but short bubbles had a great variety of rates. Very 

 small bubbles ran along ever so fast, while ones only a little 

 larger went very much more slowly. These latter blocked up 

 the tube much in the same way that a crowd blocks its own 

 egress through a doorway. However, bubbles a little larger 

 seemed to have more sense, for they shape themselves into a 

 sharpish head, with the result that they can make their way 

 along the tube more rapidly than smaller ones. Those a little 

 larger again take up a dumb-bell sort of shape, and block the 

 tube, and go more slowly again, though not so slowly as the 



NO. 1267, VOL. 49] 



smaller blocking bubbles. A little larger go somewhat more 

 rapidly again, but as the bubbles are made longer the differ- 

 ences between the rates of the quick and slow sizes become 

 rapidly less and less until pretty soon all go at the same rate, 

 .no matter how long they are. This alternation of speeds is 

 evidently connected with the ripples that are formed at the head 

 of the bubble as it passes through the liquid, much as a stick 

 moving through water makes a series of ripples upon the sur- 

 face. If the ripples are so long that the bubble has a pointed 

 head it goes fast, if it has a blunt head it goes slowly. These 

 ripples are in some cases very marked. Mr. Trouton found 

 that when a bubble of oil was allowed to rise through water 

 with which one fifty-thousandth part of caustic soda was mixed 

 the ripples became quite a feature of the figure of the bubble. 

 They at first extended as a series of rings round if, which, 

 however, soon coalesced into a spiral wave, when the bubble 

 rose rapidly through the liquid with a sort of corkscrew motion. 

 If the tube were inclined the ripples were only formed on the 

 lower surface of the bubble, the top surface floating up against 

 the containing tube, and the ripples then looked like the feet of 

 a caterpillar walking up the tube. This is not the only case in 

 which surface tension motions simulate muscular actions, and it 

 is an important question whether some of these actions are 

 similarities or simularities. 



The surface tension between the air and liquid if the bubble 

 is an air bubble, and between the two liquids if the bubble is 

 a liquid one, has a very important bearing on the rate of motion 

 of the bubble, for it is owing to this surface tension that the 

 bubble swells out and presses against the sides of the tube. In 

 consequence of this, when the surface tension is large the bubble 

 moves more slowly than with a small surface tension. It would 

 take too long to explain all the considerations by which Mr. 

 Trouton was led to conclude, by the dimensions involved, that 

 the velocity could be expressed in a series of powers of S/^5D- 

 when S is the surface tension, ,/ the acceleration of gravity, 5 

 the difference of density of the liquid and bubble, and D the 

 diameter of the tube. This series is multiplied by iJ./g5D^ where 

 /x is the viscosity of the liquid. Two assumptions are made. 

 First, that the viscosity of the material of which the bubble is 

 made is negligible ; and secondly, thai the motion produced by 

 the surface tension is negligible compared with the motion pro- 

 duced by gravity. The series he gets from his experiments 

 represents the results as accurately as can be expected, consider- 

 ing that the bubbles varied in density from air to mercury, the 

 viscosity of the liquid from i to 8^;^, and the surface tensions 

 from 2 to 370. The series Mr. Trouton gives for calculating 

 the time, T, a bubble takes to move one centimetre is 



'P _ Ai/i , A.jM*^ 1 A.i^S- 



The values of the constants cm be determined by the values he 

 gives from experiments on glycerine whose density was i "25 

 and superficial tension 63 dynis per centimetre. 



A,/ 



= 1-308, 



and 



= '0009108. 



The formula is unfortunately a very inconvenient one for using 

 to calculate the quantity that enters into it, and which is the 

 most difficult to determine, namely, the surface tension between 

 the bubble and liquid. This method of determining surface 

 tension is one of the very few by which it can be determined 

 without knowing angles of contact, which are so very difficult to 

 determine at all accurately. In this way Mr. Trouton has 

 determined the initial surface tension to be 6'$ between a bubble 

 of water and glycerine that was pretty rapidly dissolving it. The 

 ripple method could hardly be applied to this case, and it is 

 doubtful whether the jet method could be applied to the surface 

 between two liquids. 



In connection with the high power to which g is raised in 

 the formula it is interesting to note how, by altering the accel- 

 eration on the liquid by impacts or by centrifugal force we can 

 very much increase the rate at which a bubble passes along a 

 tube. This seems to be part of the rationale of the methods by 

 which a bubble in a spirit thermometer can be shaken or 

 whirled up the column. 



The whole subject is of considerable interest, and lends itself 

 to experimental investigation with very simple apparatus. A 



