Flow Properties of Fluid Systems A Davey, ~] T Guthrie ~*and C HaIP* * F i e l d P a c k a g i n g ( N e w c a s t l e ) , Station Road, Killingworth, Newcastle upon Tyne, N E 1fiORH, United Kingdom, ** The Department of Colour Chemistry, The University of Leeds, Leeds LSZ 9]T,United Kingdom, *** Wolstenholme Rird<,plc,,Springfield House, Lower Eccleshill Road, Darwen, Blackburn, BB8 OR]? Lancashire, United Kingdom,

In|r0ducli0n A rna]cr cbjectk,,o it, the dovol%~rr-eet and the use of bkcs, ~,~snishes, paints, cosrr-etk'.s a~r~dlubricants is to create ~-, iris that are respo_,usrve, ~ Thus, such corrpos~te fluids should p o s s e s s flays ckaracteristics that c h a n g e in the desired m a n n e r as the fluids are applied to a substrate through the s h e a r i n g action of tr:e o~e]ivery device or the deil-er y system.

A speciaiised branch of co-operative chemistry and pn),sics, namely r h e o m e t r y has b e e n d e v e l o p e d to stud)' the r that matter flows ~inder specified conditions Rheometric techniques have b e e n successi%l y applied to most areas associated with ~he characterisafion of fluids, ~ allowing formulators' ~o pred:~ct how a p r o d u c t will p e r f b r m in formulation, delivery and applicatior~"service Many wo~e rer by Barnes, ~ ,who co:cored the application of rheoiog:~ca] studies to a range of indus!riai preblerus h~volving dispersions, fkorr~ toothpaste to n_.c'.!ear r Rheoioo%~ is essential%; the study of fluid flay,,. It d e s c r i b e s the des of a body, b e it a solid, liquid, or gas, unde~ ihe influence of stresses. ~ h e a d i n g \,v,',r~&ers in khis field of science define r h e o i o g y as 'the science of the defbrrnation and flow of matter'.~ The teKr~ rheolog%~ is d e N v e d kern the G r e e k rhea< m,ean ing stream, ie flowing, and -oio~s a sufffx indicating the s c i e n c e or study of a particular field. The rheoiog?' of a syster:, is r~easured using inst:;urners kncmm as rheornetars (or sorrLetirnes viscorneters), it kilows that the iec'.h nique errp'o,/ed should sirr,uiate a sirqiar %~pe of shear reg:~T~e to that enco~.ntered during application by the u s e r However, the fi(:~r or cons:stency of a fluid or semi-sohd can b e a s s e s s e d in various ways including the use of inclined planes, ir~rn.ersed falling spheres, various y p e s of flow c u p s (hahn cups and k , rd cupsi ?.,r c• and so on. it is h%~ortant to ~ecognise that the latter r a n g e of tec'.h niques pr@Ade only limited infbr rnation wlhich is largely of use mainly in quaii%~ control situations. With such techniques, it is the effiux time which is b e i n g monitored, for events 'r are oc'.c~.rring uno~er ;~'iatb, ei,! imprecise conoitbns. I%,e tec
Stales o[ mallet It is possible s matter to exist in one of tkree states, the solid state, the liquid state and the g a s e o u s state. The cateSurfuce C0etli.~

ln|emali0.ul 1991 (7)

g o r y of excited state species (for e x a m p l e plasmas), is a matter of incense interest, but b e y o n d the s c o p e of this tre at~nent ~'hereto re, fbr the benefit of tris pros ent~Son, the terrn 'matLer' :-:hould k e taken to irnpi? solid ,state rnateri als, ]Liquid s!ate materials and g a s e o u s state materials.

Ided solids kieal solids obey }%>aL
-Era ideal solid may therefbre b e c o n s i d e r e d to b e co:m-p!eteiy elastic. An a p p h e d deformation is re',;ersible o n c e the su
<~= G 7 (~ ,stress (N m z), G shear n~,~-,~-i~i~s~,,J,'Trn % and 7 : stLain (which is a dimensionless t e r m )

Ideal [bids At the opposite e-rd oftLe mechanicak 'soectrurn ~are ideal fluids. For tke benefit of t?ns treatment a gas can be considered as a h-grJ), oxpar}ded liquid, T!]is allov,,,s ~.,s t(, take irLto acco~-r-t i:,oth liquids anQ g a s e s v',,ithin the general term %s WheN. a strain is applied, the ideal hquid will[ deform completely irreversibi~< This is because the strait: energ) ~ applied is dissipated ,Jvithin the system, as heat to the surroundings: A rr,ode] of ideal fluid behaviour is gkron by the 'dash pot' model% ideal fluids are said to exhibit Newtonian behaviour, b e c a u s e they o b e y Newton's laws of viscos:.% which has as one ibrm:

--- stress (N m-s), t] --- viscosih,coes . . . . . . . .
(Pa s) and

Visc0destic meteriah 'Fhosc iluids most c~,rr.morfiy encour.terod h~ e-tar yo~b/ life b.suaily lie in the m i d d l e ground witk res_rr.,ect to t k e k vis.cosity or l o w properties, b e i n g beSseer: con]pletely elasand co rr,pietel}/ viscous/inelastic tic'. (~iookian), (Nev,4onian). 7be tells viscoelastic is used to define the _-,s of ficw properties of rr, aterials, often cor_qpos:~tes, which lie in this region.

32~

Th~._~t h e o l o g i c al b e h a v i o u r of c o m p o s i..... t ~ fluids d e p e n d s o n a 1 ~.n~

r Ol ! a c t o r s

i ~!eo~s - r . c L u , . t e I r . ~ p L , ) , , ~ c , ~ i

the c h e m i c a l n a t u r e of the c o r n p o n e n t s , !he quaiRy an,i t y p e of the m i x i n g r e g i m e , the s t o r a g e stability of tine c o m p()site, the n a t u r e o f the ..~-"c-} ~...,**ilcl,~.&. . . . . . ,'r s%
occl/rrenc6-

cbelsi.)b~•

o ! N" .... I
reactlvlb7

are

all c,f coRsio.eraD!e

brld

irr. 9

i'~ost flow r e g i m e s are c o n c e r n e d wRh a n a n g u l a r d e p e n d a n c e m the appik~ation of the a-[:_p ~ s ~-~,~,_.:_, It is importar~t Lo n o t e that if n o n Laminar f l o w s a c h i e v e d (-e a t u r b u l e n t c o n d f t o n ) , r h e o i o g f c a i d a t a c a n n o t b e re]iabi,,, m e a ~u r, .S :Fh q . . . . ~~ ....... t ~~,~l a m i n a r fi(.v,~i,s o n e of s e v e r a l p r a c t i c a l test cond!,uens (rr.atherr.atica.ily ' b o u n d a r y c o n d i t i o n s ' ) that rriust b e satisfied if d a t a are to b e ~r~eanisg?i.

[[(lure |: t'~uitNeyeeed (ube d fluid under study

~},,~ ....

A

to

t h e m a i n t e n a n c e of,stab:,iity a n d ~ r ~ - d i c t e b i l l W o f b e h a v i o u r o f the c o m p o s i t e f l u i d s car, r a i n i n g t h e p a r t i c l e s

T h e rhee].ogica.i b e h a v i o u r of c o m p o s i t e fluids ~s also v e r y r n u c n d e p e u d e n t o n the s h e a r strain rate i n c u r r e d d u r i n g the s h e a r i n g action a c c o m p a n y i n g d e f o r m a t i o n or flow W h e n b w s h e a r strain r~tes are e r n p k , y e d , the f l e w :s r n a m i y c o n t r o l l e d b y the ioveL of s ~ r h c e a n d i n t e r f a c e interaction, p a r E c ; e s e p a r a t i o n abili[y, tt-e m o l a r m a s s of the film_ f a r t i n g <,~stem_, pelyrner--solvent fnteract!~ons, the p a r t i c l e sizes a n d size dfstributio<:s a n d the p a r t i c l e s h a p e s . ' D i s is b e c a u s e s u c h factors i n f l u e n c e the i n t e r n a | s t r u c t u r e a n d n a t u r e of the c a r t . p e s t s fluid. A_t h i g h e r s h e a r strain rates, the flew p r o p e r t i e s b e c o m e m o r e d e p e n d e n t o n e l e c t r o k i n e t i c p h e n o m e n a, o n steric, stabillsa tion e~,ants, o n the p h a s e ',,c!~.rne of the p a n i c l e s , o n the size d i s t i b u fion of the p a r t i c l e s a n d of the film - f e r r n m g p o i y r n e r f c c o m p o n e n t a n d the p a r tic;e s h a p e s : T h e r e are, therefore, mars162 f~ctors w h i c h i n f l u e n c e the flow n a t u r e of c o m p o s i t e fluids: U n d e r s u c h c k c u m s t a u c e s of corrp!exil), it is b's L~aito r e s o r t !o the devoloprr~ent a n d u s e of m o d e l s y s t e m s , b o ! h irk the rr.athernatfcai a n d the p h y s b cai s e n s e s , as seer: t h r o u g h rationalization o ( t h e theoretica! a n d the p r a c t i c a l a s p e c t s of the flow b e h a v i o u r of com, p o s its fluids.

Theore|icol and practical considerolionsof flow behavi0ur. To assist in u n d e r s t a n d i n q the following d i s c u s s o n it is first n e c e s s a r y to establfs.h a n u m b e r of b a s i c d e f i n i t i o n s

S~eor This m ~ y b e defir~'ed as tbe m,ovorr~er~,t ,of a laver of rnateri .- Fu~ ~ 'l~-'<'~,.t a]. relative ~r . . . . . .~:~l ~'~' ad]. ac er:t . layers. . . This. is the ~,-.~*l:

s|ress effeds T h e s e 8.1re often b e t t e r d e a l t w-th ff-orn a diag~arnrnatlc s t a n d p o i n t . .~'~..... ,g . . ..~{ . I r e p r e s e n ! s a c u b i c s e c t i o n r;f . . . .~be iluid s a m p l e u n d e r study with a s u r f a c e a r e a e r a (mZ). This is ~,~-i < 4 ~o c o u s i s t o f m a r r y infinitely Lhm, yo t -L~. ~.l.! .e .l ,. . aQ]acor~,>i..~ere..[ c e n t layers that c a n slide over e~.ch .other, r a t h e r like gne Jndividua! s nests fr @ a r e a m of o a p e r . In l--igure 2, the s a m e c u b e of fluid now ~<,sts o n a~: in] may a b l e plate, k O n top o ~ the c u b e is p l a c e d a s e c o n d plate, Q, that m o v e s with a s p e e d of Y (rn s 9 d u e to the a p p l i e d force .F(N). 'l%is c r e a t e s a r e g i o n of l a m i n a r flow b e t w e e n the plates. ~r'~'is is a fluid flov~ r e g i m e in w h i c h the p a r t k i [ e s (fbrrring iayers) of the fluid are a b l e to :r-eve srr~ooth O, o v e r o n e a n o t h e r without t u r b d e n c e .

330

2'

[igure 2: Laminar flew during shec~ringof ~ubed fluid undei study -:-----

Statbnary pJ~e ?u-',sur,ulng t h e s e b o u n d a r y c o n d i E o u s are satisfied, the %ik,wing r n a t h e m a t ! s a l t r e a t r n e n t is valid. By a p p l y i n g this fbrce, F, to the top plate, a resultant s h e a r stress, !he c o r : ' p o u e n t of stress p a r a l l e l to the a r e a of sarr~Ne unde~ consideration, is ob[air,,.ed. Thus, @ FLA, where: G = Stress (N rr:-z), F = P o r c e (N) a n d A ---/-\:ca (:r}) it i,s n o w the c o n v e n t i o r t to r e p r e s e n t ,sn~a~ .... stresses u,ing " " Tn o l d e r ~exts the G r e e k ~..... ~-~; ~ ,,,sigma), (tab" w a s LiS <-',cj.,

Sheer strain rote effects ,n ! n e s e c a n b e handi~,c e y ~-'f,,re . . . . . . . . ....... . . to ~',~i ...... 1 a n d 2. '~},~.~9 9 ,.,, the ,shear sLress a p p l i e d to the top plate c a u s e s *~,e~9 ,(,,p iaye~ +~, m ~ , , ; e L~9 laver u n d e r n e a t h a i o n q v,4th it This layer thor: p~ -f~' u~:~ a!~ng the .:~),e~ . . . . ~ b e n e a t h that a n d so on, all the w.vl~,~,~o ! h e r t h a n t h o s e p r o q d e d b y the cornpc, n e n t s of the fluS:i, it also a s s u m e s that the fluid is ~,~......... ai~,~ s t a b l e u-~,de, the C'Or'd~t~r4]< 'of the _w~e a s u r , s r r ~ e r ; t .

Serfece (oatinss Inlernational ]997 {7}

Figure3: Overallvelocityprafile of shearedcubeof liquidunderstudy 5peedV

1]

/ The sheer str i, r01e (or she0r r le) This is calculated as the cirop in veiec.i%; (~) between the top layer and the bottom layer (thickness ~), As de~,icted i-~ Figure .3. Th~s gR,+es ff
ceeffidenl 0[ viscosily <'9Ab~ ~,S 4<~fk, . . . . . . e~q as the ratio of the s::ea~r strc~ss to tt-e~ shea~ strain rate, "r] G, Y With the e x c e p t i o n of Nev~tonian fluids, the viscosity of a s y s t e m ~s m o r e c o r r e c C y c a l l e d the a p p a r e n t viscesiv], berceuse the ratio is d e p e n d e n t on the s h e a r strain tale, rather than b e i n g an a b s o l u t e value, it is also son-zetirnes r,~sforred to as s h e a r v i s c o s i ~ or dyna!7ic viscosi%s

the m a t e r i a l is resistant to Now C o n v e r s e b A if the s a m e s h e a r sEress p r o d u c e s a hig!: s h e a r sirsin rate, then t:he viscc, si%; is c o : : r e s p o n d i n g ! y iowl and the rnateria! is said to f[c:,vv easily. As ,stated abo<~ei the influence o ~ the t e n r o e r a t u r e or. flow p r o p e r t i e s c a n b e prefc.und. Fbr 1%.qostpaint, ink and coatin 9 systems, an a c c e p t a b l e r a n g e of ~ernperatures fi,r ~ p p l i c a d o n c a n b e e s t a b l i s h e d . O~.tside this range, p r o b i e m s a r i s e Thus, a 65~4-solids, p o l y e s t e r c o a t i n g m a y s p r a y v~,cll at 45~ if the solids ie,~ol vv~sre ko b e i n c r e a s e d to 809"~, As r e q u i r e d for rnany of the s o - c a ! l e d h i g h e r solktP coa@ngs, t e m p e r a t u r e s d u r i n g a~ppiication would n e e d to b e in e x c e s s of 70~163 '!'his irnp[~es that sorr~'e b / p e of tern p e r a t u r e - c o r n p o s i t i o n relationship is o p e r a t i n g :S2terk<:g the t e m p e r a t u r e c a u s e s a c h a n g e to the rate of flow: ~Ibe flow usually i n c r e a s e s . ETceptfons to this g u i d e l i n e include situations ~n which the i n c r e a s e in the t e m p e r a t u r e c a u s e s the o n s e t of chernicAi r e a c t i o n s re,suiting tn p o l y r n e r i s a tion/curing or w h e r e the i n c r e a s e in the t e m p e r a t u r e b r i n g s a b o ~ t rerpovai of ,solvent resulting in an ~qve~t 9 tious i n c r e a s e !~n the soifds !e'vel. F~ssurrnng that the ter~;perature i n c r e a s e is not b r i n g i n g a b o u t po~,/rnerisadon or solvorX ev as)oration, a s s u m p t i o n s can b e m a d e c o n c e r n i n g ,+he c h a n g e in flov,, rate arising as a result of the tep:~perature c h a n g e . ~ s the t e l n p e r a t u r e rises, the c o m p o n e n t s of the corr~positk)n are a b l e to g l i d e p a s s e d e a c h e t h e r m o r e easily Hence, the viscosi%- falls fpplicaCor~ of the :S-trrhenius r n o d e i a s s o c i a t e d with the eL}oct of terc~pera[ure c h a n g e s on r e a c t i o n rates aho~,,,,s the deterrnir:ation of. an . activatio,'.~ . . e. n e r.g y of <'o,v,, as shc,~,~n b,; the relationship: i n ' ~ : in

E

/ .->'T~

"q is the dynarr,,icwiscosRy, E.<.~<,,, 0 is the activatior:energy of i~c:vv T is !he K~Ivin teH~peratur~J a n d R is the g a s constant.

A h h o u g h !he 'Pascal s e c o n d ' (PA s) is nc,w the a c c e p t e d unit of v i s c . o s i b / t h e unit 'rrdiii F a s c a i s e c o n d ' is often u s e d (m~Pa s): the latter is p r e f e r r e d w h e n d e s c r i b i n g the flow of low to m e d i u m viscose%,, s,/sterr~s, in o l d e r literature, uni!s of ' p o i s e (P) and ce-0tipolse (cP)', Stokes (S) and can@Stokes (cS) and a varze~r of o t h e r unK fbr~.~ts m a y b e found. C",onvers~on belvveen the Pascal systerr~ and the Poise s y s t e m is simple, as OLK!ir:ed below: ! PA s ILrr.Pa s

i000 rnPa s 1 cP

It s h o u l d :be n o t e d that the visco;'i V of o. fluid is high!y d e p e n d e n t on s e v e r a l facto:s, in particular, the ternperAture of the m e a s u r e m e n t should b e q u o t e d as ~ sn~all c h a n g e , (as snR-d! AS i---2~ c a n have v e r y proft, und effects on a sTstem's r h e o l o g i c a l character. Thus, a small i n c r e a s e in the terr, peratu~e usually c a u s e s a c o n s i d e r a b l e dr.:,p in a p p a r e n t v:~scos~t K ~iowe~er, in sorr-e adhesi~;
Surface Coa|i.~ In|ernation~m 1997 (7)

q~his ,straight iiTled relationshirJ has s,I~ ~'-~~IL~es wiri~ the nx>re cor.ventional fbrn: of the .t\rrher:ius equation: lr- k := It, ,,s ~.

/T~T

Here k is the rate constant of the chernicai reaction, A is the collision ftequep.cy factor and E~ is the activation e n e r g y ibr the r e a c t i o n J~nder in~estigation. :in c h e m i c a l reaction reiatior:ships, it is c l e a r that the re.te us~.ally i n c r e a s e s as the ter~:peratt~re rises, in t h e o l o g i c a l assessrnents, the viscosity falls as the terr.perature rises. 'N;ds tat!or c a s e gl~es r i s e to the tact that !he activation e n e r g 7 of flov~ is a n e g a t i v e quanti%< At first giar;ce this r~;ay seem. to b e unusual As exarr.pies of n e g a t i v e activation e n e r g i e s arr relatlv
Measurement-types instrument Se-,'erai a p p r o a c h e s to tht- steady of tt-e flow bena~viour of fluids have been deve!o]::~ed to ,suit tire par tic.:i0.r C:_K~Un'_,stances surK:s~,nding !he need for the ;ne~Js~-rcrr~<:rlt,s to be

331

taken in the first p l a c e . M e a s u r e m e n t m a y b e n e e d e d on line, as in the a s s e s s m e n t of the d e h v e r y c h a r a c t e r i s t i c s of an ink on a press. Mea.su.rement .,.r.,~y b e n e e d e d as a r apk'i qual~tv control tool, in a c o a t i n g operation. A]so, m e a s u r e m e n t r.a~r b e ~leeded as p a r t of the c h a r a c t e r i s a t i o n of the fluid kinder r e s e a r c h / d o v e i o p m e n ~ conditions. E a c h wil] have its own c o n t r o i l i r g f~ctors a s s o c i a t e d with Gfferer:t d e g r e e s of sophistication, it fs i m p o r t a n t that the e n q u i r e r is aveare of (i) the infer rnatk)n a l r e a d y p o s s e s s e d c o n e . a m ing the fluid, (fi) the prevas condffioris which a c c o m p a rO, the rneasuremer~ts, ([i:~)the r e q u k e m e n t s of the test and @v) the !mntations of the p r o c e d u r e s in,r a s e d arid of the conditions u n d e r ,,vhich m e a s u r e r ants are taken. The qo~estion of the interpretation of e.~per,mer;tai results arises. This ira/elves a k n o w l e d g e of the v o c a b u l a r y of flow studies, r e c o g n i t i o n of trends a n d the n e e d to b e a b l e to corr-r:~,unicate the findings and their interpretation to o@ers from the point of view o< the c o n s e q u e n c e s of the findings with r e s p e c t to d e c i s i o n making, instrumentation that is available v a r i e s from the s i m p l e units (and relatively inexp e n s b e units flow cups, i n c l n e d planes, fal;ing ~ods and fa_~n:c:g ~~" ,spheres) to the m o r e com~xex ~'~~ - - units (and" r............. ~].~R..veiy e x p e n s i v e units .... c o n t r o l l e d stress r h e o m e t e r s and contrci!ed s h e a r strain rate r h e o m e ! e r s ) with their a c c o m p a ro, ing sophisticatec~ sof%,,,are p a c k a g e s fir< data rr~anipu!a tion.

Simple flow me(|suremen!syslems Flow ups A ~ p i c ' a l a r r a n g e r n e n t invo].vh-~g a flow ~up is as s k o w n m Figure 4, T r i s d e p i c t s what is essentially a r e s e r v o i r c o n taintng a know:< constant vole.me of low viscosity fluid, A s s e s s m e n t requires monitoring the time taken for the fluid to d r a i n fton~ !he r e s e r v o : z w a a d e f i n e d orifice, iocate d at the b a s e of the c u p

F[!ue 4: $chem~lcrepresenl~i~nof ~ fbw ~up~rr~ntement

..... ]IO degrees

I m p r o v e d f e a t u r e s of the ISO flow c u p s i n c | u d e the 12,0~ a n g l e of the c o n i c a i e n t r a n c e ar;d a 2.0rnrn c a p i l l a r y S t u d i e s have s h o w n that the sir~ple Zah:n c u p is the l e a s t a c c u r a t e efilu~ c;~p (with c u p s h a p e d b a s e a n d rio c a p i i ia r-_,/~.The Zahn c u p systenq :~sstiil w i d e l y u s e d b y p r i n t e r s i n t e r e s t e d in the fiov~ p r o p e r t i e s of rela@ve!,/low v i s c o s i ..... " 9 Is sirnr,!y ~ _ ty fluids. "~a] ....... -,-~, c u p s a r e e a s y to u s e ~"~ !.~.~ ....... d i p p e d into the rr.~ss of ir,k, b y u s e of its l o n g h a n d l e , aELCJ '.,ithc~ra~&'r,, A_s with l-bni c u p s , Zahr- c u p s ate v e r y e a s k y cleaned. '~[he length to diarr~eter ratio of the cylindr.cal orifice, ie the a s p e c ! ratio, v a r i e s d e p e n d i n g u p o n the orifice g e o m e t r y A high a s p e c t ratk' i m p r o v e s the sr:;ooth, n e s s of fie,s,, ~"~,is e x p l a i n s the u s e of an e l o n g a t e d orifice in an iSO cup. i hixotropic m a t e r i a l s s h o u l d b e put through the efL_.x c u p i n - m e d i a t e ) , a f e r s h e a N n g the s a m p l e and, a|so. a~ter a ~est p e r i o d . !f a |ar.ge difference o c c u r s bet~voen the ~,'o resuits, a n o t h e r m e ! h o d of flew " n e a s u r e r - e n t s h o u l d b e used. Thixotropy r e d u c e s the reproduc.biii%J of results achim, e d fbt:,r' a flow c u p m e t h o d .

Adwntoles of flow cups Flow c.ups c a n b e u s e d fb; s i m p l e fluids w:iclh 5now near ~(evsteni0.1l xa!ure. Flow c u p s c a n b e u s e d with e a s e to _measure the consistency of o~]s and to pr,c~ide a c o m p a r i s o n b e p w e e n inks The o~,Terali p r o c e d u r e is quick and the t e c h n i q u e is e a s y !o ~:se.

l)isodwnlales of flow cups Flow co.f.~s ar~3 not b.ppropr;ate R)r investigating the r n e oiogk~a! p r o p e r t i e s of uon N~-vvtonian fi_ids suclh as ~-"~'e ~'~- ~-'~id :-~,k< and paints. The m e a s u r e m e n t s require the u s e of r e i a t : v e q l a r g e s a m p l e vt.iurr-es: i ,o,,v c u p s d o not Dro
k

Falling rod viscomelry

Whilst tire flow c u p s y s i e m h a s :to uses in the paint indust,vy and the ink i n d u s t r y lot r e c o r d i n g flc,v~, tmqes b r refbrence, it is no! a p p r o p r i a t e fhr stu.dyh~.g r h e o l o g i c a ! p r o p e r t i e s of inks: Flow c u p s m e a s u r e o d y the time t a k e n k:r a l i q d d to flow t h r o u g h a fm,~d orifice, J n d e r gravX},. T'hey d o not gb,,e a p r o p e r m e a s u r e of the t h e o l o g i e s ! p r o p e r t i e s of the c o m p o s i t e fluid. T h e flow c u p s h a p e @e fiat b o t t o m e d or c o n i c a l s h a p e d orifices) d e t e r m i n e s the e n t r a n c e effects in the orifice. S h o r t o r i f i c e s d o not a.ibw l a m i n a r flays to d e v e l o p full}; s i n c e this c a u s e s n o n iinearRies in time v f s c o s i t / ~e!a tlonships, thus r e d u c i n g the se~nsifiviW/ at iev,r~ar f b w tir~'es. The !SO flc.w c u p has a c y l i n d r i c a l orifice.

332

}igu~e 3 ,skmv~s a ~pica! fal|ing s visc9 system, in its s i m p l e s t fbrm. M e a s u r e m e n t involves r e c o r d i n g the time taken for m a r k 'A', on Lhe rod, to fall b e t , r o a n the fiduciai ~ - ~ - b ' B a n d r~ p r e s e n t on ff~e r~ ~t~.r . . . . . . . . tion jacket, (as shown in the d i a g r a m be]ovv). ,~ degr<~e of t e m p e r a t u r e control can ]be m a d e ~wmilabie b y circulation of water, at the r e q u i r e d t e m p e r a t u r e , thK;ugh the tripodm o u n t e d b a s e plate, as shown. S o m e p r o t e c t b n of the fluid from dust, d r a u g h t s and t e m p e r a t u r e c h a n g e s , is p r o v i d e d b F a P e r s p e x jacket. Various l o a d s are p l a c e d on the top of the rod, ail~,vving diffbrent fbr~'es to b e a p p l i e d as the rc,,(~. #s Thus, the stress a p p l i e d c.an b e v a i e d in a c o n s i s t e n t w
Serrate Coatings ln]erna|ionel ]997 (7~

Figure 6: Schematicrepresentatbn of a typkal plate/cone assembly

[igure 5: A schematicdiagram of a typical [~lling rod arrangement

I

Pl

WeJgl~ls

A ........

r

i $r

I

1~merstair,sline

I Transparent pro~ed[ng[~cket

! i

........ e

S

rod

~mer stopsline I bk biob ~r

ou~

Water in

Advantages of the f lling rod technique J\ fhii:mg rod viscorneter enables measurem.e:~t of flow ef9
Disadvantages ~:is tec!miqu~c is generally r;ot usc-@~fbr fast u~ryir4g/c~.r ing inks, kzespec:'.t>e of the :he!hod by which ~k~s method is not appropriate to the irs;estigatlen of the rheoiogical properties of non-Newtonia:x liquids, /%s with most techniques o[ viscosity del:errnination, the Slling :od system sears little or no resemblance .c" practical process conditions associated v,4tb the dope sitbn of fluids.

Cone and pB|e rheomelry The r.s of the %~pical pbte/cor;e arrangerrLer;ts as shown h~ Figure 6. Most plates and cones are fc~brfcated f%orn very high grade stee]s. How~s-,or R is possible to use alternative rnateNa!s should parJcular circurr~stances so require. F.or example, Davison end Cuthrfe (i998), h~v,,-e used a quartz base plate in their studies of the pho tochemorheo!ogical properties o f a range o( ultra--vfoiet ]ight curable inks. 7 h e k study required that the base plate be transparent to ultra--vioiet light so tlhat simukaneous m.onitoring of the curing process could take place through rneasure:nent of the cha~lges in the flow p.<,per ties The plate and cone technique pr.c,vides a detaiied picture of the nature of the flow properties of sirnpie fluids and of complex fluids. '.~'leometers have been desfgned in a range of lev,-Is of sophistication, with differing capabilities and levels of contK~'!Of operating parameters. Put sirply; m plate a~ld cone rheometr y either the pla!e ~ernaius station

Surfe(e Coelings international | ~97 (7)

as y while the cone rotates abe,so it, thus shearing the saru pie, or the cone remains stationary while the plate rotates Plates ca~l be supplied ~n a range of dia~r~eters and the cones can be supplied such that a range of angles be~c,.,veen the cone and the plate is available. The plate cone re]afionship is a complex anal involving !he size os the plates end of the cones end the angle which exists be~,,,,een @e plane and the cone. If the cone angle is less than four degrees, the shear rate b e c o m e s effectiverF conslant across the gap. 'r'he flcsw regime can either be s p e e d controlled or torque controlled giving rise to generations of controlled stress rheometers, corLtroiied shear strain rate rheometers and instr,xnents v~rich can prc~Jide aspects at ~ both approaches.

Adwntages 0[ cone end plate units .....,_,he arts plate instrum_ents aiiow the velocity gradient to be kept constant thx~ugho ~.t the samgle during measurerr_ent Tkis Ls an :_res aspect of measurement of the flow characteristics of0. fluid, Relatlv~l~ sr;lal[ azc~ounts of sample are required LJsuaL), one gra:n of fluid wf!i s-ffice fbr an indbidual rneasurerr~ent Temperature control is easily achkeved and rr-aiutained. This aibws rneaningi~i, thermod},mamicaiiy significant data to be acqmred, it also provides a basis for replicafiSh ofindustrial temperature er.;virorrnents, n e e d e d for international comparison purposes. The cone and plate system is relatbc[y easy t : %,orate, provided basic instructior;s are follow,~sd. The system is we!! supported by sophisticated sofb,,vare ailc.v,,ing meanings interpretations of data to be made, perhaps with some underlying assunlptions being applied. The technique is particularb/ usefbi fhr !he measure-ment of race,very of structure, with time, as encountered with thfxotropic fidds s~.ch as highly str~.ctured iuks The technlque enables Lheo]ogicai properties to be reco:~ed at high shear rates, to some extent perHtitting repl~cation of shear regimes wiich arise on press or during high shear coating ( brushing ) operations. The technique is par ticula:d},,: useffi :br studying higher viscosi V materials, such as screen printing inks, high solids coatings and ofi%et inks

Disadvantagesof lhe cone end plele units Problen-~s of N.articie iarnrdng at the gap of the cone apex can arise, Therefore, this t}~e of set--up is not recorrkrriended fbr s~Lrnples of containing large par tides. Sample sPp rr-a), also be p~vavalent, at the sample wail interfbce. ~a Sam[No e.
333

T%!is a p p r o a c h is not usefis #or low viscosib~ liquid inks or :br irl~cS containing corrtpouents v,,hicn rn~y o v a p o rate to sc hue extent d u r i n g the c o u r s e of the m e a s u z e re_ant. In general, the cost of instrumentat:,on is relatively nigh. Honffever, :,f n:eamngz~i infer:nation c o n c e r n i n g the nature of the fluzds u n d e r irz',restigation is req,nired, and ff~e p e r s o n or g r o u p r~eeding s u c h iniorruation car, m e e t the c.ost, this is n o i a significant factor. (~enerally, in stud ies of the r h e o i o g i c a i p r o p e r t i e s , it p a y s to purct-~se the b e s t ,~squipr~9 that the b - d g e t ,,;vii,' allc:,~z in so c~oing, attention should b e given to the qua!:_%r of the software and to the b a c k - u p s e r v i c e avai!ab:iiq~ and cost.

Parallel plate approaches to rheological assessments F i g u r e 7 g i v e s a [.~ic.tdre c,f a h/[}k'.ai

f.~araiie! [,late

arrar 9

rnent Parallel p l a t e s can b e s u p p l i e d in a r a n g e os diarne ters, prevfdb_~g tlhe o p p o r t u n i t y s t u d y of fluids over a r a n g e of consistencies.

Figure 7: Schemoffrqrrongementof the p0roilel plate system

P~rollelplale measurementunit

e r t i e s of low viscosib; fluids, in a highly controlled and reproducLble ww~ in the OuetLe re,o d e . T~ie s y s t e m kp~,opJ~-sthe cot-trolled rotat-on of the r o s e r voir container, u n d e r spoor.lied condK.ons of terr'_perature end s h e a r ~e.gime s connbinatk;,ns c o m e in a r a n g e of sizes ~tnd geometr:~es, in atternpts at the replication os di[~Vsrent slhear r e g i m e s .

Advanlagesof |he 'bow end cyli.der (cup) approach LTse of ,c.,oncentrk~ ,cyi:~nders :~s of ps_rtic~:.iar use for the st~.dy of nr liquids i-,aving :~nter!r_,ed:~ate to lovr viscos:47~ <'baracteristk's Usua]i}~i rnJrirrial sarr~ple "osses are a ,fbature of the" approach, Little solvent e v a p o r a t i o n occurs, d u e to the sn~aN iiq u:.d-ah r~oundary in ad.d:.tion, rr, ost rheom_eters possess 8. s162 5or centre! os tke tensperature of tke cylinder, tl"_us e n s u r i n g that n]:z,irrkal solvent loss can b e rr.ade a :Feature of a s t u d y Use of a small gap in r~lation to c u p size a'b,,v s the e r e ation of an es constant s h e a r strak] r a t e

Disadva.tages of the 'bob' end r

(cup) approach

Tt iS possible that v;aii slip may occur ~:.nder certain . types of ,~near r~gJ,ne, 'I'be ff.o.jC.~ ..... COiIoerr- iAvc;bzes rocogniBor- of toe o n s e t of v4~il slip a n d of the g e n e r a l c h a r a c t e r i s t i c s oz~ wail slip, ',,~/r,en it occLlrs, v,/a]l si~p g i v e s r i s e to e r r o n e o u s p s u i t s a n d i n t e r p r e t a

Figure 8: $~hemoticrepresentoff~nof o (ono~ntrk cylindersystemin the Odette moqJe

•

---] :::i:i{.:.::::~ I~k s~mple

i

!

00,+~0%b%0s . . . . . ~+%\Ro+%o\~P,oo%ok~,~\~ 00\0%0k%~\,~ \ ~\ \ %-.%0 ".\\'> ~ "i G \ \ " \ " \ % ' b " \ ".\~\ "\% 0% \ ,.\ '.~\\ 0% 0 \"%" \ \ " %,.'.~%

~se pBte

Advantageso[ the parallel plate arrangement Tke parallel plate :.s ,caRd to b e s than the c o n e a.'-,
III

9

/

'bob'

Fluid /Reserv0ir

Disadvantagesof the parallel plate arrangemen| V.~ryh:g s h e a r strain rates can, o c c u r w:r!k i n c r e a s e d di,c.t a n c e fro:m the p l a t e c e n t r e (ie non-unffbrm s h e a r rate). V'/a!l siip rnuy arise, ~a SaH~p!e excl]-sion tK)n-i the rneasuzeNAer, t zoz~e, Call occur,

[--

Variablespeedmotor --"-7

Concentric cylinder (cup) Figure a. gives . a . sci~e:rc~at:x~ . a-rre~n~q~-~m_ent~_ ... o!" a concentric c y l i n d e r (c rap.) systeK1 d e s i g n e d fc,r ,~< ~,~.~.,.~, . . . . ..,.,-tk,~.~.~iqevv p r o p

334

Surfece Coati.gs Interna|ionul 1997 (7)

tions, u n l e s s its p r e s e n c e is r e c o g n i s e d a n d a c t e d upor< T e m p e r a t u r e control thrc, ughout the sacnNe is not e s p e cia!l}~ satisf)~ctory !L m a y take p K , i o n g e d p e r i o d s of time i',,r the reiafivo O, large s a r r p l e to r e a c h the m e a s u r e r n e n t temperature. This fs a particular nui,-ance WLen studies of the influence of the t e m p e r a t u r e of the fluid on the flow p r o p e r t i e s are b e i n g monitored. W h e r e this point b e r e f t . a s significar,.t is in studies of the activation e n e r ~ of hey< In general, relatlve4~ large a m o u n t s of ink are r e q u i r e d for n l e a s ~/rernent

Theorelicol aspeclsof flow during rheornelrical measuremenls C.ontKs ,stress r n e e r n e t e r s (CISR) are a d v a n t a g e o u s v.~hen e x a m i n i n g s~mf)~ce coa@ng si,'sterrJs (as o p p o s e d to the rnore traditional contK.iied s h e a r rate system). They allow the calculation of 'yield sW~sses' i'.~ a viscoplasfic system, H o w o v o r i the e x i s t e n c e of this p a r a r n e t e r fs a mat tar of d e b a t e in iiterature .... it a p p e a r s ~o d e p e n d on the field of study whether o n e believ<'s that the p h e n o m e n o ~ of yield stress exists. The OSR also ailov,,s a user ko e~arn Jne a sample, without b r e a k d e w n of the structure of the iiquid fbrrnuia!ion in a s e r i e s of high
For p ate a n d c o n e operations, automatic g a p setting is a fc}ature of r n o d e r n instrurne-0tatior:. This Dacilitates e a s e and reproducibiiiW of m . e a s u r e m e n t s For identical samples, Searle a n d Gouette tT~:e v~scornetens g~ve the s a m e values of absolute viscosit}. • are d e s i g n e d to .~unction with eraphasis on o n e of ~4~o o p t b n s 17mrcontrol, ,narpe[lr conx 9 os the a p p l i e d stress or control of the app],ed s h e a r strain rate. Each a p p r o a c h has its associated features, Both are c a p a b l e of providing viscesi%i values u n d e r high 8 con, co!led conditions. The b l b w l n g d i s c u s s i o n is a p p r o p r i a t e :br an instrurnent of the Searie ~
l)alapresenlolionforfluidsyslemsexperiencing rheoiogicc|lmeosuremenl '~nstr.m~ients n:Jvc a c a p a L i i i % to register the rsJag~Jit.~de ~;+~ an a p p l i e d ,shear stress or rs s h e a r strsir~ rate, wid:Jin a ra~,ge t,v.i.<'.t~ is l i m i t e d ar-d v,,ithm a s'cale es sensifiv]%; values, 'lhe size of the r n e a s u r e m e n t geometry, which gcv-e r n s the ars-ount of fluid b e i u g a s s e s s e d , r' - s t reSect this sensitNity, i e i e v a n t i n b r @ a t i o n concer niug the r n e a s - r e rr
" " ~oy The . . . . . f'. ~-:W~.~-,reK, e.r.t.i.e s ~ o - a ~• ~P_iay 'L,e s~o,wn graprs177 p b t t i n g a ,~heogrars- to show a rheoiogical relationship. '!%
Figure eT:Typkel [bw mires [~r represenleHve fluid syslems 7iscopl~slicsyslel

Thoseoperolin!lon lheprincipleof Couelle Here. the m e a s u r e m e n t geor:el:ry r e m a i n s static, while the ouker c y l i n d e r acting as fhe sa~nple reservoir cs ~b~c ]ng the S l i d ill tr~e g a p to flow The resistance to flow is the viscosi%,, as m e a s u r e d v~,ithin the s e n s i n g system. Couette Sipe viscornetexs ~.re considerc.~d to b e g e n e r a l l y rr~ore eta ]Die wkh rest.act to c e n t r b e t a k forces.

Surfnce Coelin~ In|ernationul I gg7 (7)

y~tem

%

~7siem

Those openiting on the principleof Settle H e r e the i n n e r c y l i n d e r (c,r the c o n e o f i-,~e p l a t e / c o n e s1~s-tern) rotates at a de@ned rotational s p e e d , wbi!e the s~rnple r e s e r v o k (or b a s e plate) r e m a i n s static. Ur:is is the most cornmor~ option in r h e o m e t e r d e s i g n since control of the t e m p e r a t u r e is m o r e easily achieved.

I~eudoplastk system

~;"Shear rate (s 1) J-\'~", ~_'L . . . ua~i"< . . . . . . . ~),, date. m a y be ~obkted as the aoparen,~viscosi%i @]) against ,shear strain rate (9}', as show:0 in Figure !0, m~gure,~ ...... .~oand i0 clearly s.how that the b e h a v i o u r exhibited b,; the systep;.s that could b e ex~beriencecl can b e v e r y divers~. E x a m p l e s OI
Ne onian flow T+
335

c o n s e q u e n c e of this i n c r e a s e d slip is a reduction in the viscosit~

IFigure 1O: Typk~l vis(~)s[typrofiles Viscoplastksystem I)[btent system Newt~n[~nsystem

Pseudoplastks y s ~ ~i' Shearrate [s-1] rate) may b e taken, and r a t o e d to gr,,'e a constant value of 1-1 (viscosity) ie it is an ideal fluid b e c a u s e it o b e y s Newton's i~w ofviscosfzr perfectly, SirrJ.iar!y, if the viscosity profile is inspected, 11 remains constant
Dile|ency it ~s pc, ssiblo t,t, enc'.ounter sa:r~,L,ies that incroase tneir vis cosi%~ as the shear strain rate is increased, ' ~ i s type of flow is called dNatent flow (or shear thK:'.kening). Di!atent flow can c a u s e se',&'re problen~s in sortie k~dustrial processes. Fortunately it is qsi!e rare, Systems exhibiting this V p e of Sow character tend to b e concentrated suspensions aris ing w h e n solK! r>articles are mixed wlt?~ cor:~pc,site selu!ions or dispersions containing poiyrneric film-fe:rn~ers, V',fnen at roost, the continuous rnediurn is present to the extent that the particles are just fi:i~r wetted and lubricated,
N0n-itewl0nien flo

Plasticityund viscoplasticily

The pn@ority c.f 'useful' fluids <-xlr:er!~er,,.ced, certal-eXy those e.
~brpe substar'ces do not begin to flc&~,Ju~iess sorfle tnr~esb old value of she~r is app]ied to them, ~]xarnples :adst tJltir~,ate<; the significance of an idealiseo yield stress is doper:dent u p o n the pro, duct u n d e r scrutiny.

The c a u s e of de'viation trc,rn Nevstonian bobs\dour can b e d u e to chemical interac.tions be~s~een c o m p o n e n t s and~or d u e to r~echan, ca! p h e n o m e n a . The amount of e n e r g y that musi be applied to a sarr.ple to achieve nlovenkent is d e p e n d e n t u p o n the shape, size, d e g r e e of entanglement and interactions e r a n u m b e r of ;qon-syrnK]etrical c o m p o nents for nl.ing the ink that rr:ust b e pnade to pass e a c h other fbr fic,,vv to occur. At another rate of shear, the alignment of these c o m p o n e n t s could b e dff~brent causing the develop rnenL of an apparent viscosit),. '!'he non syrr, rnetHcal corr~ ponents mvoh;ed include the pob/mer(s) a-qd the pigment(s) u s e d to fbrrr, the ink,

_~_s u b s t a n c e is said to e.)~hN.)it plastic flow if the flov,r pK~'flle sncws a straight line o n c e the 'yield' value is e x c e e d e d }~ ~naterial is said to poss~sss viscopbJstic flo,~' beh~',.do~r if the !or,7 profile shews a c u r v e d re!ationsh:.p, Both are rat
P e d0pla fidty

Thi•

\,%rher~ tire s h e a r strain r~'te e x p e r i e n c e d by a s sample J.s ir:creased, one m a y o b s e r v e a viscosity drop. This %rpe of fiovr is t e r m e d pseudopiastic flow (or shear-thinning), It is this proper%/ that would b e particularly desirable to have within a responsive ink ior~nulation as used in a ball p e n ink or in printing processes, as this could f)~cilitate m e r e e(~bcdve deposk~on. Such beha~doo, r is exhibited by er~uisions, suspensions and dispersions, The effect is d u e to e n t a n g l e m e n t t?pe interactions. At rest, the systen< has structure d u e to e-qtang!en~ent and thus a p p e a r s to ha,re a h~gh viscos]%,, i\& the shear strain rate is increased, the cor~ponents tn the s y s t e m can orientate, str;-tch and disentangle tlhernsei~,~es, allowing molecules and particles easier s l i p p a g e past one another. The

336

e.d rhe0pe•

'!%ixetroF.ic effects can kave an irnportant bearing on the success or faHuro of a surgJce coatK~g, A !hkc, trc~pic s jst~J,u is one tkat e~xk:ibit3 structure that can be k.roken d<,~;r through stlrrrrlg (skear thinning) b u t u!Do-rl cessa!ior~ of stirr;ng, the viscc'siE~ increases slowly '?his wc,~uPJLb e an ur:c~<~ sirabie %ature fc.r a writlng it, k, which is e x p e c t e d to stop Sowing when the consuH~er <'.eases writing but a desirat~qe =eature o. a paint, ,s~ihere controlled flc,\a, out is required.

]~,eop<§215 the opposite of th,p.otropy,vvhere the viscosRy of a fluid increases upon shearing,

Osdllat0ry rhe0metry Olden, the r
Surface Coetings In]ereetionul 1997 (7)

above, examining the apparent viscosib~ across a range of s h e a r strain rates ~e ur~der steady shear condiLions. Internal structure or ,nteracfions within the rnater,a! under exarninat,on ('u~crostr ucture') v.,,iiib e altered ~n m e a s u r i n g the sample.

ear viscoelastic region, the empirically d e t e r m i n e d Cox Merz Rule is applicable, v.~here the va!ue of shear viscus!% is ,denticai to the value o ~ < e cornpicx visc.osit%,, pro-;ided the values of the shear strain rate and angular ve!oci V are identical. ~..S.nonymous. (a). 1989). Th,s gbres

With m o d e r n k~str.rr,entation, it ,s possible to ir~'vestigate the v, scoeiasfic character of s u b s t a n c e u n d e r conditions of vet). b w shear, lead,ng to an appreciation of hov,,~ elastic (solid). and ho~v v~sc.ous (fluid) a sarr4'le ,s. To f%cfl,tate this. dynamic m e a s u r e m e n t of the material is m a d e by a p p ) ' i n g a smusoidal!,/variable stress (or strain) and rnea suring the resultant strain (or stress), wh.le rr-on.toring the p h a s e diff~_-rence b e t w e e n the input and o%cut signals.

q (s : q* .%:})w h e n y (i/s) -- @(rad,'s)

At its s,mpiest, a material can b e s u b j e c t e d to a systematlcaKy .ncreased s-nusoidaily-appiied stress (an 'amplitude sv,,cep'). The resulting strain is c a l c d a t e d at e a c h of the stresses, and. if eonsta.nt, tlhe m_aterial can b e sazd to beha\,e in a viscoelastic rr.anner, and to b e stable. Such tests ha~e b e e n u s e d succ.essf~-ky to determine the stab,] ~, t7 of ink fbrmulat,ons." w h e r e the best d i s p e r s e d and most stable ink was tha! v,,,,th the greatest structKe. If the material u n d e r study is a perfect solid, the p h a s e d f f fL~snce beb~.oen the two signa!s will b e 0 ~ and if a p e r f e c t fluid. 90 ~ The p h a s e diff~erence for a viscoe!ast,c rnater,al will of c o . r s e he sorr~ewhere be%',,een U~e two. and rn;c,~ b e u s e d to provide --r tk.ez ,n-brrr-atbr. about the structure of a sample, but only if the linear viscoelastic region ,s ink, a!iy established, as out!,ned above. Information on structure is g~_tthered by performing a f~e-q~.enct~ s w e e p to derive fi~rther inlormat, on about the sample. Tris apprc.ach has b e e n successfully applied to ink fornmiafio:zs. ~ In ark osc,l!ation exper,:caer:t, the str~-m wave lags beh, nd the s!ress ,.,~av<~ b y the p h a s e a~gle (6). The strain wave applied has a strain arrpiRude. ~ and a stress arr~'pi,tude. @~ The stra,n wawe m a y b e used to calculate the storage rr.odulus. (,S'). the quantity of strain ener.~7 reversibly stored ,n the subs:ance, and the loss modulus. (G"). the ener<<,; irreve'rsibiy lost to the surroundings: These can be represented as C'

. ~ cos~ ar.d C"

. sin&

The values of G' and G" may b e used to c a ] c u i a t e a loss factor. (ta'.t ~). the ratio b e t w e e n the ener95r store'd and e n e r g y lost Thus. tan 5 = G"/G' It is possible to der:_ve n u m e r o u s other fL.nctions to assist the description e r a sample. Llbese ars generally obtained through soft;Tare p a c k a g e s a v a ! a b ! e fbr post--processing of the p h a s e data collected if-urn the r h e o m e t e r as the p r o c e s s inw:,ives cornpio.'.' nlatherr-atics: Such functions include !he c o m p l e x m o d d u s . C*. and cornpiex dynamic viscost,/, q*. These k..ncfions are rnathe:r~atical represents tions of the shear ~nod,Jus and v~scosity ~ e s p e c t v o c / a s the sum of a 'real' and 'imaginary' p a r t of the rnanpuiation. The var,ation of the values C'. C" and '~1~ as a result of appi,ed frequency prey, des the m.echar:ical 'spectrup:_.' ]'[-lese ,.~.d~ c t a ,i .; d, z• <19.7~7/~,r~-R"r~'~,• l.,o..r~
Serfe~e Ceefings Inferne|ionel ] ?97 (7)

Th.e rule of Gc.x and Merz appl, es only when mechanical interact, errs w, thin fhe molecular structure o f t h e so.bstance u n d e r test are Lespon&ble fDr the v, scos,% values. Other inte~act, ons such as h y d r o g e n b o n d i n g can c a u s e !ar~e de-,hfions fK;m trkis behaviour, providing fLrther charac ter,st~c inf:;r~nat~on to the rheoiog~st.

r]q~/USi the m e s s . f o m e n t of the rheoLoo~y of a coating 2,rmu iatior~, by steady shear and/or osc;]iator? shoal t e c h n i q . e s can pr.ov~de details of the fiov~J character u n d e r a wide ~ange of conditions.

Ma|hema|ical m0delling e[ theological behavi0ur. in rnak,ng comparisons/~etween data it is u s e g i to employ a model to de._.'crlbe the rrx~'ok, g:.cal beLa',~k:ur of samples :~tuoieo.. 7r
~It.roe of the m o r e p o p u l a r (and uselu!) eJ~arnpies u s e d to d e s c r i b e shear-.thinnmg fluids are the p o w e r law m o d e l of Ostwaid.-de 'Tt%_e].e. the S,sko m o d e l ar:d the Cross m o d e l 7he basis of these m o d e l s ,s shown below. rc'v.,er lay',.:

I] = k'~~

Shsko:

"q

Cross:

%';-q : ( k 9 ~ "r[---~.

T < +k'.f'~

Bar nes et al r', have shown that u n s p e o f i e d fbr mulations c an be rr-odei!ed us,ng the p o w e r !a,s~ mode', as b o r n e out b y prac'.tical e x p e r i e n c e during ~esearch.

lhe concept0[ 10ckiness' in the de~felopmeJ:,t and applicatlo.u of ink ibrmulatio.us, partlcularbF those emplo~Fed m the more c o r ~ n t , o n a i app'ication areas such as lithography, the ccncept of'tack' is vet. F irr-portarA Tack rrL~y be some,,~L'~Ltk;,oso~y definoo as the Istickiness' o f a s . b s t a n c e . '~

"!\~ck is of great prac@cal concern., o:r,gmai]y rr.eas.red qual,tat,vely b y s m e a r i n g a ill-< of approprlate ink onto a glass by a finger, and assesskig the pu!ling ~-sistance when .*he finger was sharp!y tapped. A nunlber of instru <
337

sassing a d e g r e e of tack have b e e n found to b e advanta g e o u s in letterpress (slr~arp print) and off;set iithograpky ( d e a n printing), although e x c e s s k e tackiness can c a u s e m,o:~e pr.obieu-s than it so~ves through picking of the sub st[ate and difficulties in transiel. The probiern was attacked in some detail using a parallel plate visc.om, eter, a 'Tackrneter' :~ Green considered that the viscosky the yield value, the surgice tension, adhesion, and cohesion •177177177162 i~.'iay a role in the ma<:ifbstation ,_"f tack. ExperhY~entaion showed that tack was prirr~ar]|y due to vis cesky and yield value. Measurement of inks, tb_eugh reta-fienal viscerr, e!ry at high s p e e d s typical of app!icat~on (abo,,~e any questionable 'yield' value), s u g g e s t e d that tack was sernehow related to the w~scosity of the mk at tha: speed. The p h e n o m e n o n of tack has b e e n the sub~ect of i:<:terest for s o m e thy'.e. ~,n Generally it is r o c o g n i s e d that tack is related to viscosRy in a m a n n e r not %setelucidated. Equipment for rneasuNng tack behaviour has improved a great deal, (ICT T~ckoscooe and toe ~e*'ate~'~-...... ~ ..... ~'} as has the -ndeBtandir~g of the nature of tack and its con s e q u e n c e s for the behavlour of composite fluids, it has ~1~ ~ shear ',ris b e e n fbund that, iu rheo[oqicai anal)~ses, ~[~ cosi%~ rueasurernents do not gi-,'o a c o m p l e t e characteNsa tion of an ink. 'Stringiness' has b e e n reported, to b e d~.e to a sample having a high extensional viscosity s ......

The correct formulation of a reaper:age ink formulat:.on, so that :_t p o s s e s s e s the required d e g r e e of tackiness, pro-d u c e s cleaner irnages and less surfhce heterogenelty ceupied with strenger a p p e a r a n c e than would an 'under-tacky', cors,er~_tional printing ink or an 'c;vertacbf conventional printing ink. This is b e c a u s e the correct tack level ensures Lhe better transfer of the ink during distributior: to print, if this better transf:er was achieved through the inclusion e r a random-coil poiyrner, it is possible that, despite p o s s e s s i n g a d v a n t a g e o u s shear-thnmmg abilities (a!fgnment of p o l y m e r chains resulting k: the a p p a r e n t v i s c o s R y 1] d r o p p i n g with increasing shear strata rate, ~,), this randorn-coi! p o l y m e r could also b e tensfon-thk~kening due to elongation of the chain on stretching, (entangien~.ent of chains c a u s i n g resfstance to a!fgnn-_,erit on pulling results in the extensional %scos:4y "qE i-qcreasg_lg with extensional s h e a r strain rate ~_.)c a u s i n g a d e g r e e of tackiness, as fiL.strated in Figure 1 i.

Figure ]1: Shem-lh[nning er~d p~ssib[e fensbn4hkken[ng ~r randem c~.~[[pdymer Shearing

~P random ceil

[•

q .

Shear . thi,m].ng

km an "ri I thickening/

Formationo[ the ink fiJm The rheo!ogy of the i!< plays all important role in_ ensuring theft tr~e ink can be applied to a substrata successfuil~/: it has a part to play in ensuring t h < the '~',retfilm can dry or cure to a reliable solid film state, capable of fi;!fillir~,g its purpose, in the case of wrki-qg ink fbrrr, uiations, this is to pro,,ffde a strongly ce|our~d, opaque, conin~eus Line, e~sui!ab]e quail b~ to safis(%, d e m a n d s for correct hue, [me qua!k? and in terms of fastness to light, solvents, tarrperfng and the like. R,r printipg irLks, this is to ~ro,v[de g o o d densiti~ g,oc,d u i f o r "' ~-- :~' -- the -~,r~i-~es gloss %v~-i a-nS sc.~c,n. The cheic'.e of pigment can be
Sagging,dumping and levelling : o a r n i e y Whittingsta]l ~, has c'.orJsidered toe irr~'F,ortduce o f ~heo!og}~ in ensuring tne correct levelling b e h a v b u r o< paints. This is b e c a u s e the surf~ces to be painted can b e the most unR,rgk,'ing, ,~equk:mg the use of what might b e the rnost unforghdng of surface coaffngs. Gravhy-drg;en eIlects s ~ x i as s a g g i n g and slumping of the coaEng, through incorrect levelling, can c a u s e Lmsight!y brushmark retention in the fiirn after it has dried if the r h e o ! o g y is not correct. Of marcs irnportance, certainly to ink& is leveLling. Sagging, levelling and slumping are dri,,en parfiai!y by gravR7; but also b y surfhce tension effects as the,/ are influenced b y s p r e a d i n g p h e n o m e n a aud g o v e r n e d by the apparent vie cosi%7 of the fc'rrr,uiation..A certain d e g r e e of !eveiifng is clearij desirable to assist ~eliab!e film' ~brr:~aJen. However, ie~,~eiiing should not b e so :rrmch that the definitk:~n of the ' p i n t ' is alk,wed to ,ueteriorate: Levelling and spreading of a wet ink fihn are ilbstrated in Figure 12. in pa, Ex systems, p r o b l e m s arising from difficulties in levelling are s e e n in such effects as runs, o r a n g e p e e l del}Jcts and p o o r (:,retail surface coverage,

Figure 12: Levelling d a surface co~fing after ~991icalien

Figure ] 2 ~epresents a coating that has iust b e e n applied b a substrata. The coating &hc,ws r i d g e s which c o r r e s p o n d to the application marks. Previded that the flow character of the coating is such that ~t v.,,ill a i b w the formulation to flow surfhce tension effects and interracial events, together with gravitational effects, c o u p i e d vith angular oriemation e~Lec!s will c a u s e the film. to s p r e a d and level to form a film. ~-'a~lure to achie,,
PVP d e n o t e s poiy(vinyi pyrroLidene), used as a S m f b K" ing p o l y m e r in the contin4o~.s rnedh,.m.

S k r i a r representations can be m a d e fbr spray depositk)n, ibr ink-is! deposition, for dip d e p o s f t o n , for screen deposition and fk,r e a c h of the m a n , / m e t h o d s of appl)4ug corr~, posite fluids to a solid substrata.

Clearly, the type of polymer(s) selected and the quantities included in forrrl.ulations, n e e d to b e careffily controlled and b a l a n c e d if optimurn peri~;rrnance is to b e ach,eved.

L!i• "J.%e f!cmr proP, erties of r f'Ju~d'-' :-~ r,; the nature of the filrnof f.4id created at the surface or interface 'R~,us, the rheoiogica! properties, in turn, have an effect ou

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Surface Coatings lnlema|ionul 1997 (7)

other events which fb!low depositiou. T h e s e include wet tmg, filr_rl forma.t.on and film qua
References ] O-'ut'%r,e. ]'TI ~.r-d bin, r' i P%,ys,cal C h e m i c a " %soect..4 of "),fsTners ,~pp'icaEor-s, Sur+%ce C'.o~ings ! u v i e w s , O.] ~ " TC~r~\ 0.r,c~" C - o b u r Gnenli.sts' rp,_SSC, Clatlon. ,,obL~r '.- ). .,.O .. ~.' , Q 9o,.,,~, 1.5

}L, r~'nr'.'rr' ]@@A

2 Bell, D, E u r o p e a n Coatings journal, 802, i992. 8 Barnes, HA, D i s p e r s b n .K~eoiogy 1980, Royal Socfety of Ghemfstryl London, i 981.

Professional Qualifications

4 Schramrn. G, introd-ct, en to PracticailR~.eoio9% Haake Instruments, H a a k e Grr~b}i, D T$00 Karlsr uhe 4 i, r'~'~cl/~

104~,

9

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5 Battles ]:~8%89 'Nr,~l [g' ar;d V'./'alters. I.~,p~,i l• !o Rheo|o,p~i Nl.~e/erl Oxfbrd 1989. 6 Gowie,_TMC, Pdy:mers: O h e n i s t r y and PLysics of M o d e r n Materials, ./r.,terte.zt Boo,](~. Bucks, 1978 T Athey RD, E u r o p e a n Coat~ngsjournal, 3, p p • 1992

O

1~

Do you want to gain professional qualifications relevant to your employment?

8 Biorr., BE, .S_merican ink Maker, 69, p p 53--65, i99!. 9 Cultrone, L. The C-oncept of Kkeoior 'I[zo:.zJde SLd, PUbiiC'8~/(.)f/i B,]!k~gharr, Clevuiand, 1980.

you want to be elected to Q anDo International Register of

10 barnes, ~js~, and Wdlters, K, Rheologk:a Acta, ~4, p p 82.8-826, ~9do ~ ' ~U, l] 9 1995

']-: PoSrners and 9

k

recognised surface coatings specialists?

iburnai, 1.8~, p 84

] ?, H a r t b r d , T and Chas~-), K, ~sr~er,can ink Makeri p p 42-49, 1994. 18 Rob:~nson G, K~eoio97 p p 91, 92---i01, 199 i. 14 Pavim, MS andYhdo, KJ~.,.Smerican ink Maker, p p i6 28, •

O

Are you employed in a position of responsibility within the surface coatings industry?

O

Do you hold an academic qualification relevant to the surface coating technology?

15 ,_,~<~...r ~ ~,-,.,~,:.,.~.~-:~,in Printing ink ~4.s~.iai Leach. RN., (Ed)., .SP_~ep._r;.x.t,London p p 688-69_7, ! 988. ] 6 Green. H, Industrial ~ i e o i o g y and ptheolog, cal

Structures, C'h~;smaz~' arid ;~/,.4/!, London, i 949. 1? C.;ar.Li!-.L.~ ~' A. "Fhe' ie-~=,~,~.~.,~.:;...,.-."*>,a-~a -~,.... C-haracterisatk',n c;f Stabilfsafion of Bronze Pc~r162 Dfspersbns, PhD. Thesis, Departrr~ent of Golou,: Chem:~stry Th~s Unb/ersfty of Leeds, L e e d s LS2 9.y!t 18 Chr,sfie, R, Pigments: S?_uctures and Synthetic P"ocedures, Surface Coatinqs Ray,eves, ,.~"-':~and

If you answer yes to any of these questions, you could be eligible for Professional Membership of the Oil & Colour Chemists' Association.

99 ~,3, 19 !--'oarnie7 v~drittingh~21, i" Surfi:~ce Ooat, ngs international, jOOffk\, ~4, p p 360--368,199 i. II

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7;:ii:i 7iF::~OUI

M~RKE~ !i

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S~rFece Colllin!p Inlernalien~il 1el# 1Ill

: ):.:.:[:~;,

Please contact the International Membership Secretary Tel +44 (0) 181 908 1086; Fax +44 (0) 181 908 1219', E-Mail Member-sec @occa.org.u k.

339