8/17/2019 Calibration of the Rolling Ball Vicometer

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V O L U M E

25, NO. ,

M A R C H

1 9 5 3

50?

Table

111

Lactic Acid Content

of

Heavy Steep Liquor as

Lactic Acid (Dry Basis)

Determined by Ether Extraction for

58

Hours

Conditions

Acidified and evaporated before extraction

Acidified

but not evaporated

before

extraction

Sei ther acidified

nor

evaporatedbefore extraction

2 2 . 8

2 4 . 0

1 2 . 4

tract ion time. Similar extractions have been conducted on steep

liquor which was acidified but not evaporated, and also on sam-

ples which were neither acidified nor evaporated (Figure

1

Table

111).

CONCLUSIONS

Lactic acid present in heavy steep liquor must exist partially

as

a

salt which may or may not be extracted with ether; in either

caqe it would not be included in the final alkali titration.

Direct extraction of heavy steep liquor after acidification with

sulfuric acid yields results which agree well with values obtained

by the oxidation-distillation technique on pretreated samples.

On the other hand, values obtained by the standard extraction

twhniq ue were about

1%

lower.

It

does not seem likely that

thii. is due to

loss

of volatile acids during evaporation, as heavy

st wp liquor is produced by a concentration operation which should

rcmove such volatiles. Friedemann and Kend all( 4) have shown

that

determination of lactic acid in urine by ether extraction

alv ays results in a loss of lactic acid due to oxidation by organic

peroxides formed during evaporation and extraction. There

also exists the possibility of lactic acid condensation during evapo-

ration, which would result in lowering the apparent lactic acid

content determined by extraction.

Although the extended ether extraction of acidified heavy steep

liquor (not evaporated) yields reliable results which are in agree-

ment with the values obtained by the modified Friedemann tech-

nique, the oxidation-distillation procedure is recommended be-

cause of th e shor t time required for analysis.

LITERATURE CITED

(1)

Elgart,

S.,

and Harris, J.

S I IND

ENG.

C H E V . ,A N A L .

ED. 2”

2 )

Friedemann,

T.

E.,

J .

B i o l .

Chem.,

76,75 (1928).

13)

Friedemann,

T.

E.,

and

Graeser, J.

B., Ib id . , 100, 291 (1933).

(4)

Frjedemann,

T.

E., and Kendall,

A.

I.,

Ib id . , 82, 23 (1929).

(5) Fries,

H., Biochem . Z.,

35,368 (1911).

(6) Kerr,

R.

W. “Chemistry and Industry

of

Ptarch,” 2nd ed.,

7 )

Kondo, K.,

Biochem. Z.,

45 88

1912).

(8)

Leach,

A.

E., and Winton, A.

L.,

“Food Inspection and Analy-

(9) Mendel,

B .

and Goldscheider, I.,

Biochem . Z. ,

164, 163 (1926).

758

(1940).

Chap. 11 New

York,

Academic Press, 1960.

sis,’’4th ed., New York John Wiley Sons 1936.

(10) Pigman, 11’.

Ti’.

and Wolfrom,

M . L., Advances in Carbohydrate

C h e m. , 1,257 (1944).

(11)

Somogyi, M.,

J . Bid . C h e m . , 90,725 (1931).

112) Trov. H.

C.. and Sharp.

P. F., Cor ne l l Cn ic . ,

A g r .

Ezpt. Sta..

iGemoirs ,

179 (1935):

(13) Van Slyke, D.

D., J .

Bid . Chem . , 32, 455 (1917).

(14)

Wolf C G. L. . Phys iol . , 48,

341

(1914).

RECEIVEDo r review January 17, 1952.

Accepted

O c t o b e r 27 ,

1952.

Cal ibrat ion

o f

the Rol l ing Bal l Viscometer

H . W. L E WI S

Bell Telephone Laboratories, Murray Hill, N. J .

N 1943, Hubbard and Brown 1 ) carried out

a

systematic

1 experimental calibration and dimensional analysis of a rolling

ball viscometer. The y determined a dimensionless calibration

curve, which enables one to design a viscometer of this type t o

measure a ny given range of viscosities.

It

is the purpose of this

note to show that one can, to good approximation, derive this

calibration curve from a simple approximate treatment of the

problem in terms of t he hydrodynamics of viscous fluids

2 ) .

IVe consider a cylindrical tube of diameter D , inclined at an

angle 9 to t he horizontal, and filled with a fluid of viscosity

,LA

and density

p , .

SVe suppose to be rolling down the tube with

velocity V a spherical ball of diameter

d ,

and density pa We

will use a cylindrical coordinate system, with Z-axis parallel to

the axis

of

the tube, with polar angles referred to a vertical plane

through th e 2-auk, a nd with the origin at the center of the

sphere. We Tvill also make the approximation th at the gap

between the sphere and t he tube is small compared to t he diam-

eter of either one, so that the sphere nearly fills the tube-this

is the usual, practical situation, and makes the calculation pos-

sible. We will systematically neglect higher powers of

D - d ) / D .

Now if we call the distance betn-een the sphere and the wall

of the tube u 7 9 , Z) , a little consideration of the geometry will

show that

So

we have to consider the flow of a viscous fluid through a nar-

row

channel of width given by

1 ) .

The total flow through this

channel will be

D2V

since we will, everyn-here except in the

expression D - d ) , neglect the differencebetu-een and d.

Now, i t is well known tha t th e f low of a viscous liquid through

a narron- channel of th is sort gives rise to a parabolic velocity

profile at any given point. In particular,

if

L is the mean veloc-

ity of the fluid in the gap, then

d 2 i l b r 2 =

12;

/u2,

where

r

is

our

radial cylindrical coordinate. Bu t the longitudinal gradient of

pressure

is

given by

p LPu/dr* = 12p

u/u2,

so

tha t our problem may

now be stated as follows: rye have to determine the distribution

of

G

as a function of

9

and

2, so

that the total difference of

pressure is enough to balance the re ig ht of th e sphere, and the

total flow across any plane Z = constant is equal to D 2 V .

This will determine p as a function of

V ,

n.hich is the problem

we have set ourselves.

K e will use the fol lo ~~i ngrocedure: for each value of

2 ,

we

will distribute the flow velocity, as a function of

9,

in such a way

that the longitudinal

pi

essure gradient is independent

of

-this

implieb tha t we

x-ill

neglect all components of velocity perpendic-

ular to th e axis of the tube.

Thus, we write

u

79 ,

Z)

=

B

2 )

y9 Z )

2)

The total flux through any plane perpendicular to the axis of

the tube \vi11 then he

flux = f

L 79,

Z )

x

u(8, Z ) X D d 9

3)

=

; 2) x u3 9, Z )

d 8

Substitu ting t he expression

for u

from Equation 1, and perform-

ing the integral, we find

[5 +

8a

+

2 4 a a

+

1 6 4

4 )

x

D

D - d ) 3B Z )

16

lux Fz

8/17/2019 Calibration of the Rolling Ball Vicometer

2/2

508

1 .o

where

Y = [ D 4 D 2 4 2 2 ] / 2 D

-

d )

Bu t this must be independent of Z, and must be equal to

so that we find

D V ,

10

4 DT.’

D

d)3[5

+ 18a + 2 4 a 2 +

1 6 a 3 ]

5 ) T0

  Z )

=

D

Consequently, the longitudinal pressure gradient is

1CY

(6)

and the total pressure drop along the tube, due to the ball, is

48

p

DT’

D ) 3 [ 5

+

18a

+

2 4 a 2

+

1601~1

rad

p

=

A N

L Y T I C A L C

H

M I S T Y

0 - E X P E R I M E N T A L , L I Q U I D S

- E X P E R I M E N T A L , A I

R

H E O R E T I C A L . NO

I I

grad

p dZ = 10 I C 10 6

lo5 I 4

10-3

r a 3 u .

A P =

rn

[ d]6’2x

Figure 1. Plot of Theoretical Equation 9’with Experimental

Points

7 )

E

5

with the calibration constant K of Hubbard and Brown, in terms

where, if we call the integral

8 r / 3 ,

thereby defining

a

number

I ,

we have

7 ’ )

1

I =

1/2 . \ / a

21’’’

0.398

5

In passing from Equation 6 to 7, we have defined a quantity

by the equation

2

= a

nd have again neglected terms which

contribute only in higher orders of

D d ) / D .

Thus , for example,

the limits on the integrals are not really infinite, but depend upon

D / D d ) .

This pressure drop mus t now support the sphere, so that

7r

r ~ a

p l ) g

sin 8

= - ~ 2 ~ p

i 4

and

of which Equation

9

is

7

D

- d 5 2

D - d

K = -

o

[ T ] = 0.0891

[ ]‘

9’)

In Figure

1

has been plotted the expression

for K

given by

Equation 9’, the points measured by Hubbard and Brown, and

the points calculated by them from other experimental data.

The fit, considering the simplifications in the calculation, is

satisfactory. I t can serve

for

the design of rolling ball viscom-

eters, although, for precision work, the usual calibration in

terms of fluids of known viscosity should be carried out . Equa-

tion 9 should, of course, be used directly, wi thout going through

the definition

of

K .

LITERATURE CITED

(1) Hubbard,

R.

M . and Brown, G . G .

IND.

NG.CHEM.,

NAL.

2)

Lamb, H., “Hydrodynamics,” New

Y o r k

Dover Publications,

ED., 5,

212 1943).

1945.

which is our final result.

It

will be convenient to compare this

RECEIVEDor

review

July 7

1952. Accep ted October

15

1952.

Ident i f i cat io n of Flavonoid ompounds by Fi l ter Paper hrom atography

Additional R f Values and

olor

Tests

HELEN WARREN CASTEEL

AND

SIMON H. WENDER

University

of

Oklahoma, Norman, Okla.

APER chromatographic techniques applicable to flavonoid

Pcompounds have been developed by Bate-Smith and Westall

1,

9) and by Gage, Douglass, and Wender 3) . Because of the

interest indicated by many research workers in these paper chro-

matographic studies

of

flavonoids, the present investigation was

undertaken to extend the usefulness of th is technique by the de-

termination of

Rf

values

for

a number of flavonoid compounds not

yet reported in the seven solvent systems listed.

The colors produced by chromogenic sprays when considered in

conjunction with the R, value often aid in the tentative classifica-

tion of an unidentified flavonoid pigment into one of the major

subdivisions of flavonoid compounds. Therefore, t he colors pro-

duced on paper by chromogenic sprays and certain of the newly

studied flavonoids were also determined.

EXPERIMENTAL

Experimental apparatus, materials. and procedures used cor-

A newerespond BB nearly as possible to those of Gage

e t al.

3).

model “Chromatocab” chamber (Chromatography Division,

University Apparatus Co., Berkeley, Calif.) was used in the pres-

ent study, however. This chamber was much better sealed and

better insulated than th e previous model used. Thus, uniform

saturation, indicated by movement

of

solvent fronts through

equal distances for all strips within the chamber, was obtained

if

sufficient time (usually 24 hours) was allowed

for

saturation.

Also rat e of movement on t he paper was usually much more

rapid in the newer chamber.

A

250-ml., all-glass spraying flask (University Apparatus Co.)

operated by compressed air a t

5

pounds pressure delivered an even

mist of chromogenic reagent . The spray was controlled by an

air hole covered by the thumb during delivery.

RESULTS AND DISCUSSION

Table I lists the R/ values obtained for twenty-one flavonoid

compounds in seven different solvent systems. These listed

values represent average

R f

values

for

each compound. Some

variation in Rt of

a

pigment occurred from time to time, but the

variation was usually less than 1 0. 04 Rf value and, in most cases,

was less than 50 .0 2 Rr value.

Some of the flavonoid samples used in this s tudy were found by