Journal of the Institute of Petroleum, Vol. 26, No. 206

P t o i / i t c

JOURNAL OF

THE INSTITUTE OF PETROLEUM

F O U N D E D 1 9 1 3 I N C O R P O R A T E D 1 9 1 4

Vol. 26 DECEMBER 1940 No. 206

CONTENTS

Properties of Clay Suspensions. By G. D . Hobson • 533 Index to Transactions. Vol.

.

•

Subject

■

Abstracts . . . .

Publications Received

• 535A

Index to Abstracts. Vol.

• 537A

• - Subject

• 54/A

Books Reviewed and Received in

•

A

Institute Notes i

P u b lis h e d by T h e In s titu te o£ P e tro le u m . A d d r e s s : c /o T h e U n iv e rs ity o f B irm in g h a m , E d g b a a to n ,

B irm in g h a m , 15.

P rin te d in G re a t B rita in b y R ich ard C lay and C o m p a n y , L td ., B u ngay, Suffolk,

A l l rig h ts o f P u b lica tio n or T ran slation are R eserved. P r i c e

7

6

T H E I N S T I T U T E O F P E T R O L E U M

C O U N C IL , 1 9 3 9 -4 0

PRESID EN T:

Prof. A . W . N ash, M .Sc.

PAST-PRESID EN TS : A lfred C. Adam s

Lt.-Col. S. J. M. Auld, O.B.E., M .C., D.Sc.

Prof. J. S. S. Brame, C.B.E., F.I.C.

The Rf. Hon. Lord Cadm an, C .C .M .G ., D.Sc., F.R.S.

T. Dew hursf, A .R .C .S . A . E. Dunstan, D.Sc., F .I.C Sir Thomas H. Holland,

K .C .S.I., K.C.I.E., D.Sc., F.R.S.

J. K e w le y , M .A ., F.I.C.

V IC E-P R ES ID EN TS :

A sh le y C a rle r, A .M .I.M ech.E. I J. M cConnell Sanders, F.I.C.

C . D ailey, M.I.E.E. | F. B. Thole, D.Sc., F.I.C.

F. H. G arn e r, Ph.D., M .Sc., F.I.C.

M EM BERS O F C O U N C IL : G . H. Coxon

A . Frank D abell, M.I.M ech.E.

E. A . Evans, M .I.A.E.

E. B. Evans, Ph.D., M .Sc., F.I.C.

W . E. C o o d a y , A.R.S.M ., D.I.C.

A C. Hartley, O.B.E., F.C .C .I.

Prof. V. C . Illing, M .A J. S. Jackson, B.Sc., F.I.C.

J. A . O rie l, M .C ., M .A.

E. R. Redgrove, Ph.D., B.Sc.

C. A . P. Southwell, M .C ., B.Sc.

H. C. Ten, B.Sc., D.I.C.

A . Beeb y Thompson, O.B.E.

A . W a d e , D.Sc., A .R .C .S.

W . J. W ilson , F.I.C., A .C .C .I.

C. W . W o o d , F.I.C.

Arthur W . Eastlake, A.M .I.M ech.E., H onorary Se cre ta ry

H O N O R A R Y E D IT O R : Dr. A . E. Dunstan H O N O R A R Y A S S O C IA T E E D IT O R : Dr. F. H. C a rn e r H O N O R A R Y T R E A S U R E R : The Rt. Hon. Lord Plender, G.B.E.

S E C R E T A R Y : S. J. A sfb ury, M A

E > Vo l. 2 6 . N o . 2 0 6 . D e c e mb e r 1 9 4 0 .

F U R T H E R I N V E S T I G A T I O N S O F T H E P R O P E R T I E S O F C L A Y S U S P E N S I O N S . *

B y G. D.

P h.D ., D .I.C., A .M .Inst.P et.

Su m m a r y.

A n u m b e r of c la y su sp e n sio n s h a v e b e e n e x am in ed in a c ap illa ry tu b e v isc o m e ter u n d e r d iffere n t p re s s u re g ra d ie n ts . D a ta w ore o b ta in e d o n th e re la tio n s h ip s botw oen r a te o f flow a n d p re s s u re g ra d ie n t, c o n c e n tra tio n a n d

“ v isc o sity ,” sim p le a n d co m p lex su sp en sio n s, a n d o n th e e ffects of h e atin g ,

“ v isc o sity ’’-te m p e ra tu re coefficients a n d ageing.

T h e H a ts e h e k c o n ce n tric c y lin d e r v isc o m e ter d id n o t p ro v o v e ry s a tis ­ fa c to ry fo r e x am in in g th e s e su sp en sio n s. T h e p h en o m e n o n o f s e d im e n ta tio n u n d e r s h e a r in a c o n ce n tric c y lin d e r v isc o m e te r w as in v e s tig a te d .

A tte m p ts to d e te rm in e y ield v a lu e s d ire c tly b y u sin g c y lin d e rs a n d v a n es in a to rsio n a p p a r a tu s b ro u g h t to lig h t a n in te re s tin g fe a tu re w h ich is p ro b a b ly c o u p le d w ith th ix o tro p y .

P re lim in a ry w o rk o n t h e e s tim a tio n of t h e a m o u n t o f w a te r “ b o u n d ” b y d ifferen t c la y s w a s u n d e rta k e n , a n d a p p a r e n tly a m o u n ts u p to 2 5 % o r m o re of t h e w e ig h t o f t h e d r y c la y a re h e ld th u s .

I . Th e Ca p i l l a r y Vi s c o m e t e r.

I n a n earlier p u b lic a tio n 1 th e re su lts o f viscom etric m easurem ents on suspensions of Stockolite an d A quagel were described. The sam e ap p a ra tu s has been applied to exam ine a n u m b er o f clays a n d shales, some of which have been used in drilling m uds. Briefly, th e viscom eter w as o f th e p ip e tte ty p e , w ith interchangeable capillaries, a n d em ployed suction to draw a know n volum e of m u d in to th e m easuring-bulb. The a p p a ra tu s w as sim ple a n d cheap to c o n s tru c t; i t h a d no drainage error. On th e o th er h an d , a fairly large volum e o f m u d was required (350 c.c.), a n d working losses occurred w hen th e bulb w as cleaned betw een th e observations.

These losses increased w ith increasing “ viscosity ” o f th e m ud. T here was a n u p p er lim it to th e pressure g rad ien t w hich could be applied when using a given capillary. The presence of a h y d ro static-h ead correction an d probable errors in th e form used fixed a lower lim it to th e pressure g rad ien t w hich could reasonably be applied w ith a given capillary. T his correc­

tio n was a n ap p ro x im ate one for a tru e liquid, an d th erefo re p ro b ab ly ra th e r less satisfacto ry for m uds. K inetic-energy corrections were applied to th e d a ta . L ittle is know n a b o u t the. value o f th e coefficient in o f th e kinetic-energy correction in th e case o f th ese anom alous fluids, b u t it seem ed preferable to use a n ap p ro x im ate form ra th e r th a n to o m it th e correction. I t w as possible to shake o r s tir th e m u d alm o st im m ed iately before a m easurem ent. This w as o f service w hen th e clay suspensions sedim ented rela tiv e ly quickly. The m uds could be stirre d during a n observation, th u s providing a sim ple te s t for thix o tro p y .

I f C unningham ’s work 2 re a lly showed th a t sm all differences in pressure affected th e “ viscosity,” a n d n o t m erely th ix o tro p ic effects, a s suggested

- * T h e g re a te r p a r t o f th e first tw o se c tio n s is su m m ariz e d fro m a th esis a p p ro v e d fo r th e D egree o f D o c to r o f P h ilo so p h y in th e U n iv e rs ity o f L o n d o n , 1936.

OO

by McMillen,3 a n d th e effect does n o t reach its m axim um in stantaneously or in a few seconds a t th e m ost, it cannot appreciably affect th e re su lts in mnmaPIT rif

, “ u d 1S k e p t Undcr tho sam e pressure rig h t u p to the m om ent o f entering th e capillary, w hatever th e pressure g rad ien t used I t is clear, as A m brose an d Loomis,'* an d McMillen ® p o in t out, th a t if a th ix o tro p ic m aterial does n o t a tta in equilibrium in a concentric cylinder ro ta tin g viscom eter m 30 m inutes, or m ore in som e instances, ‘it will Y e t i f a W S i fe\ Cq' " librium in a GaPiHary o f th e usual length.

k

I 5 ,°f shearing is necessary for th e a tta in m e n t o f this qm libnum , th e possibility exists th a t th e th ix o tro p ic s ta te during th e passage through th e capillary will n o t be fa r rem oved from th a t obtaining im m ediately before entering th e capillary.

AH th e m uds were m ade up w ith d istilled w ater, th e shales an d clays I M M Cr The oonr°rei ne,(?eSS!U,y ’ and fch°y "'cro screened to pass 60-mesh

concentratio n s have been expressed as th e percentages by we fh irl « f

SUSpCnsions’ and were d eterm ined by h eatin g weighed sam ples to dryness a t 110° C. U nless otherw ise s ta te d th e dim en“ - WCr° a t 2°° C‘ T he b i n a r i e s h a d th e following

I N . Length: 11-580 cm NnHiiiQ . no i*} ! _ Radius . 0 0-134 cm. I I N Ton nth • n iA1N- J-engtn : 11-361 cm. Radius . 0.0i32 cm_

I f f . Length: 11-044 cm.

Radius : 0-0638 cm.

The d a ta have been in te rp re te d in tw o w ays :__

? a th e c?rr®cted pressure g rad ien t an d th e tim e of filling of o f a h v i ’n ^ . eq,u r^ e n t or a p p a re n t viscosity was calculated as th a t o f a h y p o th e tic al norm al liquid according to th e following equation

t, = _ r a F p

8 V (L -(- nR ) 8t:(L -f- nR )

w here R a n d L are th e radius a n d len g th o f th e capillary respectively,

is th e d ensity o f th e m ud, V = m easurhig volum e o f viscom eter

. ,, „ . „ tim e of filling

m is th e coefficient of th e kinetic-energy correction, n th e coefficient

of th e C ouette end-correction, an d P is th e corrected pressure The eq u iv alen t viscosity calcu lated for each observation was p lo tte d E t e s r " * " “ T ,M m U lo d i SOTpW <»..

H O B S O N : F U R T H E R I N V E S T I G A T I O N S O F

(ib) The q u a n tity was p lo tte d ag ain st a fte r applyin kinetic-energy correction to th e pressure gradient.

t £ a

Since th e ra te of flow changed a little in each observation a n d th e h y d ro ­ sta tic an d kinetic-energy corrections were b u t approxim ate, i t is to th e m u st be ^ dd n 0 t tk e absolute values o f th e resu lts th a t th e chief a tte n tio n m u st be paid. The equivalent viscosities have been expressed in term s of

to

v e d m glVG S° me ldea 0 f th e m agnitudes o f th e q u a n titie s in-

T H E P R O P E R T I E S O F C R A Y S U S P E N S I O N S .

F io . 1.

M e a su rem e n ts in c ap illa ry I W a t 20° C. :—

A llu v ial cla y O : Ga = 30-85% , Ob = 42-70% , Gc =-- 40-52% .

A llu v ia l clay 77 : H a = 31-72% , H b = 37-05% , 77c = 41-42% .

B lu e sh a le 7 : 7 a = 37-37% , 76 = 49-16% , 7c = 58-55% .

B lu e sh ale J : J a = 35-61% , J b = 51-11% , J c = 57-99% .

ah Vc.LOQ.iTr (Cm./see).

5 3 5

5 3 6

H O B S O N : F U R T H E R I N V E S T I G A T I O N S O F

Forms o f the “ Viscosity ” Rate-of.flow Curves.

T he form s o f th e curves re la tin g eq u iv alen t viscosity an d ra te o f flow seem to lie betw een th e lim iting ty p es show n b y A quagel a n d Stockolitc.

I h e A quagel ty p e shows a g re a te r dependence o f th e equ iv alen t viscosity on th e ra te of flow, th e form er q u a n tity decreasing rap id ly as th e la tte r increases a t low ra te s o f flow, an d th e curve becom ing m ore or less parallel to the rate-of-flow a Xls a t high ra te s o f flow. T he S tockolite curves show less dependence on th e r a te o f flow.1 The low er concentrations o f th e il,?T -St VC CUrV0S !n T Ilke fche S tockolite ty p e (Fig. 1, Ga, J a , la ), whereas

h e higher concentrations sim u lated th e A quagel ty p e (Fig. 1 lib ) N one o f th e clays q u ite conform ed to th e Stockolite ty p e o f curve, b u t blue T onflnn -r^' A lluYla l clay 11 ’ alIuvial d a y R , and unw eathered .London clay h a d a fan: resem blance to th e A quagel ty p e.

W hilst th e curves generally showed th e “ viscosity ” to fall w ith in ­ creased r a te of shear, th e re were certain exceptions. The increase in viscosity o f a 40 p er cent. S tockolite suspension a t high ra te s o f flow as a. tea y been n o te d .1 A n o u tstan d in g ty p e o f curve w as sliown by alluvial clay G (Fig. 1, Gc). T his curve was sigm oidal. A fter a very rap id decrease m eq u iv alen t viscosity w ith increased r a te of flow th e curve revealed a rise in « viscosity ” a t higher ra te s o f flow. This was follow ed by a fairly ra p id fall in “ viscosity ” a t th e h ighest ra te s o f flow used. A possible explanation o f th e e x trao rd in ary behaviour m ay be as follows : I h e in itia l drop in “ viscosity ” is caused by shearing off of a

? m , ° f a round a com plex p article, o r th e overcom ing of forces w hich te n d to give rigidity to th e suspension (this m ay explain th e “ vis­

cosity red u ctio n for a ll th e clays, though th e p articles in th em are n o t necessarily complex). I h e rise in “ viscosity ” is due to increasing b reak ­ down o f th e com plex p articles (Oden has shown th a t for equal concen­

tra tio n s fine p articles give m ore viscous suspensions th a n coarse ones).

In detail, th e rise m ay be caused b y (a) th e com ponents o f th e com plex p articles each assum ing fluid envelopes a n d /o r (b) increased loss o f energy due to collisions a n d ro tatio n . A t a certain ra te o f flow th is breakdow n is com plete, a n d th e effect o f th e reduction in size of th e fluid envelopes on

i el bef m u t0/ SSert itself’ th u s leadin& to a second drop , g1 y a highest ra te s o f flow. The slippage suggested by

m ay Play a Pa r t„ln tijis fill;il stage, or m ay be th e en tire cause o th e drop m viscosity. I f th e la tte r suggestion is tru e , th e n th e assum ption th a t th e sm aller p articles ta k e on fluid envelopes is no longer necessary. A o p e rm an e n t change occurred, for, a fte r m aking th e m easure­

m en ts in decreasing order o f pressure gradients, a check d eterm ination un d e r th e in itia l pressure g rad ie n t showed v ery close agreem ent w ith th e first m easurem ent.

Form o f the Flow-curves.

The p eculiarities of th e eq u iv alen t viscosity-rate-of-flow curves have,

flow-curves, b u t th a t w hich shows up

in th e o th er

” “ ° ^ ePr.ef n ta tlo n 18 nofc necessarily so read ily ap p a re n t

m th e other. A n u m b er o f flow-curves showed a steepening a t th e hm hest

ra te s of flow (Fig. 2, K b ’, He, Gc). I n som e distances th is was n o t a change

6000

5 0 0 0

4 0 0 0

3 0 0 0

2 0 0 0

1 0 0 0

M easu rem en ts in c a p illa ry I W a t 20° C. :—

A llu v ial clay 0 : Oa = 30-85% , Ob = 42-70%, Gc = 49-52% . A lluvial clay H : H a = 31*72%, l i b = 37-65%, H e = 41-42% . B luo sh ale I : l a = 37-37% , 16 = 49-16%, l e = 58-55% . B lu e sh ale J : J o = 35-61% , J 6 = 51-11%, J e = 57-99% . C lay K : K a = 32-57% , X 6 = 39-91% , Xe = 46-41% . M e a su rem e n ts in cap illa ry I I N a t 20° C. :—

B lue shale, J : J o ' = 35-61% .

Clay K : H o ' = 32-57% , Ä 6 ' = 39-91% .

2300

F io . 2,

[To face p. ^537.

T H E P R O P E R T I E S O F C L A Y S U S P E N S I O N S . 5 3 7

in m obility, b u t w as a t le a st p a rtly d ue to air coming o u t o f solution. The cases o f a tru e increase in m obility were possibly exam ples o f slippage or loss o f fluid envelopes. I n o th er instances th e flow-curves becam e less steep a t th e h ighest ra te s o f flow (Fig. 2, J a '). T his pro b ab ly re su lte d from turbulence, w ith th e possible ad d itio n al fac to r of breakdow n o f com plex

p articles.

A lthough some o f th e flow-curves were s till stra ig h t a t th e low est ra te s o f flow used, m an y of th em d id show cu rv a tu re tow ards th e origin. The B ingham hypothesis dem ands such c u rv atu re even though slip be absent, an d if slip be p resen t, th e cu rv atu re is g re ate r, a n d th e curve m a y even pass th ro u g h th e origin, as B uckingham assum ed in th e derivation o f his equation, or m ay in tersect th e stress axis a t a m easurable value, as observed b y K een, S co tt B lair, an d C row ther.7> 8

W hilst th e flow-curves of blue shale L , shale P , a n d clay K were essen­

tia lly stra ig h t lines, ex cep t a t th e low est ra te s of flow, some o f th e o th er clays, an d especially th e higher concentrations, gave flow-curves which curved th ro u g h o u t, w ith th e re su lt t h a t a reasonable m easurem ent of th e ir slopes was difficult or impossible.

I n conform ity w ith th e observations o f H a ll,9 a n d S co tt B lair an d C row ther,8 i t w as found t h a t th e slope o f th e p a r t of th e flow-curves corresponding to stage IV o f th e Ia tte rs ’ curves ivas g re a te r th e narrow er th e capillary—i.e., th e m obility was higher in th e narrow capillary.

Effect o f Stirring, etc., on the Measurements.

I n th e b u lk o f th e m easurem ents th e s ta n d a rd procedure was to stir th e m u d for 25 sec. im m ediately before th e m easurem ent, and a t a stead y ra te during th e m easurem ent. This stirrin g was b y no m eans vigorous, b u t i t was found possible in m ost cases to o b tain m ore consistent resu lts w ith stirrin g during th e m easurem ents th a n w hen stirrin g w as suspended.

The exceptions were som e very d ilu te suspensions o f fractions o f London clay a n d th ere, no d oubt, th e irregularities were due to turbulence.

O m itting th e cases o f fractions o f London clay, stirrin g during a m easure­

m e n t was found to give a lower value for th e “ viscosity ” or a higher value for th e m obility th a n w as observed in th e absence o f stirring. T hus stirrin g increased th e m obility of a S tockolitc-A quagel suspension b y ab o u t

10 p e r cent.

A ny d isturbance m ight be expected to te n d to prom ote tu rb u le n t flow.

Such a ten d en cy would be g rea ter th e m ore vigorous th e stirring, an d for a fixed m ethod o f stirrin g i t would be g re a te r th e less dense an d th e less viscous th e fluid. I f th e fluid were thixotropic, th e n e tt effect o f stirring during a m easurem ent w ould be m an ifest as an increase or decrease in th e

“ viscosity,” according as th e a p p a re n t increase in “ viscosity ” resulting from a n y turbulence crea ted exceeded or was less th a n a n y decrease in

“ viscosity ” consequent on th ix o tro p ic breakdow n.

I t m u st be recognized t h a t if a n y sta n d a rd m eth o d o f tre a tm e n t is

a d o p ted w ith a th ix o tro p ic m u d — e.g., stirrin g during a n observation,

n o t stirring, or stirrin g vigorously before a n observation—th en , provided

t h a t th e m easurem ents are m ade in s tric t order o f increasing or decreasing

pressure gradients, th e re su lts m ay be expected to lie on a sm ooth curve,

5 3 8 H O B S O N : F U R T H E R I N V E S T I G A T I O N S O F

b u t th e curve obtained for th e increasing order o f pressure grad ien ts will n o t necessarily coincide w ith th a t obtain ed for th e reverse order. The reason lies in th e fa c t th a t th e tre a tm e n t, w h atev er its n a tu re , will only in rare cases m ain tain th e in itia l s ta te o f th ix o tro p ic breakdow n during a series of m easurem ents. In general i t will eith er fail to m ain tain it, or it will increase it. N otw ithstanding, u n d er uniform tre a tm e n t th e change in thixotropic s ta te m ay be expected to be gradual, an d hence a sm ooth curve will resu lt. On th is account, m obilities a n d stress in te rc e p ts m ay differ a little according as observations are m ade in ascending or de­

scending order of pressure gradients.

Relationships between Concentration and the “ Viscosity ” or M obility o f the Suspensions.

A lthough th e “ viscosities ” a t given ra te s o f flow can be p lo tte d against th e concentration b y weight, in a tte m p ts to find a relationship betw een

“ viscosity ” a n d concentration, i t is desirable to use a less a rb itra ry q u an tity , e.g., th e u ltim a te viscosity— th e asy m p to tic value tow ards which th e “ viscosity ”-rate-of-flow curves seem to te n d in m ost cases__

or th e value, i.e., th e m obility, o b tain ed from th e slope o f th e flow-curves in stage IV w hen th e y are lin ear or n early so. The reciprocal o f th e m obility has th e dim ensions o f a viscosity. F u rth erm o re, i t would seem b e tter to express th e concentration in te rm s o f volum e ra th e r th a n weight, for i t is th e size o f th e p articles a n d th e ir to ta l effective bulk which, o th er things being equal, determ ine th e “ viscosity ” o f a suspension, a n d i t is clear th a t th e relationship betw een percentage b y volum e a n d percentage by w eight is n o t linear unless th e densities of th e suspended m aterial an d th e suspending m edium are equal. There is a n a d d itio n al com plicating fe atu ie in th a t th e p articles are p ro b ab ly in tim a te ly associated w ith a p o rtion o f th e suspending m edium , m aking th e ir effective bu lk ap p re­

ciably g re ate r th a n th a t o f th e p articles alone. H ow ever, th is featu re has been o m itte d from th e following sim ple discussion.

I n order to calculate th e concentration b y volum e from th a t b y w eight in th e absence o f d ire ct determ inations o f th e densities o f th e clay particles, a d en sity value o f 2-6 was used, which, while som ew hat below a series o f com puted a p p a re n t densities, probably errs in th e rig h t direction.

E in ste in ’s equation for th e “ viscosity ” o f a suspension of rigid spheres is v], =

)(1 + 2 wher e <£ is th e volum e fraction th e spheres co n stitu te o f th e entire suspension. This equation assum es th a t th e spheres do n o t influence one another. The suspensions exam ined do n o t obey th is linear relationship, b u t th e “ viscosity ” increased a t a g re a te r ra te , a resu lt to be expected from th e high concentrations used (Fig. 3). I n addition, th e p articles were m ost likely p laty , an d m ay n o t have fulfilled th e condition o f rigidity. Bingham and D u rh am ’s work on infusorial e a rth a n d English china-clay led th e m to th e conclusion th a t finely divided substances in suspension depress th e fluidity 0f th e liquids in which th e y are suspended b y a m o u n ts which are d irectly proportional to th e volum e o f solid.11 This m ay be expressed by th e equation (I — f k ) , where

<j> is th e volum e fraction o f th e solid.

T H E P R O P E R T I E S O F C R A Y S U S P E N S I O N S , 5 3 9

The percentage by volum e has been p lo tte d against th e m obility (Fig, 4).

I n no case was a s tra ig h t line obtained. N evertheless, th e cu rv atu re was n o t g reat. A quagel w as found to ap p ro x im ate m ore closely to E in ste in ’s equation th a n to B ingham and D u rh am ’s, w hereas Stockolite a n d th e o th er clays were, on th e whole, n ea rer to B ingham an d D u rh am ’s. The closer agreem ent o f A quagel w ith E in stein ’s eq u atio n w as perhaps to be expected, since th e m axim um concentration was only 1-86 p e r cent., w hilst th e o th e r suspensions w ent u p to 35 p e r cent, o f clay b y volume.

Fi g. 3.

M e a su rem e n ts a t 20° C. :—

G— a llu v ia l cla y G ; J — b lu e sh ale J ; I — b lu e sh a le I ; L — b lu e sh a le L ; S — S to c k o lite. C urves G, J a n d I aro fo r c ap illa ry U N ; L f o r c a p illa ry I W , a n d S fo r c ap illa ry I N .

Relationships between Sim ple and Complex Suspensions.

In a n a tte m p t to find if a n y ap p ro x im ate sim ple relationship exists

betw een th e “ viscosity ” or th e m obility o f com posite suspensions an d th e

values for sim ple suspensions, a m ix tu re o f Stockolite an d Aquagel, a n d

th re e fractions o f u n w eathered L ondon clay were used. The suspensions

were m ade u p so th a t th e ra tio of a given m a te ria l or fractio n to th e to ta l

volum e p resen t was th e sam e in th e sim ple suspension as in th e com posite

suspension. I n using th e above m eth o d th e ra tio o f th e effective volum e

of th e solid to free-w ater space w as n o t necessarily identical in th e tw o

cases, a n d w hen it differed, i t w ould be higher in th e case o f th e com posite

suspension— a circum stance which w ould in d ic ate th a t its “ viscosity ”

should exceed th a t derived m erely from consideration of th e “ viscosities ”

o f th e sim ple suspensions. I t w ould therefore hav e been m ore a ccu rate to

5 4 0 ■ H O B S O N : F U B T H E B I N V E S T I G A T I O N S O F

T H E P R O P E R T I E S O F C L A Y S U S P E N S I O N S . 5 4 1

have m ade u p th e sim ple suspensions so th a t th e ratio o f th e effective volum e o f solid to th e volum e o f free w a te r w as th e sam e as in th e com­

posite suspension, b u t lack o f knowledge o f th e w a te r-“ binding ” pow er o f th e various fractions precluded this.

The increm ents to th e viscosity of w ater caused b y th e sep ara te fractions or m aterials a t given ra te s of flow were sum m ed a n d added to th e v is­

co sity o f w ater. T he su m m ate curve was found to lie w ell below th a t a c tu a lly obtained for th e com posite suspension. This was n o t unexpected, for w ith every m a terial th e “ viscosity ” increased a t a g re a te r ra te th a n th e am o u n t of solid p resent. Several o th er m ethods were tried , including a n extended form o f B ingham a n d D u rh am ’s equation, b u t th e re su lts wore even less satisfacto ry . F in ally , th e hypothesis w as used t h a t th e ad d itio n o f a substance reduced th e “ fluidity ” of a suspension containing a second substance, in th e sam e proportion as th e first substance reduced th e fluidity o f w ater in a sim ple suspension, where th e ra tio of w ater to th a t substance w as th e sam e as in th e com posite suspension.

F o r L ondon clay, th re e fractions o f w hich were used, tw o fractions were d e a lt w ith as above, an d th e h y p o th etical m ixed suspension was supposed to reduce th e “ fluidity ” o f th e th ird fraction b y a proportion th e sam e as i t its e lf reduced th e fluidity o f w ater— i.e., th e “ fluidity ” o f a m ix tu re A ,B , . . . X a t a given ra te of flow is as follows :—

“ fluidity ” of A “ fluidity ” o f B ^ fluidity of w a t e r ' fluidity of w a ter " 111 1 y 0 ,

Tab l e I.

Stockolite-A quagel Su sp en sio n .

R a te o f flow, cm ./sec.

“ F lu id ity ” (rhes). “ V isco sity ” (poise).

Calc. O bs. % e rro r.

S u m m atio n o f vise, in crem .

O bserved. % e rro r.

30 15-6 10-3 - 4 - 3 0-0442 0-0611 - 2 7 - 9

00 17-9 1 8 1 - 1 - 0 0-0408 0-0550 - 2 6 - 0

90 19-2 19-2 0-0 0-0386 0-0520 - 2 5 - 7

120 20-3 20-1 0-7 0-0371 0-0495 - 2 5 - 0

150 21-1 20-9 1-6 0-0360 0-0480 - 2 5 - 0

180 21-0 21-5 0-3 0 0 3 5 3 0-0465 - 2 4 - 0

210 21 -9 22-0 - 0 - 0 0-0347 0-0454 - 2 3 - 3

240 21-6 22-7 - 4 - 7 0-0337 0-0440 - 2 1 - 0

all th e d a ta being for th e sam e ra te o f flow, a n d th e ratio o f A ,B , . . . X to w a te r in th e sim ple suspensions being th e sam e as in th e com posite

Fig. 4.

v d e n o te s c u rv e fo r p e rce n ta g e b y v o lu m e.

w „ ,, ,, w eig h t.

G is a llu v ia l clay G ; J is b lu e sh a le J ; I is b lu e sh ale I ; L is b lu e sh ale L ; S is S tockolito.

F u ll lin e s a re fo r c ap illa ry I W ; b ro k e n lin e s fo r c a p illa ry I I J i , e x c e p t in th e case o f S to c k o lite w h ere t h e r e s u lts a re fo r c ap illa ry I N . T h e o rd in a te s of th e S to ck o lito c u rv es h o v e b een h a lv e d .

5 4 2 H O B S O N : F U R T H E R I N V E S T I G A T I O N S O F

Ta b h; n . Unweathered L ondon Clay.

R a to o f flow, cm . /sec.

“ F lu id ity ” (rhes). “ V isco sity ” (poise).

Calc. Obs. % erro r.

S u m m a tio n o f vise, in crem .

O bserved. % erro r.

15 1-92 3 1 - 3 8 - 0 0-222 0-322 - 3 1 - 0

30 4-15 4-0 - 9-9 0-147 0-216 - 3 2 - 1

50 5-8 0-3 - 8-0 0-117 0-159 - 2 0 - 1

80 7-2 7-6 - 5-2 0-090 0-132 - 2 7 - 3

110 8-1 8-7 - G-9 0-087 0-115 - 2 4 - 2

140 8-84 9-3 - 4-9 0-082 0-108 - 2 3 - 9

170 9-5 10-1 - 6-0 0-078 0-099 - 2 1 - 0

suspension. I n T ables I an d I I th e re su lts so obtain ed are com pared w ith those reached from th e sum m ation o f “ viscosity ” increm ents.

Tables

a n d

show th a t th e re su lts reached b y th e la s t m eth o d agree moro closely w ith observed values th a n do th e sum m ations of viscosity increm ents. The large error for th e low est ra te o f flow in T able I I is probably d ue to inaccuracies in th e ex p erim en tal d a ta , for i t is m o st difficult to m ake th e m easurem ents a t th e low est ra te s of flow -with cer­

ta in ty .

A n a tu ra l extension to th e above hypothesis is its application to th e relationship betw een concentration a n d m obility for a single clay. This gives log

— log ’/>„ + j — ■ 99(7 . log a, w here C is th e fractio n b y volum e of solid in th e suspension a n d a is th o ra tio of th e m o b ility o f a suspension w ith 1 p er cent, b y volum e o f solid to th e fluidity o f w ater. M oderate agreem ent w ith th is equ atio n w as shown b y th e Stockolite d a ta , a n d those for blue shale I . A lluvial clay G and blue shale J gave curves o f a sim ilar form , a n d th o la tte r show ed quite good agreem ent w ith th e extended form o f the eq u atio n w hich m akes some allowance for “ bou n d ” w ater (Fig. 5).

Stress Intercept.

T h e in tercep t on th e stress axis obtained b y ex trap o latin g th e stream -line p o rtio n of th e flow-curves has received a v a rie ty o f nam es. I t has been called th e “ s ta tic rig id ity ” b y K een .12 T e rz a g h i13 criticized this, an d suggested “ shearing resistance.” B uckingham has used “ shearing s tre n g th ,” a n d B ingham “ yield v alu e.” T he significant physical facto r is th o critical shearing stress req u ired to in itia te flow as assum ed in the B ingham hypothesis. T his is th ree-q u a rters o f th e stress in tercep t, and in spite o f th e general application o f th e various term s to th e stress in te r­

cept, i t w ould seem preferable to reserve th em for th e q u a n tity w hich is considered in th e general theory. F o r th e p resen t purpose “ yield value ” will be ad o p ted , an d ta k e n as th ree-q u arters of th e stress intercept.

W here possible, e x tra p o latio n o f th e stream -line p o rtio n o f th e flow

curves w as carried out, an d yield values were m easured, ranging from

zero u p to several h u n d re d dynes/sq. cm. T he values varied w idely for

T H E P R O P E R T I E S O P C L A Y S U S P E N S I O N S .

F io . 5.

C u rv es I a n d I I re p re s e n t th e e q u a tio n

9 D C

■A. = ■Air®1 - w hore iA„ is th e flu id ity of w a te r a t 20° C., a n d ‘ a ’ h a s th e v a lu e s of 0'95 a n d 0-90 resp ec tiv e ly . C urves l a a n d I l a

m a

re p re s e n t th e e q u a tio n ip, — <pwa l ~ ka, w hore k is t h e ra tio of th e effective v o lu m e of th e su s p en d e d so lid to i ts a c tu a l v o lu m e a n d is g iv en a v a lu e of 1-5 hero, a n d ‘ a ’ h a s v a lu e s o f 0-95 a n d 0-90 resp ectiv ely . C urve O show s d a ta fo r a llu v ial clay <3; / ' for b lu e sh a le I ; J fo r b lu e sh ale J ; S fo r S to ck o lite. C urves O, I ' , a n d J a re fo r c ap illa ry I I N , a n d c u rv e 8 is fo r c ap illa ry I N .

544

th e different clays, a n d increased rap id ly w ith increase in concentration of th e clay.

Effect o f Heating the Suspensions.

A s a resu lt o f a series of m easurem ents of th e “ viscosity ” o f m uds a t

different tem p eratu res, C raft an d E x n e r 14 concluded t h a t for high con­

centrations an d also for b entonites th e c< viscosity ” falls off w ith rise in te m p era tu re u p to a b o u t 60° C., and th e n increases a t still higher te m p e ra ­ tures. These observations were m ade in a S torm er viscom eter using a co n sta n t d n v in g -w e ig h t; consequently a n y change in th e “ viscosity ” of th is ty p e o f m edium would be exaggerated. I n addition, th e y do n o t sta te w h a t precautions were ta k en ag a in st evaporation losses; w hether th e one sam ple w as k e p t in th e in stru m en t th ro u g h o u t th e series of o b se rv a tio n s;

w hether th e concentration increased du rin g th e series o f o b serv atio n s; an d w hether th e viscosity ” a t th e in itial te m p eratu re w as unchanged by heatin g an d th e sam e curve was obtained if th e observations were rep eated in descending order o f tem peratures.

P relim in ary a tte m p ts to determ ine a “ viscosity ’’-te m p e ra tu re coeffi­

cient for these clay suspensions led to some peculiar results w hen th e m easurem ents were m ade in rising order o f tem p eratu res, b u t n o t so for m easurem ents in th e reverse order, th e sam e sam ple being used thro u g h o u t.

I t was clear, therefore, th a t some change was ta k in g place w hich w as unlike th e m ere fall in viscosity w ith rise in te m p era tu re shown b y tru e liquids.

A 16-69 p er cent, suspension of clay N w as divided in to a num ber of p arts, each of which was heated to one of a series of tem peratures, ranging from 20 C. to 99° C., for a period of 7 hours. E v ap o ra tio n losses were prevented, an d a fte r stan d in g over-night, th e “ viscosity ” of each sam ple was m easured a t 20° C. The “ viscosity ” rate-of-flow curves as a whole showed th ere w as a n increase in “ viscosity ” which a tta in e d a m axim um in th e sam ples h e ated to 70-80° C., an d for sam ples h e a te d above th a t tem p eratu re range th e “ viscosity ” fell off. The flow-curves showed a fairly d istin c t division into th ree p arts, b u t th e inferences from com parisons of corresponding p a rts were sim ilar. T he stress in tercep t a tta in e d a m ax i­

m um over th e ran g e 60-80° C., w hilst th e showed a continuous m obility

increase u p to th e highest te m p eratu re used. Over th e full range th e m o b ility lncreased 14-18 p er cent., according to th e p o rtio n o f th e flow-curves considered, and th e m axim um values for th e stress in tercep t were 34-52 p er cent, higher th a n for th e sam ple which was m a in tain ed a t a te m p e ratu re of 20° C.

A 32-94 per cent, suspension o f th e sam e clay was h eated to 55° C. an d th e “ viscosity ” m easurem ents com pared w ith those of a 16-69 p er cent, suspension sim ilarly treated . The percentage increases in “ viscosity ” , m o b ility ’ alK^ sl ress in te rc e p t in te rm s of th e values for u n h eated sam ples were m uch g re a te r in th e m ore co ncentrated suspension. Sim ilar “ vis­

cosity increases were observed to have ta k e n place in o th er clay suspen­

sions a fte r heatin g to 40° C.

T H E P R O P E R T I E S O F C L A Y S U S P E N S I O N S . 5 4 5

T ests on a suspension h ea te d a t 45° C. for varying periods showed th a t th e change w as p ro b ab ly com plete after 6-10 hours. F in ally , th e p e r­

m anence of th e change was exam ined. F o r th is purpose th e 16-69 per cent, suspension which h ad been h eated to 90° C. for 7 hours was re-exam ined a fter standing for a m onth. T he results showed th e change to be p e r­

m anent.

I t is clear th a t th e hysteresis in th e prelim inary essays a t m easuring a

“ viscosity ’’-te m p e ra tu re coefficient was due to non-reversiblo changes which se t in in previously u n h eated suspensions. I t follows, therefore, t h a t w hether th e “ viscosity ” will ap p ear to increase or decrease as th e te m p e ratu re is first raised, will depend on th e relative m agnitudes o f tw o factors which, in these cases, operate in opposite directions for th e lower tem p eratu res a t a n y ra te :—

(a) A norm al decrease in “ viscosity ” (with rise in tem p eratu re)

resulting from th e decrease in viscosity o f th e suspending m edium . T his is reversed on reducing th e tem p eratu re.

(b) A change in “ viscosity ” due to th e heating which is n o t rem oved on lowering th e tem p era tu re, and, as far as th e present m easurem ents go, is seem ingly perm anent.

T his second facto r will n o t appear in m easurem ents m ade in descending order of tem peratures, provided th a t th e “ v is c o s ity ” change has been allowed to a tta in its m axim um a t th e highest tem p e ratu re used. I f th a t s ta te has n o t been reached, th e te m p eratu re coefficient m ay be exaggerated if h eatin g raises th e “ viscosity.” On th e o ther hand, for observations m ade in rising order of tem p eratu res on previously unheated suspensions, an ap p a re n tly low or even negative value -will bo obtained in th e presence o f th is factor.

T he findings described seem to be a t variance w ith those of th e B urm ah Oil C om pany,15 b u t i t m ay be th a t all clays do n o t behave alike. Y et, in th e absence of inform ation regarding th e experim ental details m entioned, th e p resen t w ork appears to offer a reasonable explanation of C raft and E x n e r’s results.

Effect o f Temperature on the M obility and “ Viscosity ” o f the M uds.

A ccording to H atsc h ck ,18 th e te m p eratu re coefficient o f “ viscosity ” in suspensoid sols is m erely th a t of th e dispersion m edium . I n contrast, th e te m p e ra tu re coefficient of em ulsoid sols “ is alw ays m arkedly g rea ter th a n t h a t of th e dispersion m edium .”

F o r 10 a n d 40 p e r cent. Stockolite suspensions th e relativ e changes for th e range 10-30° C. wore slightly less th a n for w ater. T he sam e was tru e o f 20 p er cent. Stockolite tre a te d w ith 1-998 p er cent, of caustic soda.

Two other clays were exam ined. Since th e ir flow-curves -were n o t linear in stago IV , b u t showed a sm all fairly uniform cu rv atu re, i t w-as n o t possible to m easure th e — ■ in th e usual m anner. C onsequently th e d a ta

m obility

were com pared em pirically. T he m ean slopes of th e curves fo r sim ilar

ranges of ^ (rates o f shear) were m easured, an d from these th e percentage

5 4 6 H O B S O N : I T J R T H B B I N V E S T I G A T I O N S O F

changes in -¿ k fflty for th e in terv als 40 - 20° C., 30 - 20° C., a n d 40 — 30 G. were o b tain ed and com pared w ith th e values derived from th e equivalent viscosity-rate-of-flow curves an d th e viscosity changes for w ater. T he changes calculated from th e flow-curves approached m ore closely to those fo r w ater th a n did those o b tain ed from th e “ viscosity ” curves. I n th e form er case, for a 59-91 p e r cent, blue shale I suspension th e agreem ent was w ithin a little m ore th a n 1 p er cent., w hilst for th e 40-65 p er cent, clay K suspension, w hich was p ro b ab ly m ore colloidal, th e m ean change was a b o u t 4 p er cent, less th a n for w ater.

A 37-63 p er cent, suspension of clay Ar h a d a — X — a t 55° C which m obility

was 46 p er cent, of its value a t 20° C. The viscosity o f w a ter a t 55° C. is 50 p er cent, o f its value a t 20° C. H ence th e change was slightly greater th a n th a t for w ater.

A sound opinion as to th e effect of rise in tem p eratu re on th e stress in te r­

cept can n o t be given from th e p re sen t d a ta , for th e flow-curves n o t being linear in stage IV rendered ex trap o latio n unreliable.

Ageing.

H all 9 found th a t “ th e consistency of a clay slip changes during th e first tw o days, p ro b ab ly due to th e swelling o f gel colloids, an d m ore on th e first d a y th a n in la te r periods. All th e d eterm inations w ith one capillary m u st be m ade in one d a y due to th e tim e effect on th e consistency o f th e slip.” E x cep tin g th e cases of th e Stockolite suspensions, th e “ viscosity ” m easurem ents here described have n o t been m ade on th e d a y on w hich th e suspensions were prepared, a n d in only th ree instances— 38-28 p er cent.

blue shale L , 51-11 p e r cent, blue shale J , an d a n A quagel suspension were m easurem ents carried o u t on th e first d a y a fte r p re p aratio n . N a tu ra lly flow-curves were draw n only fo r d a ta ob tain ed on th e sam e dav!

Stockolite suspensions o f concentrations 20, 30, a n d 40 p e r cent, were exam ined on th e d a y of p rep aratio n an d again a fte r in te rv a ls o f 35 days, 31 days, an d 8 days, respectively, b u t no indication was found o f a n y change’

in “ viscosity ” w ith age.

The increased effect o f caustic soda a n d hydrochloric acid on Stockolite as com pared w ith m easurem ents m ade w ithin a sh o rt tim e o f adding th e reag en t has been n o te d .1 F o r sod a-treated A quagel sm all irregularities in th e curves freq u en tly coincided w ith over-night in terv als.

The suspension consisting o f a m ix tu re o f 20 p er cent. Stockolite an d 2-925 p e r cent. A quagel show ed a v ery strong increase in “ viscosity ” or decrease in m obility w ith age. Com paring m easurem ents m ade w ithin a d ay or tw o o f its p rep aratio n w ith those m ade nine m onths la te r, th e la tte r revealed a “ viscosity ” increase of a b o u t 40 p er cent, fo r observations u n d er sim ilar conditions, a n d ex am in atio n o f th e flow-curves showed th a t n o t only h a d th e m obility decreased, b u t th e stress in te rc e p t h ad increased by 3/-5 p e r cent. This suspension se t ” slowly to a gelatinous m ass w ith w ell-m arked solid a n d elastic properties, y e t a few m om ents’ shaking converted it in to th e original liquid w ith no signs o f a n y “ solid ” lum ps.

Some clay suspensions showed no im p o rta n t differences in m obility

T H E P R O P E R T I E S O F C L A Y S U S P E N S I O N S . 5 4 7

betw een being a few days and several m onths old, w h ilst others showed considerable differences betw een being tw o or th re e days a n d te n days to several m onths old.

I t is possible th a t th e “ viscosity ” increases are concom itant w ith slight volum etric contractions, for a sm all increase in d en sity w as n o te d in a suspension of clay

betw een being th ree days a n d seven weeks old.

Distribution o f Particle Sizes, Surface Factors and Inferences fro m the Chemical Analyses o f some of the Clays.

A n a tte m p t w as m ade to determ ine th e app ro x im ate size d istrib u tio n of th e p articles in a few of th e clays, an d th u s to arrive a t an estim ate of th e relativ e to ta l surface p er gram o f each clay, w ith a view to finding w hether or n o t th is facto r gives a clue to th e fluid an d o ther properties of th e suspen­

sions. The p ip e tte m eth o d o f m echanical analysis w as adopted, using a suspension containing ab o u t 2 p e r cent, b y w eight of solids in d istilled w ater. (The suspensions were p repared b y d iluting th o se u sed for

“ viscosity ” m easurem ents, which were all several m onths old.)

The assum ptions involved in th e application of S tokes’ law to th e m echanical analysis of sedim ents are well known. The bulk o f th e p articles in a clay will be p la ty ra th e r th a n spherical, a n d th e ir “ effective radii ” are th e radii o f im aginary spheres o f th e sam e m ate ria l which would sink in w ate r w ith th e sam e velocities as th e p articles in question. The specific gravities of th e particles probably v a ry a little , a n d th ere m ay be adsorption o f th e suspending m edium .

Fig. 6 shows th e cum ulative curves from which th e size-distribution curves were derived by graphical m ethods. U sing graphical m ethods again, surface d istrib u tio n curves were obtained, and thence th e relative to ta l surface p er gram o f each clay w as estim ate d . I n th is estim ation th e assum ption was m ade th a t th e p articles were spherical an d of uniform specific grav ity . The effective rad ii o f th e cum ulative curve were em ­ ployed. I f th e p articles were lam in ar ra th e r th a n spherical, th e ir falling velocities m ight be assum ed to be, on th e average, considerably less th a n for spheres of th e sam e weight. The norm al m eth o d o f using S tokes’ law would m ean th a t a single lam in ar particle would be rep resen ted as m ore th a n one sm all sphere. T hus, w hilst a lam inar p article has a g reater surface th a n a sphere o f equal weight, th e fa c t th a t its lower falling velocity leads to its in te rp re ta tio n as m ore th a n one sm all sphere will give a to ta l surface facto r n eare r th e tr u th th a n th e sm all spherical particle o f equal weight. F urtherm ore, if th e re is a fair degree o f geom etrical sim ilarity in th e p articles o f the different clays, relativ e estim ates will n o t be so seriously d istu rb ed by using spheres as th e basis for calculation.

Joseph 17 has em phasized th e im portance o f th e silica^-sesquioxide ratio

as a guide to th e p la stic ity of clays. The higher this ra tio th e g reater th e

degree of swelling and dispersibility, th e m ore viscous th e suspensions, th e

g re a te r th e h e a t of w etting, adsorption of basic dyes an d base exchange,18

th e higher is th e electrokinetic p o te n tia l w hen containing a given cation,

in th e absence o f added electro ly te.19 (According to Sm oluchowski’s

equation, th e “ viscosity ” of a suspension is a function o f th e square of th e

electrokinetic p o te n tia l o f th e particles.) M attson considered th e h y d ratio n

5 4 8 H O B S O N : F U R T H E R I N V E S T I G A T I O N S O F

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T H E P R O P E R T I E S O F C L A Y S U S P E N S I O N S . 5 4 9

of th e clay to increase w ith th e exchange capacity— i.e., w ith th e ra tio of silica to sesquioxides.

I t will be a p p a re n t th a t these sta te m e n ts concerning th e effects o f silica- sesquioxide ratio s require some qualification, p articu larly w ith reg ard to p a rtic le sizes.

I n a few cases th e fractio n o f a clay having a falling velocity o f less th a n 1 m m ./sec. a t ab o u t 18° C. w as se p a ra te d b y elu triatio n an d sen t for analysis u nder D r. H . F . H arw ood. H ow ever, th re e fractions em bracing th e whole of th e London clay were analysed, a n d th e silica-sesquioxide ra tio w as found to be highest in th e coarsest fraction— a re su lt to be expected, since m ost q u artz w as likely to be p re se n t in it. Y et i t was eq u ally clear th a t th e finest fraction gave th e m o st viscous suspensions. On th e o th er hand, p ractically th e whole o f th e S tockolite a n d th e A quagel w as finer th a n 200- m esh I.M.M. (the a c tu a l size d istrib u tio n was n o t determ ined). Stockolite is a high-grade china-clay, a n d analyses o f ty p ic a l china-clays give th e silica-sesquioxide ra tio as 1-13 to 1-22. D a ta in th e A quagel p a m p h le t p u t th e ra tio for th a t m a te ria l a t 2-26, a n d u n d o u b ted ly A quagel form ed th e m ore viscous supensions.

I n T able I I I are liste d a nu m b er o f th e p ro p erties of four o f th e clays analysed. I t is n o t possible to give relativ e values to some of th e properties, an d th e clays can m erely be placed in order in th e se respects.

T ab l e I I I . A llu v ia l

c la y Q. C lay A'. M o ttle d c la y M .

B lu e sh ale J . D ecreasin g o rd e r o f “ v isc o sity ” -

p ro d u c in g pow er 4 3 2 I

D ecreasin g o rd e r o f stre ss in te rc e p t-

p ro d u c in g p o w er 1 3 4 2

R e la tiv e v a lu e s o f e s tim a te d to ta l

su rface p e r g ra m o f c la y . 6-7 6-3 1 0 2-8

S ilica-sesq u io x id e r a tio o f fine fra c ­

tio n s e p a ra te d b y e lu tria tio n 1-89 2-99 2-82 2-42

The resu lts o f analyses p u t five clays in order o f th e ir “ viscosity ’’-pro­

ducing power, b u t a six th was a m arked exception. F u rth erm o re, w hen th e relativ e values o f th e estim a te d to ta l surface p er gram wrere considered, th re e clays fell in th e order o f th e ir “ viscosity ’’-producing power, w hilst th e fo u rth was o u tstanding. I t seems, therefore, th a t m any factors m ay h av e to be ta k e n in to account in order to p red ict th e “ viscosity ’’-producing pow er o f a clay.

I I .

Am brose and Loomis 20 used a concentric cylinder viscom eter to exam ine a 5 p er cent, b en to n ite suspension. Briefly, th e ir conclusions were as follows : On a curve w here to rq u e was p lo tte d ag ain st th e ra te of revolution, th e y found t h a t w hen m easurem ents ivere m ade a t successively higher

P R

5 5 0

H O B S O N : F U R T H E R I N V E S T I G A T I O N S O F

? T P l Whlch decreased m steps, th e form er curve lay consTant 1 e nf r i V 0me Z T t h ° t0rqUe increascd for a a t a c o n stan t ra te of revolution. A su b sta n tia lly co n stan t deflection could be a tta in e d b y subjecting th e fluid to a co n stan t an g u lar velocity for th irtv m inutes ,,p to several h o u rs.” The tim e necessary to break dow n th e I I I L n T b e riUm, ber Wr angUlar Vel° cit^ an d sheari»g s t r e s s ^ s o r t e r ra te o f s h ^ r A

iiemati0in ° t * g elw h ich h a d been o b je c te d to a high a speed o f 3-68 r.p.s gC ” X tOTqUe occurred in 50 m inutes a t

Through th e kind offices o f Mr. L. G. G abriel, i t was possible to borrow LW h n t erffl?Di ^ ntnC Cyhnder viscom cter from Messrs. Colas P roducts t f p e n s f f i n t TU I !1GS S0°,n, aPp f f ed in usinS i t for th e exam ination o f clay p e n s i o n s . I t w as n o t feasible to fill i t thro u g h th e ta p , as advised •

as a p t to be tra p p e d an d th e suspended cylinder displaced w ith th e m ore S S Z i r d “ T * absence o f a — ta n t te m p eratu re c h a m S te m p eratu re control was n o t v e ry satisfactory. H ow ever certain

o f th e suspensions were exam ined by using it.

Relaxation and Rigidity.

i t s ^ e f w i ” 101' ^ 1'11'101' ^ ' 18 ^ Sted a Httle " i t h th e m iter cylinder sta tio n a ry sIowH until1 ^ r e a c h e d quickly a t A and th e n nmTe

t l T - + i a VaIue >vluch’ xt seem ed< ^ u l d persist indefinitely unless th e in stru m e n t w as disturbed. The final value was n o t th e zero observed on suspending th e in n er cylinder, showing th a t some m uds are a n S h e f ^ E rS lgd a m easurable stre ss‘ ^ h a r d s o n , 2* an d McDowell a n a u sn e r iiave m ade sim ilar observations. T heir findings— (a) th a t th e

n tic a l stresses were difficult to determ ine accu rately 21 an d (b) th a t if the S t y t ™ S T h e ed f e ? fleCti0n dr0PPed

- f n e c t contffiued S r a f le l t r(daxatlon curve (deflection p lo tte d against tim e) - w ere borne o u t ^ folIowing before th c d isturbance 22 ere borne out. Thus, th e in stru m e n t can be em ployed for th e rough com parison o f critical shearing stresses or “ yield values.” °

Lag, Breakdown, Thixotrojnc Recovery, etc.

Various a p p a re n tly anom alous re su lts arose from th e p ro tra c te d lag of

8

o ro ta tio n o f th e o u ter cyhnder an d th e in stan tan eo u s “ viscosity ” and I S f l d ' K x i u ° l at li”™ lh*

equilibrium S g « ' » tru e value for th ix itro p ic

arose c? « cef n ° cylinder viscom eter, a t tim es th e suspicion 1 i ° tt0 n ? ^ eSpeCiaUy concentrated, even 4 h o m i g a v f e l f v ^ mUf ’ a n d saxnPles ta k °n a fte r shearing one m ud for th e bottom s o f th ,nee xons o f 38-2 p er cent, a n d 42-87 p e r cent, a t r-nL; i er a n d o u ter cylinders, respectively T heoretical

S t S Z i " “ ~ * * * i J L J t S S S i

T H E P R O P E R T I E S O F C L A Y S U S P E N S I O N ’S . 5 5 1

I n order to in v estig ate th e m a tte r fu rth er, a sim ple viscom eter was constructed, consisting of tw o concentric glass cylinders, th e inner one n o t q u ite reaching to th e b o tto m of th e o u ter one an d being capable of ro tatio n . A know n w eight of 80—120-mesh (I.M.M.) sa n d was add ed to a 4-19 p er cent. A quagel suspension an d shaken well. Some o f th e m ix tu re was poured in to th e viscom eter, and a like q u a n tity o f th e m ix tu re was poured in to a tw in a p p a ratu s, th e inner cylinder o f which w as not, however, ro ta te d . W hen th e m ate ria l in th e first in stru m e n t h a d been sheared for 40 m in u tes a t 3-69 r.p.s., th e m ate ria l betw een th e tw o cylinders was rem oved in each case, and afterw ards t h a t w ith in th e o u ter cylinder b u t below th e inner cylinder w as also rem oved. The percentage o f san d in each of th e four sam ples w as determ ined.

Tarl e X V .

P e rc e n ta g e o f san d . S h e a red U n s h ea red

sam p le. sam p le.

U p p e r p o rtio n b etw een th e cy lin d ers . 3-55% 7-70%

L o w er p o rtio n b elo w th e in n e r cy lin d e r 14-95% 6-10%

I n a second experim ent crushed oil shale (80-120-mesh I.M.M.) w as added to th e A quagel w hich w as p u t in th e viscom eter. The d a rk colour of th e shale rendered th e m ovem ents of th e p articles v ery clear. A gain a tw in sam ple was se t up, b u t n o t subjected to shearing. I n th e unsheared sam ple th ere were no signs o f sinking o f th e shale p articles ; m erely a little w ater separation on th e surface o f th e Aquagel. I n th e sheared sam ple, a t low ra te s of ro ta tio n of th e inner cylinder, th e shale p articles sank along sp iral p a th s an d accum ulated ju s t below th e b o tto m o f th e inner cylinder

— i.e., ju s t below th e zone o f shearing. N o change w as seen in th e m aterial well below th e in n er cylinder. On raising th e ra te o f ro ta tio n of th e inner cylinder, a speed was a tta in e d above which a new phenom enon appeared.

A series of parallel bands w as observed in th e suspension, tow ards th e edges o f which shale p articles could be seen m oving quickly upw ards an d dow nw ards from th e m iddle o f th e bands. These bands seem ed to sink slowly dow n th e cylinder, b u t were ever replaced b y fresh bands a t th e top.

No accum ulation o f oil shale w as evident in th e region below th e inner cylinder. U n d o u b ted ly th is w as a tu rb u le n t condition u n d er which the p artic les d id n o t sedim ent, w hereas u nder stream -line conditions, which m u st be realized for o rd in ary viscom etric m easurem ents, sedim entation took place.

According to B a rr,23 T aylor h a s exam ined th e general case o f con­

centric cylinder viscom eters in w hich b o th cylinders ro ta te in th e sam e or opposite directions, an d has obtained a form ula which reduces to :—

n c~a2cP 71y

\ { a + b )v 2 ~ 0-0571/2 + 0-00056

for th e case where only th e inner cylinder ro ta te s. Q c is th e critical speed

of ro tatio n of th e in n er cylinder for tu rb u len ce ; v is th e kinem atic vis-

c o s ity ; a is th e rad iu s o f th e in n er cy lin d e r; b is th e rad iu s o f th e o u ter cylinder; d = b - a ; / = 1 - The form ula assum es t j | | sm all, b u t Lewis found critical speeds in excellent agreem ent w ith i t up to - = 0-71. A ccurate centring and m ounting o f th e cylinders is essential, a n d th e ir lengths should be m an y tim es th e ir diam eters. W hen in s ta b ility arises, i t is three-dim ensional, o utw ard ra d ia l flow occurring a t in terv als o f ap p ro x im ately 2d along th e cylinders. This was a b o u t th e w idth of th e bands observed here.

One very viscous clay suspension failed to give an y signs of separation alth o u g h tu rb u len ce was n o t ap p aren t, b u t a second showed sedim en­

ta tio n , as is proved b y th e following d a ta :—

Ta b l e V.

T im e o f sh e a rin g o r s t a n d in g : 4 h r.

R a to o f r e v o lu tio n o f in n e r cy lin d e r in sh e a re d sam p le : 2-3 r.p .s.

5 5 2 H O B S O N : F U R T H E R i n v e s t i g a t i o n s o f

U p p e r p o rtio n b e tw ee n th e c y lin d ers . L ow er p o rtio n below th e in n e r c y lin d e r

C o n cen tratio n . S h eared

sam p le.

32-10%

50-54%

U n sh ea re d sam ple.

_ 38-57%

40-63%

T hus, alth o u g h a concentric cylinder viscom eter o f th e H a tsc h e k ty p e would, a t first sight, seem superior to capillary in stru m en ts, since thixo- tro p ic equilibrium could be a tta in e d , in practice, in exam ining th ick heterogeneous clay suspensions, m an y difficulties arise. Lag, induced sedim entation and th e length o f tim e needed for a fair definition o f th e to rq u e -ra te o f shear curve are am ong these, an d its m ain value would therefore a p p ear to be for d em o n stratin g th e presence o f th ix o tro p y .

I I I .

The in te rc e p t on th e stress axis o b tain ed b y ex tra p o latio n of th e p a rt ot th e flow-curve representing essentially stream -line flow is a function of th e yield value as used in th e B uckingham equation, being A o f th a t q u a n tity . I n a drilling m ud th e yield value is a n ex trem ely im p o rta n t p ro p erty . I t s d irect m easurem ent, a n d th e investigation of its changes w ith tim e and o th e r factors in th ix o tro p ic m uds, are m a tte rs of no little consequence. To exam ine these p o in ts seem s ra th e r beyond th e scope of th e procedure used in th e o rd in ary deriv atio n o f th e stress intercept.

A num ber of w orkers have p aid som e a tte n tio n to th e d irect m easure­

m en t o f yield values, b u t i t is n o t im probable th a t th e facto r exam ined in

some instances was n o t e x a c tly th a t involved in th e B uckingham equation

n o r was it sim ply re la te d to it. Meyer * used a th in p late w hich was

allow ed to fall edgewise m th e m ud. In v estig atio n showed th a t this

a p p a re n tly sim ple m ethod is fra u g h t w ith m an y p ractical difficulties, an d