Gatha, K M

Gokhale, N R

English

IACS Institutional Repository

CORRECTION FOR STOKES’ LAWN. R. GOKHALE and K. M. GATHAPhysics Depautment, Institute or Soibnck, Bombay-1 Bec&ived foi publication. May 22, 1958A B S T R A C T .  Millikan’s con-cotion to Stokes’ law for water droplets falling through ttir has been measured, Some necessary improvements over Millikan’s method have been introduced. The present direct nioasureinont yields tho value A = 0.701 for the relevant correction constantINTRODUOTIONTo study the rate of evaporation of unattached water droplets, they have been allowed to evaporate at a controlled temperature and pressure within Millikan’s oil-drop apparatus, containing air at some specified relative humidity With the help of Stokes’ law, the droplet radii have been calculated by measuring the values of velocity under gravity at intervals in the usual manner. The range of the droplet radii iii tho prosejit series of experiments varies from 5 X 1 cm to 2 X 10”  ^ cm. Since such droplet radn are not large compared to the mean free path in air at room temperature and atmospheric pressure, Millikan’s correc­tion to Stokes’ law has been experimentally determined for water droplets falling through air.Ml LJ.J K A N ’ S COR M NOTI ON TO S T O K R S ’ LAWTn gases a t ordinary pressures the slip due to molecular inhomogoneities makes Stokes’ law slightly incorrect even for spheres with radii as large as 0.006 mm Mill’kan lias suggested th at the usual Stokes’ law should be replaced by an equa­tion of the general form,64X -  67riyi2F,(l+^7/i2)-iwhere I is the molecular mean free path in air and A'(1)(2)where A  and B  are constants depending on the nature of the gas and the drop substance, while C is equal to 1.25 Millikan determined the values of by the oil-drop method, for a wide range of tho ratio IjR, for different drop substances and media.The correction (1+.47/72)^1 can also be written as where 6is a constant and p  is the pressure.521522 N. R. Ookhah and K ,  i f .  OatJian  E  T 10 U M I N  A 'r  1 O N  O F  A ' F O H W A T E R  D R O P L E  T 8 l ^ ' L L I N O  t h r o u g h  A I RI t  may be noted that as the readings m the present series of experiments are taken at atmospheric pressure, the second term in equation (2) would be­come quite negligible and A ' is equal to AThe higher rate of evaporation of water, as compared to that (jf oil, makes the application of Millikan’s procedure to determine the value of A ' for water rather difficult. In order to avoid any appreciable evaporation of the observed droplet, the following three precautions have been taken;(i) The air inside the chamber was made saturated with water Vapour by keeping four small water-boats inside this chamber (n) W ith the above arrangement the air inside the chamber is made saturated for plane water surface. lIowoAmr, small drops \|rith radii of the order of 1()~  ^ to 10“® cm will evaporate as the vapoun pressure on a convex surface is more than that on a plane surface H e n ^  beforeTABLE IObserved relation between and {llpfi)pQ Igg I («OP) OIf '(^yXlO!* v/XlO-'* e j j X l O i f  n ( h o c ) (cm.^sec) ( c n i /H o c )  ( o .b ii,) (e.s.u.) x lOsRx l OB ji? (cm ^Ipn  (cm) o fH g) I1 2 3 4 5 6 7 8 \) 1 0 1 1 1 2T " 40 .0 3 .2 2.025 25.31 17 91 3 5.970 70 89 4 142 76.40 316.02 25.3 4 .5 3 202 18.00 17.46 3 5.820 69.69 5.208 76.30 251.73 8 .5 14.7 9.530 5.511 21.36 4 5.340 6 6 . 2 0 8.984 76.40 145.64 14 0 8 . 8 5.786 9 204 16.60 3 5.533 67.39 7.001 76.35 187 15 30.7 6 . 2 2 638 13.06 11 73 2 5.865 70 06 4 729 76.45 276.76b 21.5 5 3 3.768 15.29 17.02 3 5 673 68  52 5.649 76 45 231.57 16.0 7 .3 5.063 1 1 . 1 0 16.74 3 5.580 67,76 6 549 76.40 199.88 4 1 .0 1 1 . 0 1.975 7.364 6.042 1 6.042 71.47 4.091 76.40 320.0» 7 .6 24 .6 10.80 3.294 21 .31 4 6.327 65.70 9.666 76.60 136.710 11.9 1 2 . 0 6.808 6.760 16.28 3 5.426 66.63 7.600 76.50 172.11 1 9 .9 9 .9 8.183 8.183 21.54 4 6 385 66,19 8.326 76 35 167.31 2 27 .6 6 . 8 2.935 11.91 11.70 2 5.860 69.95 4.986 76.30 262.8Correction for Stokes^ Law 523starting to take observations on a (iroi)let, ooiisiderable spraying caused numerous droplets to enter the chamber and evaporate for some time. This procedure further reduced the rate of evapoi-ation of the droplet under observation(iii) l"he time for which the dropltJl was under observation was minimized so as to make its evaporation negligible for all practical purposes. The procedure of taking observations has therefore been altered from that followed by Millikan The velocity iindor giavity for the droplet was measured and almost immediately its velocity in the opposite direction, with the electric field on, was notedOnly two such observations wore recorded for each droplet. The variation in the values of the electronic (iharge ascertained by preliminary observations, was from 5 x 1 0 “ "^ e.s.u. to 6 x  10~^“ e.su. for the dorplet radii in the present series of experiments. Hemje it was possible to guess correctly the value of v when the same was small, ft is for this reason that the value is chosen equal to or less than  4.A number of preliminary observations were taken to calculate approximately the value of e .^ J3ut only those observations, with n bclv'cen 1 and 4 were used-> { l I p R )1 . V arm tioii of e'ifs against {Ijplt).for further calculations. These observations are presented in Table I. In  making these calculations, the density of the liquid (t=  0.996 gm cm"®, the density524 N , R . O o k h a h  a n d  K .  M ,  O a th aof the medium 0.00129 gm cm"“ and the visoosity of the medium 183.2 X10"“ dynes sq. cm. per unit vel. grad, have been used. Further, one divi­sion of the tele-microsoope equals 0.081 cm. The second column of Table I gives the values of the time tg taken by the droplet to traverse one division in the tele­microscope under the gravitational field alone. Whereas, the third column gives the values of the time tf taken by the dorplet to travel one such division when the electric field is applied. After calculating Vg and Vj, is calculatedwith F — 2.1 S3 volts cm"^ The values and e^ “l^  are presented in the eighth and ninth columns respectively The tenth column gives the values ol R  and the last column gives the values of (\i2iR) varying between 130.7 and 320.The gi’aph showing tlie variation of against (I j 'p R ) ib shown in figure 1. The points lie fairly well on a straight line that passes through the calculated value of when {^jpR) is zero The constant h was calculated Irom the slope of this straight line giving 6‘ ~ 0.000512 Taking / — 0.6x10"“ cm and no|)ing that J — h ip l, the value of A was calculated giving A — 0 701.U K F  K H E  N C S A , 1912, E leolronM illikan, J\ A , 1920, Phys, Rev., 15, 545 M illikan, K. A ,  1023, Phys. Rev.. 21, 217 M ilhkan, H. A„ 1923, Phys Rev., 22, 1.Htolcc, 1851, Cambr. Trans, 9 rfi MnilmnnUral and Physical Papers 8 , 59.

Correction for Stokes' Law

http://arxiv.iacs.res.in:8080/jspui/bitstream/10821/2138/1/Correction%20for%20stokes%20law_N%20R%20Gokhale.pdf

Correction for Stokes' Law

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