DIFFUSION KINETICS OF HETEROGENSOUS CHEMICAL PROCESSES: REACTION WHICH TAKES PLACE AT THE SOLID-LIQUID INTERFACE

• Document Type: CREST
• Collection: General CIA Records
• Document Number (FOIA) /ESDN (CREST): CIA-RDP80-00809A000600280053-2
• Release Decision: RIPPUB
• Original Classification: C
• Document Page Count: 5
• Document Creation Date: December 22, 2016
• Document Release Date: October 12, 2011
• Sequence Number: 53
• Publication Date: January 11, 1950
• Content Type: REPORT

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CLASSIFICATION COIW.7 IPIAI. CQ 'F -"' %'T1AL
CENTRAL INTELLIGENCE AGENCY REPOF
INFORMATION FROM
FOREIGN DOCUMENTS OR RADIO BROADCASTS CD F
LANGUAGE Russian
DATE
WHERE
HOW
PUBLISHED ) clnthly periodical
SUBJECT Scientific - Physical
TIII COCU024T CONTAINS IIIOIIATIO^ AI/CCTI94 TM1 IAflfIAL PITAMCI
00 TUx UItrIO ITATII 111TMIM TMC ^CAIIII CI CII:9IAOI At, 19
I. A. c.. al AND al, AO AICMOIO. MYNA:*
II$IOI oil TIl I XYILAT1?I
O! 111 LQIt%ITI IM AMT IAIICI TO AI OA ITMOIICIO PII10I IC PIG.
w1O1TIp IT LAW. IIVAM104CT10I 01 TM.I M. IN
MOMIIITCD.
900a Concepts
The total speed of any heteroaeneods chemical conversion consists of the
speed with which the reagents are transported to the place of reaction and the
speed of the chemical reaction as such. The speed of the chemical canversicn
Is of particular interest to the chemist -- for that reason the diffusion k1-
notice of heterogeneous chemical reactions in solution have, been neglected
hitherto, and na well developed quantitative .henry exists. An attempt is be-
ing -de to fill this gap. This paper deals v.tli< reactions at the solid-liquid
interphase for laminar flow; the second paper w. 11 develop the theoy for tur-
bulent flow; the third paper vill deal with reactions at the liquid-l1go.id
rather flan solid-11qu1d interphase; and the fourth will analyze cases of ocu-
posits kinetics.
In practice, a liquid which transports matter usually floe so fast that
the flow takes place at large Reynolds' numbers, for a hydrodynamic boundary
layer develops nn the surface of the solid aad ecmetimee essentially turbulent
conditions are established.
Hitherto Nernst's theory of the motionless diffusion layer, with` a con-
stant concentration in the body of liquid due to stirring has been used =I-
vareally almobt without change. The diffusion current (jj in accordance with
that theory can be expressed mathematically an follower
J=D ce~Ci
Cl = ccIncentration at the place of reaction, i.e., on the surface of the
solid.
C0 = concentration at the outer boundary of the diffusion layer, which
ie egaal to the average concentration of the entire solution.
50X1-HUM
DATE DIST. // dear 1950
NO. OF PAGES 5
SUPPLEMENT TO
REPORT NO.
THIS IS UNEVALUATED INFORMATION
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CONFIflEHTIAL
50X1-HUM
The values of p determined by experiment from observed values ~t 4 ar
o - wiaun of the aiffusion layer.
found to be 6ependout upon the flow velocity u of the liquid, its viscosity
an
l th
diff
a
e
usion coefficient D. Absolute values of of the order
10-2 l0-4 centimeters verefound by using the ex reeeion for Nernst'a dif-
fusion layer, while he actual layer thickness found from hvdrr,dvr,amic -I-
results :.a1 been noted long ago, but the attempts to develop a a new ew t hearj((,()hv,cksn,
fxao`-Sausenetekiy) #4 not go far enough. On the. bar band a t-
-1u
a
y
pe
Dy the author in connection with the treataaent of concentration polarization in
,alectroysie lot. Zhur. E'iz. shim, Vol. 13, p 355, 1944) was found to be fully
The complicated equations of Xavier-3tokee, which deal with the stationary
flow of viscous liquids and relate the velocity components Vi of the liquid
and the pressure (p) in it tc external forces acting upon the body of the liq-
uid, can be considerably simplified to cover the conditions involv6l in this
came. At high Reynolds' numbers, the flow can be regarded as consisting of
two regions -- the region of nonvi.ecous flow at a distance from the Jolid cut -
face and the region of viscous flow in direct proximity to that surface (PranAtl
b
oundary layer theory).
Aeeuming that the boundary layer is very thin (a condition corresponding
to the actual eta?.e of affairs in this case), it is obvious that the speed will
change rapidly in a direction perpendicular to the surface of the solid, but not
along this surface. Directing the y axis perpendicularly to the wall, assuming
that the flow takes place along the x axis, and making a fPw further eimplifica-
ticane, the equations of.Prendtl are obtained from the Navier-Stokes equations.
Applying Prandtl's equations to flat solid bodies or those having a all curva-
ture, the following working relationships are obtained for the effective, thick-
ness of the boundary layer (go)
(k= rate of flow outside of the boundary layer) and for the components
of velocity.
c)
In foruviating the basic equations for the transport of a substance to
the reaction surface in a r:.rrlme liquid, the co-calleC. I);.le'e .o:raber (indi-
cated as Pe) can be introduced to advantage. Pekl.e'e uumt,;r is similar to
Reynolds' number, except that it measures diffusion rather than the flow of
.liquid. Comparing Pekle's number with Reynolds number, we obtain Prandtl'o
number (9)? I aCle
Vf 8x'
(3) Pea ID a __VL
In liquids Prendtl'H number is always large in comparison with unity. In
gases, on the other hand(flov of fluidic this case),Prandtl's number is of the
order of unity.
C4)
Because of the mail value of the diffusion coefficient, Pekle's number
attains large values even for the lowest velocities, even when the correspond-
ing Reynolds' number is still small in comparison with unity. Therefore, mo-
lecular diffusion in liquids may practically always be disregarded in eP a?i-
eat with the eonvective treoepoR of a gKbetance; for large Pekle's na~ess,
- 2 -
00 F L i~ AL
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thn eLM.- =amizag may be applied to convective diffusion as was applied
preoioua]y to the flow of a liquid around a body for large Reynolds, num
bars.
constant. However, this condition cannot obtain at the reaction surface. A
thin layer in which a rapid change of concentration takes place must exist
close to the reaction surface.
regions, as was done for large Reynolds' numbers; 1.;., he region of constant
concentration remote from the reaction surface and the region of rapid chaagg
very thin layer of liquid, is similar to the Prandtl boun l t,
dart' layer; the vis-
cosity of the liquid, which is basically unimportant in the flow volume, plays
appears in the liquid layer adjoining the reaction surface. This layer can
The concept of diffusion houndary Layer Is ob_vl Ugly a gene ski ..~.
two concepts is the fact that n lignad'e velocity of floe In _~__ _._
"- _ o uiffuoicw uCria7o-
ary layer can by no means be aseamed to equal zero. On the contrary, the dif-
fusion and convection flows of the substance here have the same order of values.
The diffusion boundary layer !a analogoue to the heat boundary layer in the
theory of heat transmission in liquids. There is, however, a real quentltative
- ~h--._ _. __
difference `
etwee
butioa of the substance, are different from the analogous properties of the heat
boundary layer.
In the diffusion process, the role of kinematic: viacosity is usurpee.ly by the
coefficient of diffusion D which is numerically almost a thousand times emallsr.
Therefore, the diffusion boundary layer also must be considerably thinner than
the Prendtl boundary layer.
IDVIS a0 (ns)-1/3
SO.
Thus, for Pr approximately 103, the thickness of the diffusion boundary
layer is approximately one-tenth the thickness of the Prandtl boundary layer.
Therefore, the tangential component of the liquid's velocity of motion at the
periphery of the diffusion boundary layer is only 10 percent of the velocity
at a point remote f;cm the solid surface. The following relationship can be
S tiD~'3 vq Uo'
Cs )
This shows that the thickness of the diffusion boundary layer is
inversely proportional to the square root of the velocity Uo of the imping-
ing flow Md increases in proportion to the square root of the distance x
from the advance point of the liquid flow to the body, the thickness is also
dependent upon the liquid's viscosity and the coefficient of diffusion of the
particles (see below).
oil,
^
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50X1-HUM
Calculations show that, in the diffusion boundary layer, the ccac,Datratign
of the solution increases r&pidly and that tho increase may be considered linear
in the firot approximation.
Therefore, the expression for diffusion current may be represented approxi-
mately in the fora Jdi.: = Jo/13f i.e., in tie ae form as in NeraeU't: tbecey.
Now, however, S? is a completely determined function of the liquid's prop-
erties and velocity.
Solutions of Equations of Diffusion Kinetics
disk it could be shown that 13 CI
where (J = angular velocity of the disk.
Problwe to thle connection are frequently encountered in electro-
chemi.stry. For the density of a diffusion current (J) at the surface of n
The full diffusion current (Ilim) on one side of the plate was found
lam" CK-c4s.
(7)
where C. the so-called drag coefficient) represents a ratio of the frictional
force tangential to the plate to the dynamic head and ce'. be expressed as fol-
lowe 1,33
Re
71- XY4
In the preceding examples cases of forced connection vero conaidered.
At high PVMdtl nmabers,, the following expressions apply for the density of
the diffusion oar7eat at the plate the full current (I), and the thick-
ness of the diffusion current (b`1) 1/
r 4
Y I g l c_)C-c 0 4
J ~4~.54 ~Pr1 L 4P(C va x,4
o~F Cn
r~~;dG =o.7~ (~r) % g(x)c_c, +P~~~~~ 11 bl ,
-~f: "1Y .1~
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Lance from the lower edge of the plate and is only elightlydependent upon the
concentration of the solution.
4. The Problem of Internal Flow, Particularly in a Pipe
cal. of the Poiseille flow in pipes, is established only in the SO-callmd exit
section of the pipe. At the entrance of the pipe a boundary layer is formed,
the thickness of which grows gradually in the entrance section until the whole
cross section of the pipe is filled by the layer, and further flow takes place
according to Poleoille. The length of the entrance section is by no means
small -- to give an example, it has the dimensions of 50 diameters at Re
2500. The saa6 conditions obtain in regard to diffusion, except that the entrance
section is much longer and may exten over th
...h
l
,_- _e --_
e
o
e
~_ a~C03-5) 3/s e"
pro 5)
er$xponent of S is unclear in the original; 4/3 appears to be the logical
The diffusion boundary layer fille the whole cross section of the pipe at
As Pra+105, the length of the entrance section becomes so long than it
practically always extends over the whole length of the pipe.
Agreement With 8xperimental Data
In prior work done by the author, good agreement was obtained in experi-
ments of an electrochemical nature. Lecause of the complex hydrodynamic condi-
ticm encountered there, this agreement was que.litativd rather than quanitative.
In particular, the reason for the divergence of results obtained by various
authors on the problem of dependence of diffusion current upon velocity was
brought to light. Various authors pointed out the "potential" (expauential)
natui a of this dependence, but they differed on the value of the exponent, the
indices ranging from 0.5 to 1; this circumstance was due to the different de-
grees of turbulence in the various experiments. A com+rison was also muds
with experimental data on the dependence of current upon coefficients of dif-
fusion and viscosity, good agreement being found in this case. Recently, Suer
conducted special measurements to experimentally verify, our formulae for flow
around a rotating disk. These carefully conducted measurements showed that the
theory for the disk is in good quanitative agreement with experiment (cf. Vu.
liver and B. Kabanov, Zhur Piz Shim, Vol 22, p 53, 1948).
Nonetheless, a considerable part of the relations obtained are in need of
further experimental verification, since the neceasary experimental data are
not to be found in print. This relates particularly to diffusion currents in
the region cf turbulent transport of substance in the boundary layer and at the
intexphase liquid-gee.
C, 0P:r,:
AL
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