By ". W . Vina"and ". ". Craig

AB ST RAC T

T he V iscosi ty of sulphur ic- acid solut ions used for the elecrolyte in lead - acidstorage batter ies is a factor affecting the d iffusion of the electrolyte through theporous material of the plates and separators . T he decreased capacity of batteriesat low temperatures is attr ibutable in part to increase in viscosity of the electrolyte. Storage batteries are commonly used under widely d ifferent cond it ions oftemperature, but data for the viscosity of the electroly te at temperatuers below0°C . have not been previously available. T he viscosity of sulphuric- acid solu

t ions containing 10 to 50 per cent acid has now beenmeasured over a temperaturerange from + 30° C . to — 50° (1, themeasurements for some solut ions being limited ,

however, by their freez ing points . Below 0°C . the viscosity of the solut ions

increases rapidly as the temperature is d iminished .

CO"TE"TS

I . Introduct ionII . T he apparatus

1 . "escr ipt ion of appara tus2. Calibrat ion of the viscometer

III . E xper imental resultsIV . "iscussion of the r esul ts

1 . Accur acy of the measurements2 . C ompar ison wi th previous determinations

V . SummaryV I . Acknowledgement s

I . I"TRO""CTIO"

Storage batteries of the lead - acid type are now used under suchwidely differing conditions of temperature and rate of discharge thatan extension of our knowledge of the baSi c properties of sulphuricacid solutions which are employed for the electrolyte is desirable .

Resistivity and viscosity of the solutions are two of the more imporEtant properties of the electrolyte which affect the performance b

batteries.The useful vo ltage of a battery 18 decreased as the I

‘

eSlS t -

fity of the electrolyte increases . The V iscosity affects the ratis o

diffusion of the electro lyte through the porous material of the p a te

?and separators.Increase in viscosity results in decreased capac

ity 0

a battery. B oth resistivity and viscosity are , therefore , factorsd Tit

e

rmining the amoun t of electrical energy which a battery can e v

2;under specified conditions of temperature and rate of d i scla

a

ggi

.

a part of a comprehensive investigation of the properties an e avi orof battery electrolytes and separators the viscosity of sulphuric

- acid781

Bureau of Standards Journal of Research [VO"10

solutions from10 to 50 percent HZSO4 have been measured . Theviscosity measurements have been made over a temperature rangefrom 30

° C . to 50° C . insofar as the temperatures were above the

freezing points of the solutions . In the present paper the results ofthese viscosity measurements are given

, and in a later paper we expectto give the results of our work on the resrstance of battery separatorsand the resistivity of sulphuric- acid solutions .

Although several authors have published values for the V iscosityof sulphuric - acid solutions at ord inary temperatures and above , dataare not available in the literature for temperatures below 0° C . W ag

ner 1 measured the viscosity of d ilute solutions,

tospecific gravity

,at temperatures of 15° to 45° C . "unstan and

W ilson 2 measured the viscosity of a largenumber of solutions rangingfrom dilute to concentrated acid at 25

° C .

Rhodes and B arbour 3 also measured the viscos ity of a large numberof solutions ranging from dilute to concentrated acid . Their measurements were made at and 75° C . Their paper is

.the only

one,which we have found

,giving viscosities at temperatures as low

as 0° C . In the same year B ingham and Stone 4 published the resultsof their measurements on solutions from 1 1 to 97 percent acid at

and 40° C .

"runert 5 measured the viscosity of sulphuric - acid solutions fromto molar at temperatures of and 80

° C .

In a later section of this paper the values reported by the aboveauthors are compared wi th the present d eterminations . Such a comparison , however, is necessarily limited to few values since our Workextended to low temperatures while previous work was mostly confined to measurements at higher temperatures .

II.T H E APPARAT"S

1 . "E SCR IPT IO"OF APPARA T "S

The viscosity measurements were mad e by timing the di scharge of afixed volume of solution thr ough the capillary tube of a viscometermade of Pyrex glass . The ratio of the length of the capillary to itsdiameter was approximately 100. A diagram of the apparatus whichwas employed is shown in figure 1 . The liqui d was drawn up in theviscometer above index A and

“

then released . T he passage of theminiscus from A to B was timed .

The viscometer and the tube surrounding it,containing one of the

sulphuric- acid solutions , or a liqui d used for calibrating the instrument , were placed in a temperatur e- controlled bath in a "ewarflask of clear glass . Thi s was provided wi th a stirrer . For measur ements at 20° C . and above , the temperatur e was regulated and heldconstant by the addition of small portions of warm or cold water to thewater in the "ewar flask . At temperatures below 20° C . the water inthe "ewar flask was replaced by alcohol and the temperature wasadj usted and held constant during each experiment by adding smallportions of solid carbon dioxide

.

l Ann.dPhys. , vol . 254, p . 259, 1883, and vol. 5, p . 31 , 1890.2J vol . 91 , p . 83, 1907. An important correction to all of their resultswas published in Proc.Chem. Soc . , vol . 30, p . 104, 1914.

8 Ind . and E ng.C hem. , vol . 15, p . 850, 1923.

J vol . 27 , p . 701 , 1923 .

5vol . 145, p . 394, 1925.

Viscosity of Sulphuric Acid

Reference lines etched on the viscometer androunding it served to

.

fiX.

th° position of the viscometel

i' tellii tivl

gt

to

s

tlietube . The level of

.

liquid in the tube was adjusted for each exper i

ment to o

an etched line on the tube (0 in the diagram ) before d rawincr

the liqmd up into the viscometer . Slight adjustments in level o f of?)hqu id were accomplished by raising or lowering the thermometer to

"ewa r F/a sk

B S a mnd hwwu

FI""RE 1 .

—Vz'

scometer and temperature—controlled bath.

provided with two bulbs , the lower bulb alwaysbeing

immersed in the

liqui d . Thi s aided materially in equalizing temperatures before the

ll qui d passed . thr ough the capillary tube .

_1 731 4 5.

—33 - 6

Bureau of Standards Journal'

of Research [VO"10

The temperature was read on a thermometer whi ch was placeddirectly in the solutions to be measured and ad j acent to the capillaryo f the viscometer . The thermometer employed for temperaturesabove 1

° C . was a mercury- in- glass type graduated in tenth degrees,

and estimations were made to 0 01 ° C . B elow - 1° C . and above

—20° C . a mercury - in- glass thermometer was also used . Thi s was

graduated in degrees,estimations being made to C . B elow 20

°

C.a toluene - in—glass thermometer was used . This was also graduated

in degrees and estimations were mad e to 0 1 ° C . All of these thermometers had been calibrated previously and corrections were appliedto the readings . As a further check of the read ings of the toluenethermometer

,the viscometer was replaced by a platinum resistance

thermometer and it was found that the conditions of the experimentafforded sufficient opportunity for drainage in the toluene thermometer .

The temperature of the solutions was observed frequently duringeach measurement and the average temperature calculated . Somedeterminations were made so quickly that the temperature wasobserved only at the beginning and end of the discharge . In . determinations of longer duration

,the temperature was observed 6 or

8 times .

2. CA"IBRATIO" OF T HE V ISCOMETER

The viscometer was calibrated by measuring the time of discharge ofliquids of known viscosity . T hese included distilled water

,sucrose

solutions , ethyl - alcohol solutions , and two standardized oils . Thesucrose solutions were prepared by weight from standard samples of .

sucrose . One solut ion containing 20 percent and two other solutionscontaining 40 percent of sucrose were employed . Four

'

solutions ofethyl alcohol and water were used . T hese

'

containedand percent alcohol by weight .

The time of discharge for each liquid,except the oils

,was measured

at several temperatures , six determinations being made at eachtemperature . The oils were measured only at 25 °

C .,since the vis

cosity of these samples had been certified at thi s temperature .

"

The values of viscosity , p , for water, sucrosesolutions , and alcoholsolutions were taken from the International Critical Tables 6 exceptthat a correction to the value for 40 percent sucrose solution at 10° C .

was necessary .

7

In computing the kinematic viscosities, 5, for the purpose of cali

brating the viscometer , the densities , p, of water and the solutionsemployed have been taken from the International Critical Tables andfrom Bureau of Standards Te'chnologic Paper "o . 100 .

The densitiesof the OllS were determined experimentally at 25° CThe constants of the viscometer

,A and B

,were evaluated graphi

cally 8by plotting the computed ratios of kinematic viscosities to time

the calibrating liquids as ordinates against

(t measured time of discharge in seconds ) . The results of the calibration measurements are shown in figure 2 . The value of A (the inter

V ol . 5, pp . 10, 22, and 23.

7 J. Rheology , vol . 3 , p . 500, 1932.

9 l l lgg ins, C ollected Researches , "ational Physical "aboratory, vol. 1 1 , p . 12, 1914.

Viscosity of Sulphuri c Acid

cept of the straight line on the y- axis ) and the value o f B (the slope o fthe straight line ) were found to be and res

pec tively .

Calibration of the viscometer was necessarily ex tended over a widerange because of th e large variation in viscosity o f sulphuric - acidsolutions from + 30

° to — 50° C . The calibration curve

,however

,

shows no evid ence of turbulent flow within the range for which thisviscometer was actually used .

W ith the exception of the alcohol solutions,the maximum deviation

,u

pt

1 percent and 15 ou t of 16 points for sucrose solutions,water and the

oils are within one half of 1 percent of corresponding points on the_line . The values obtained with alcohol solutions are

,with one

exception , above the line . Six out of ten o f the alcohol points liewithin 1 percent of the line

,but these determinations have been given

less weight in drawing the line,because values for the viscosity of

alcohol solutions appear to be known less accurately than the others .

of any value of from the calibration line as drawn (fig . 2 ) is less than

A Sue/rose SO""nous

0 WA rm3: CFW /F/é

'

o 04 5

0 000/ 0 0002 0 000 4

T /Mf 55 C0/Y0 5)

FI""R E 2 .

— Calibration curve of the viscometer

III . E XP E R IME "TA" R E S""TS

The time of discharge of a specified volume of solution.

under testhaving been measured at a temperature T the kinematic viscositywas calculated from the equation

in whi ch is the kinematic viscosity , t the time of flow in seconds

and A and B are constants for the instrument which was used . T he

values of A and B were determined by the methodo

describcd in a

previous section . E igh t different solutions of sulphuric acid rangingin composition from to percent by weight of

H280 40

wer

§measur ed at temperatur es between — 50° and + 25

“

C .

— 58 and

+ 77° These solutions were

prepared from Cp acid an

distilled water .They did not contain lead sulphate wh ich is normally

present in small amounts in battery electrolytes .

H S0The composition of these solutions , expressed as percent 2. 4 .

was determined by titrating two weighed portions of each solution ,

Bureau of S tandards Journal Of Research [Vot. 10

T he percentages so obtained wereand As a check on these determinations the

g'

of each solution was measured by'

calibra tedO

hyd romcters which could be read to T he densities at 25° C .

were then. calculated and converted to percentages by usmg data inthe Interna tional Critical Tables . The average d ifference betweenthe measurements by titration and specific gravity was less than

specific gravity at

- 4 0 °- 2 0

"f / 0 °

7[MPl'

fi’A rus t

"

°c

F ianna 3 .

—P lot of the experimenta l determinations .

percent . T he resul ts given in this paper are based upon the valuesd e termined by titration .

T he experimental results are shown in figure 3 . In le tting thesecurves we have followed a suggestion , made by C . S . r agoe , of thisB ureau

, th a t the reciprocal ol’

log (20 >< l< inema tic viscosity in cen tis tokes ) be .

plo tted agains t temperature . Mr . Cr agoe had foundprevious ly 1 11 the ms e o f oils tha t an approximately linear relationshipexrs ts be tween this function and. the tempera ture . T he present workindica tes th a t a similar relationship may exist for electrolytes .

T he ind ividua l points shown in figure 3 are,for the mos t part, av

erage results o f 6 or 8 independent determinations . Some experi

Vi scos ity ‘2/ S ulphu r ic Ac id.

men ts we re.

repea ted a t slightly « Iill'

e rent tempe ra tnree . These a re

shown Hi this hgure by c lo sely mlj ac ent po ints .

Since the expe rimental resul ts co nhl be plo t ted as nenrlv s t raigh tlines o n It ltt l‘

Fn W attle ,

l l l tm’

pu llt tlnn lt lu l (ove r i t few

degrees ) ce llh be made eas l ly and ac c ura te l y . T he va lues o f the

func tion

le g visco sity )

AMI)a l

mmnm 4 , "inema ti c li t /{ lll t ltt lfj of It fi’l l l m lu lumn.

war" run," (wll ih Ii)“( T r "Ji l l thfl fi“ V tt ll l tm t

'

tslt lt l htt l l i ll"

abscissas (tiff .T he scale o f kinema tic V is mm ty ,

exp ressed an

Bureau of S tandards Journal of Research [Vot. 10

centistokes at the left of the diagram , has been calculated to correspondwith the scale at the right . The figure shows two branches of thefreezing point curve which limit the isothermals at the lower temperatures

. V alues for water taken from the International Critical Tablesare plotted at 0 percent in this figure .

In order to compute the viscosity of these solutions from the kinematic viscosity it is necessary to know the density of each solution ateach temperature . W e have employed existing data as given in theInternational Critical Tables for temperatures above 0° C . as a basis

FI""R E 5 .

— Absolute vi scosity of sulphuric- aci d solutions .

and found that the linear relation proved to be true . A cnometer

o f Pyrex lass W ith graduated stem was used for this purpolsg

r

. On the

Viscosity of Sulphuric Acid

extrapolated value was.

The difl‘

erence between these valuesis negligible in calculating the absolute viscosities .

The V iscosity expressed in centipoises is given in figure 5 .To this

figure has been added a scale of specific gravities at 25° C . co rresponding to the scale of percentages , in order to indicate more clea rly therange of solutions which are customarily used in storage ba t teries .

Table 1 gives the numerical values for the kinematic viscosi ty ,the

absolute viscosity , and the fluidity (reciprocal o f absolute viscosi ty )for sulphuric - acid solutions . In this table the viscosi ties are given tofour significant figures for values less than which are above0° C . The remainder of the table is uniformly given to three significant figures .

T AB "E 1 .

— V iscosity and flui dity of solutions of sulphuric acid

T empera Percent Absolute T empera Absolute£1280 4 viscosity

Flmd lty ture (° C . ) viscosityFlu'd 'ly

In dealin with stora e batteries it is convenient to employ thevalues for fl

t

ii idi ty ,since

gthe capacity of the battery and the ll

md igyof the solution vary together and inverse relationships are t iere y

avoided . An analysis of the data in table 1 shows that the percentage

change in fluidi ty of sulphuric- acid solutions W ith changein ten

l

ipera

ture is practically the same for a specnfiedtemperature interva irre

spectiveof the concentration of the acid . That is , i f some tempera

Bureau of Standards Journal of Research [VO"10

ture,such as 25° C .

,be chosen as standard and the fluidity of each

solution at that temperature called 100 percent , the fluid ity of eachsolution at other temperatures will increase or decrease in the sameproportion . Thi s is shown in table If the fluidi ty of any sul

phuric- acid solution within the range covered by thi s paper is known

at 25° C . ,the approxim ate fluidity at any other t emperature may be

calculated . The application of thi s simple relation,whi ch 18

0

th? samefor the sulphur ic - acid solutions as for water , is probably hmi ted tosolutions whose se - called “ specific viscosity " at var i ous

o

concentra

tions is a constant or nearly constant quantity with change in temperature . The term specific viscosity is applied to the ratio of the absoluteviscosity of the solution to the absolute viscosity of water at the sametemperature .

T AB"E 2 .

-Percent change in fluidi ty wi th temperature

W ater

i v . "ISC"SSIO" OF T H E R E S""TS

1 . ACC"RACY OF T H E MEAS"REME"TS

The experimental determinations plotted in figure 3 are mostlyaverages of repeated measurements , in some cases as many as 6 or 8repetitions having been made . The average deviation of any pointfrom its curve as drawn in figure 3 does not exceed percent above1°C .

, or percent below 1° C . The number of points exceed

ing a deviation of 1 percent from the curve is 4 for the temperaturesabove 1

°

C . and 6 below thi s temperature out of a total Of 70 points .

The drawing of curves for figure 4 from whi ch the values given intable 1 have been calculated has reduced deviations to a smallerpercentage .

The measurements are sub j ect to systematic errors from severalsources . W e have endeavored to avoid systematic errors in calibrating the instrument by using a variety of solutions and oils for whi chthe viscosity is known . Since the time of discharge of the Oils at 25° C .

was equal to the longer periods required at the lowest temperatures for

the su phuri c - acid solutions, drainage errors at the low temperatures arebelieved to be negligible . Referring to figure 2

,it seems probable

that any systematic errors in the constants of the instrument do notexceed percent . The error caused by change in dimensions of theglass was calculated to be negligible

.

Viscosity of Sulphur ic Acid

Systematic errors in determining the composition o f the solu tionhave been avoided as far as possible by checking the results o f titra

1310 11 8 .

by measurements of specific gravity . The final resul ts givenin thi s paper are based on the titrations alone

,but the difference

between the two methods of standardizing the solu tions would notchange the V iscosities by as much as percent

.

Accidental errors in measuring the temperature of the solutionswere mi nimi zed by repetitions of the discharges

. At temperaturesabove 1

° C . the error in temperature of a single determination didnot exceed Thi s would correspond to p ercent error in theviscosity at 25

° C . B elow 1° C . the viscosity increases rapid ly wi th

decreasmg temperatures . At these temperatures the thermometerreadings were estimated to tenth degrees and the average o f 6 or 8determi nations were probably correct to 0 2° which corresponds to 2percent Of the V iscosity at — 40

° C . The errors arising from thetemperatur e measurements are therefore somewhat variable with thetemperature , but are estimated to be percent at 25° C .

, per

cent at 0° C .,and percent at — 40° C .

The errors in timing the discharges were minimized also by repetitions of the experiment . For a few of the fastest discharges theerror in timing may have amounted to percent . For most of thedeterminations

,however

,the error in timing probably did not exceed

percent and at the low temperatures percent .

The last of the accidental sources Of error to be mentioned is thead j ustment of the head of the solution . The head was 10 cm so

that an error of mm would correspond to percent in the

viscosity measurement .

- The actual error from this source in thefinal results was probably not more than percent .

In view of the estimated magni tude of the possible errors givenabove

,it is believed that the values above 1

° C . are not in errorby more than 1 percent . The values below 1

° C . vary somewhatin accuracy according to the temperature

,the uncertainty being from

1 to 3 percent . These statements are based , however, on the assumption that the viscosities for the liquids used in calibrating the V i seometer

,as given in the International Critical Tables , are suffic1ently

accur ate for the purpose .

2. COMPAR ISO"S W ITH PREV IO"S "ETERMI"ATIO"S

Comparisons have been made with the results ob tained by otherswho have been mentioned in the introductory paragraphs . Sincethese earlier results cannot be calculated readily to the same percentages and temperatures , the compari son has been made graphi cally in

figure 6.The curves have been drawn through the pom ts plotted

for the present results as given in table 1 . The results of other workershave been plotted by di stinctive characters . E xcellent agreemen t

between the results of "runert , W agner , B ingham , and Stone (except

near 12 percent) and the results of the present investiga tionhas been

found.In figure 6 we have plotted also the values fo r sulphuric

- ar idsolutions selected for the International Critical Tables .

°

9 V ol. 5, p . 12.

V . S"MMARY

Measurements of the viscosity of sulphuric - acid solutions containing 10 to 50 percent acid have been made over a temperaturerangefrom + 30

° to — 50°C .

,except as the measurements were hmmed

by freezing points .

Ferret‘

s/ 7 Hz «5 04

FI""R E 6.

- Comparison of values for the viscosity of sulphuric- acid solutions .

T he viscosity of these solutions at 0° C . is about times as greatas a t + 30° C .

,but at 50

°

C . the viscosity is 28 times as great .

Fluidities of the solutions have been calculated,since these are

more simply related to changes in storage - battery capacity than theabsolute viscosity

.

The.percentage change in fluidity o f these solutions with temper

ature us very nearly the same irrespective of the percentage of acidcontained in the so lution

.

V iscos ity of S ulphur ic Ac id

V I . AC""OW "E ""ME "T S

The authors wish to thank C . S .lragoe fo r permissio n to use his

linear method o f calcu la ting the resul ts in ad vance o f his own pub

lication describing i t . They a re also indebted fo r helpful advic e to

"r . ". E . "orsey and W . l l . lIerseheI and It . 0 . l la rdy . It) . l l .

Potter kind ly cal ibrated the pycnome ter used fo r c hecking the den

si ties .

W ASHI""T O",March 1 1

,1933 .