EVAPORATION OF VERY SMALL WATER DROPLETS

• Document Type: CREST
• Collection: General CIA Records
• Document Number (FOIA) /ESDN (CREST): CIA-RDP82-00039R000100120036-9
• Release Decision: RIPPUB
• Original Classification: S
• Document Page Count: 13
• Document Creation Date: December 22, 2016
• Document Release Date: May 18, 2012
• Sequence Number: 36
• Publication Date: June 27, 1951
• Content Type: REPORT

Declassified in Part - Sanitized Copy Approved for Release 2012/05/18 : CIA-RDP82-00039R000100120036-9
?Lm Rr*Tstrr1cf n? Vs7 wat.r Drop:*t,4
M. P Toltyes' and Yip 9hie4~
I.ts ~..~E Yt t til J'c 1 age y. N~ z
50X1 -HUM
50X1 -HUM
fit; h pi4:
!w.
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 M. P. Tiaatge~r end K. Y.. Shveta
E
E
Although the eeaporstioa of drops has bwn a tudiW both experia snt~all~r
Declassified in Part - Sanitized Copy Approved for Release 2012/05/18 : CIA-RDP82-00039R000100120036-9
and thenretio..1317, the problem is still tar foa aatvsd.
resides` the well?known classic works of )(ixwes,l and dtsfgn experimental
atudiaa on the cvaporation of drops have Wen contributed by Lange it (2),
V,vrubov (a), Fro~eiing (3), ?ir&deiean (4), Kiryukhiti (s), Zak (6), 9tai'okadoa.
aka(`a (7), Jaranayev (8), ad otiaraj FEuks (9), L ybcnaon (10), and Franks1'
t].2) wr titan theoretical works cm tho aub jaot, The results of these heo?
retical stun iea roui not bt uaad, however, in he study rft tt~e ava,jn7Eatio.n
r drn;1a (XEtcLLL J ieb Ulan 1L0 ?). One of J c main ~~t'tf.ts et he
'4~~or~t,lc~A1 Wt ?K5 VU the reeI2mE-tion that eetu~*atior~ vaI ~,r conC~r~tration
e>! s t,ed rn the cz~rf i Ear t ? fi, ever rntitdrop M t ~ flows ti`rc+f~ tw
st.trry of 1A5ee, this 3saum;.tion placed an ~r~ec~i, ~t~~ c~~nci tin Utin the
`1' U'e~G,)tr wrt1k t, ~-N iv" ecenunt this 1'b~t t,t the valor cuncntrat,ian
rrE t: auri'dce 't` an eva,yor~kt~~~ dre~ i~ ditf~-rett !`ram urt;trttion ar le*ld
to cone1 tct aoz wt-i cn a i1`3'e r nc~t tbly f run trt t t
ty u,a tti,ry wr,ict-
dhc ^et make pr< riaioa f or train mare accurate c nd; t i' re
i , Val, r Conrentrator~ ~En tn~ ;)ropeurt'esce .
t:vaporet11on under natural conditions cor~e~at,e c,i tie follnwins piocceee1
,
trarwdi tinn es` moLeeuleie from the liquid to the taaeou mediuati (actual evipor-
etion), trarieitien ot` the vapor molecules tto the liquid elate ("adheeior,N
of the vapor ioleculea to the liquid eurr'aoa ? thet is, condene~tion), and
diffusion of the vapor noleculee froa the liquid r~urxace into the surrounding
mediusi.
The first proceae is detstjned by the physical ocarscters,Ucs oEP the
1
drop (tei p.rature and awlecult weight). The number o! ao]Eeoulea ub3,o of
escaping from the liquid i
,
by the rat town tOra1s.
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50X1 -HUM
:ate ~R
~ *t
 Declassified in Part - Sanitized Copy Approved for Release 2012/05/18 : CIA-RDP82-00039R000100120036-9
where Ate arsnCd 1' the form4w L ? of RT 1n
In hie work (3) b'rueelin save as the fcr'rula fr t,~-e epeld of evbpm`
rrattton! `
p p
_F: 0
A is easily Been, this :expression ie practically identical with
(2) for wbter (because of the en*aJ,l value of alpha N. ).
:U' . (1)
RT
wore pn is niuLauJ vapor prneuI'ei P La aK 1$ Uler wetdht, 1! 1. the t re
t
tare at the liquid, A is the dw conetsntj and a1p~e 0 ii the coefficient ,
of acooreodetion (this ooeffioient has loni$ b*i Ikea u unity for 41
uids inching water), This ooeioient has been receMly determined gttit*
rtliab.y for eevers.l Uquida. According to &1t4 (32) the aoelrioient o=
accorwdation for water is o.0Y-0'3 for teopereturen fros o to 15. This
volute ayreee with the Yalu. of alphas P whic#i 8arsngiv obuthed frog: t1:eoret4
teal consideration.
The munher of vapor aclsoulea condenain~ on the rnuld surface is d.t.t.
mead by s eta ilar formula. Diftuairn oil vapor m 1eculeb, w:,ich o'tt'r'iined
$p(d+bl o! Evurormtion da ot-vi M blur e~auiA.l to tit d;flererce ho'en .ri.'
iret r evnporat~on) arid e~'conr (t ondenentian ) pr,nce-baee.
oeeit;r7eti31nt the diftviton cuvZf~cibnt as D &rurop ridius ~' ro
and eubstttutin` ~n trfnr 4ula t:,t concentration r, in the p1McA off' th' vapor
hreenure p, we obtain the tol.nwing conditic-rs on the drop'e etutaeer
..~, ~? A j.or r= r? (2)
r
Formula (2) or (Z') deterairiee the concentration on the drop'a surface
11 M fvaporation_ of an lrwovable Drro!P. -- The 3tationa_7 Process.
The email drops (r 4 lo" f o~) wfiSah coepoee toes and clouds have by
fallsn velocities, and therefore under ordinary conditions they raspy be
considered to be tntiovable with reepoot to air. This rectorti there!'ore trill
apply not oe*1 to evaporation of iIIava11e dropI b to ewaporatlon or
s MIU drops under ataa pherio eondi.
Declassified in Part - Sanitized Copy Approved for Release 2012/05/18 : CIA-RDP82-00039R000100120036-9
 The hagc sgwtion at dif Aistis in spllq1as3. aoo4iaata t~ thti oisn
Rtii bo of eh. _ui rs
Ths bwndar~ oanditi~a~ue w s
:bi s e p0 , -. 7)J a A ( C, -
)'1. r'* C~0 j
6
Thr solution of .qut.tz 0) which utioti~ the aooditioris (-,) sot
C
4aj1 r $.
. the waps ' osaoeotrstiea on us dnp surftoe io I
C(r.) ""' -' (61
A _
Forlmwls (b) shows that the tapor ccnorn trstion on the su'tsce of wail drops
is notably different fray the saturation aa. `
T 4$ss4t otr1ogoblfton is obtained tin ( S ) b siaple ditferan
tistioor
EDrri ' ry
Thin equation shows that vAryeiaa11 dx'ope Wi I1 havd high ernpor tion
'n di' sir.
The change in drop aus is ~qusl to
tvi
`The taage in the drop's surf ace is equal to
s ~. ~'DcM
.. ..9~', s (i?)
where
ie the densit7 of the li
uid
q
.
f
Pormnl&i 6i4 tatkzisU'o u classic for!Iulss under the eon-
dition that Del;Are. `
The ohange of drop rediua M'inaperstiwnt it dettnsd by tM torrula s
... ADc,. - - i
~t " 1 to rp p
Fran this fonsula, the lifetias.at ? dreg os initial ndisr ro is gi en by
Declassified in Part - Sanitized Copy Approved for Release 2012/05/18 : CIA-RDP82-00039R000100120036-9
 Declassified in Part - Sanitized Copy Approved for Release 2012/05/18 : CIA-RDP82-00039R000100120036-9
113.4
~-1. I greet dietii c. trai thr drop.
~1t A2aI1Rt1t S~ ?JG "i * st
r
The tom obtaiiod hrld .Uy :~ 4r7 +ir, bit thqerr 'mood
tar moist &1r. To do tbie, o ?,,, , nrpootirir, rholl bo
uI. L sporotian at ra Zrro-rblo Gam, Tbo NsumStatiooarPiaoess
The etteot of the noet*ticnar7 condition in the on atiaa of an
.5 tW
movable drop na inreetigited by PWco , bat spin ender the~oendition tI&t
sat LrAtson raper conoentr&tionf on the dropteartaao~ It weuld
theretore be jnEsridtjjg to reopin th.ta gnootion for tho .Ore aeourate boaa-
`henoe the flow in
lorry conditions 'r-4e*u',u1 abon.
i.cth F t
f~r?
then1 by vaina 'uoundary condition (1l), we rind
E(t)= p Irr.
a~ AD
r
L
'
ii r . w sirj .
VN
r Ii
The
oubititatod in ill the = i for o and the osu.atti
f
mm a
thq form:
Z
,re wet
The uaundary cor~ttions are s
+;t:iO, of
/ ! 1 A fpir.r6 (t>o).
~ r Ac ~
The basic equation toe the nor tationar oceee oar br written in b
FJ.
I solution or equation (L2) ie teen by the expreesion
~
cr
1o r d s FCC)
P` yDCc-t
Eiy eatlafy-ing Us bouadar~ oondition on the iustsoe, t~ obtain the foUo.
trig integral .gwion for ~ ' dotirainstion et ?(t):
_ P ~Fc'cd! -
ri:t, + )
w
;?
- i
where
I, = -L .
?
I
Cr.A
v
The r~4tvtioa of this ego q sa b. reps od is the I3ag Hemet
ai.'.
t
F'Ct) .'L$-KC'1iU4
U-
(12)
(15)
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 Declassified in Part - Sanitized Copy Approved for Release 2012/05/18 : CIA-RDP82-00039R000100120036-9
pr'es upon tloi i saor'ttlf3n1. Thy ?irstmi 4 othe eerlee core
s a while the toL awin xatraddoe
r'ieAo,de t' th' eta*ionsry Proce
g
n
th+~ correcttoa ter the nnn etMtiunir~r prccse3 (actually5 the order of the
when ~ PI,ute
end K ie tM !'onotioo. It is auuMd loan tibe
swnLi.a that s daa not .4 Frith tla.. Slnos Chi patrrtafl is lu'N,
r k(I') ....1 I,(,.. .}.
4nd ub ain
It 6
r9A
F(t)ri-'
we We the a oUa aip&ieion of the PInaU.S
Celit
This torte 1
4
t,e eterminad b;i thy ords+r n?" A).
Tht~+ 'arrectic,i 2te no ltptbi`! or valor trope, be.atac evaporatlon of
,. .
Cu, tnuov*bts rh?op c&ri t coneidored futr eccurahi,r u a nun et,a.
tionsry proceed.
It is tors ditt.cult tic: eveluste th-r el!uct of t1~: iecresae in drop else
during its .veportton
The rough ev4uat~or of this ett ct which di. Fake wade (g) ehove that
it cannot be disregarded. There are serious mathetaticai obetae es the
accursto eveluattoa of this etteat.
It is eoaetLnes necesrarry to consider that the m&xinur eoncantration ct
varlea with Cite in order to 3alou1atei the speed of evaporation of the drop.
It em l e aaeua ed to vftZ"7 frith tiae, we hive inatosd of (15)
r
whore
M~
~~
th. lorwula which bolds tN,1tionar7 pra
i-;. L'(A.))vt
eto eMsluaOe tha influence o! ~ the non~et~tiionar'
c(t) iCt)
The aolubl.on of 41N last .quatilon is wilt farad aad is it the taco
. r(t) = j;c"(q'4) 4(~) irj5J4V , (16)
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 Declassified in Part - Sanitized Copy Approved for Release 2012/05/18 : CIA-RDP82-00039R000100120036-9
' WXt~t I Ij1 ttrn't n erto i ? ? ?? (y), ?1 th ir t o~ L(t, !o I f+~'Mf~ :
tr' } f *igPP$i ~ C11~- R~- QR1A CE flU t. ~-I* UY L14 (~1P4Pd U~7CiIll l ~ I't$ ~~tf ~y
cone tder tho i _i heat ! t! usion
(rT) _ , {rte
~.:.
at `un!
Sri
:i i t~ounaery :I),1-stjorn3
t ,ld rYl~-al'Ji un.. ~I ~c)L J4, "T~j (Ir'ci ~ uu' ` '1~~~~Iy F.
~~-~'~us of ha~l+ Ltlbvro~ d~~~~,u~d~r-~ Gr
I'+E':1' ;nf, ?. t,~ i'
~-1 ( ?
z,.3
intruse thl~ u.itnkt
IF
1
?(r2 O Tyr, ~
?r rtre
e;it ~j1i11 Y;1L b's z`. ii t y
a,
%,.=-Jr: k
a1kC1o1"j~ t.o 'Ili
_4 4
?
r
'0
IfI
~,,,
11 ?.. I-__--rl- Y __.ra ..~. Gts It 1? 1 a-
I ~~ylaki. u% t.
r,
rA 4 T d'r
-.--- _-L__U f -
r
Ifl~it balur,oe rn&y be written with urft~i' r
1
~N-rtn
I(: t s ; 4a
ern yaw:n "r1y tnt' tN )
'1+- -.a"tt-rrE,4ur~ ' 'C1`Ati6 R'! + pa
,., n
1-.uF . t r tlT -
t4C1; i .t&(y !n + Pty : n1, nw.,~
.1 5P - c 7. 7.l rti r r
h-irt,L is thF1 latent heat of dra ration), or
_ AP
_____ - - -n-- -- (( u._) ?
rd ,~~~r
.;ustituting the v1Llues o! and F tram ;16) and i6), we obtain the ;'oi1-~w
rag integrai egvition for determination of the temporat u 'e r1eoreas e :
1
5tcW+p')
/:_ ~-
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 Declassified in Part - Sanitized Copy Approved for Release 2012/05/18 : CIA-RDP82-00039R000100120036-9
wtieio
rs
od to~!_lO
gNii . tLon @$i Lb. obmai
The ,AIt ?nto
~ccP-t,Ps)=B erj4 ('[**-a') i:::i:bl hors
ou i' ? known tUMtt Of To
k - . )P%.I
i; (.) I + '1 ' J ' 2' 4-Ar. .
ba oonld by tts stbod of ao .ucutirn oPPraad t o~ns
~uttivn ~'~,
not rtthout oonsldarab1~ diSlio3t7: h~WwYer.
e d~oreals o t o drop can bye !oand ror7 si*ply it u eon-
Th. 1~ePperatur
tatiio~'' prooooo~ Tae heat flow in this aaae is expressed
ridtt the quooin
the s+ra-a fonaul.a u the spied at ~-aporatiofI
Q*1Tr.).