Rotating vane rheometry—areview

J. Non-Newtonian Fluid Mech. 98 (2001) 1–14

Review

Rotating vane rheometry — a review

Howard Anthony Barnesa,∗, Quoc Dzuy Nguyenba Unilever Research Port Sunlight, Port Sunlight, Bebington, Wirral, Merseyside CH63 3JW, UK

b Department of Chemical Engineering, University of Adelaide, SA 5005, Australia

Received 30 October 2000; received in revised form 19 December 2000

Abstract

The use of rotating vane geometries for the measurement of the flow properties of very non-Newtonian liquids hasbecome increasingly popular over the last 20 years. Originally, these geometries were used to measure the apparentyield stresses of inorganic dispersions, but have more recently been used to measure other rheological parametersalso. These include the low-strain modulus and the steady-state flow-curves of structured liquids. The particularadvantages of the vane geometry are its simplicity of fabrication, ease of cleaning and more than anything else,its elimination of serious wall-slip effects. The development of the vane technique and the theory to go with it,together with its use in various areas are described, where these areas include inorganic colloidal dispersions, foods,bioengineering fermentation broths, etc. © 2001 Elsevier Science B.V. All rights reserved.

Keywords:Vane; Shear thinning; Yield stress

1. Introduction

The vane geometry, in its various forms has grown in popularity as a simple but effective meansof measuring the properties of non-Newtonian fluids that would otherwise display large slip effects atsmooth walls. It also offers a way of introducing the testing element — a thin-bladed vane- into a structuredliquid with the minimum amount of disturbance to the sample, making it very suitable for materials suchas clay suspensions, muds and other gelled liquids. With the introduction of an outer wall sometimesroughened or otherwise suitably modified, the vane geometry is also very useful as a general means ofmeasuring the viscosity of difficult liquids, especially when combined with the latest controlled-stressrheometers.

∗ Corresponding author. Tel.:+44-151-641-3529; fax:+44-151-641-1829.E-mail address:[email protected] (H.A. Barnes).

0377-0257/01/$ – see front matter © 2001 Elsevier Science B.V. All rights reserved.PII: S0377-0257(01)00095-7

2 H.A. Barnes, Q.D. Nguyen / J. Non-Newtonian Fluid Mech. 98 (2001) 1–14

2. History

One of the earliest uses of the vane geometry may be traced back to 1936 when Russel employed a‘small glass vane’ to study the coagulation of sodium clay gels [1]. His primary reason for using the vanegeometry instead of the cylinder of a Schwedoff-Hatschek viscometer for shearing the suspension was toeliminate ‘the possibility of slipping’. Then a vane geometry has been available for the Haake viscometer(Gebrueder Haake, Karlsruhe, Germany) since 1955 as a variant of their solid cylindrical SV rotor, seeFig. 1. It is known as the ‘star-shaped’ FL rotor, where the ‘FL’ nomenclature derives from the Germanword ‘flügel’ which can be translated as ‘wings’ or ‘vanes’. This six-bladed vane was, according to thecompany, introduced to overcome slip problems and to measure yield stress. A very old manual for theoriginal Rotovisco 1 (RV1) viscometer recommends the use of the vane ‘for coarse, disperse systems; ifslippage is expected with smooth rotors and for very thixotropic fluids’. The latest manual for the RV1model states that ‘yield points are determined from the peaks of a shear-stress/time curve’, when start-upexperiments are performed (see later discussion on precise definition of yield-stress in this situation).Also from Fig. 1, we see, from a practical point of view, how much easier it is to fabricate a vane toprevent slipping, compared with the carefully ribbed cylinder shown next to it, which is another means ofeliminating the slip problem. Certain Brookfield laboratory and on-line viscometers have also embodiedvane-like geometries for many years, especially for the measurement of paper pulp and paint.

However, over the last 20 years, the vane geometry has been taken up more enthusiastically than everbefore. Its renaissance started in Australia in the early 1980s when one of us (QDN) was a research studentof David Boger’s at the Chemical Engineering Department at Monash University in Melbourne, trying tomeasure the flow properties of a ‘red-mud’ (bauxite waste) filter-cake produced by the Alcoa companyof Australia. Since a mud filter-cake looks like a piece of wet clay, it was thought that there must be

Fig. 1. Haake viscometer SV geometries, showing the six-bladed vane (SV2FL), and the corresponding serrated (SV2P) andsmooth (SV2) cylinders.

H.A. Barnes, Q.D. Nguyen / J. Non-Newtonian Fluid Mech. 98 (2001) 1–14 3

some existing techniques in soil mechanics for determining ‘strength’. A colleague working in the areaof civil engineering directed attention to several such methods, which included the vane, the penetratingcone, compression and shear cells, etc., which were all used to determine the shear strength of soil. Allthese were tried, but it was found that the vane method was the simplest to use and most applicable in arheological context [2].

The use of the vane was developed further in Australia by Nguyen and Boger [3,4], especially for thepractical measurement of the yield stress of concentrated suspensions, with Keentok [5] concerned withthe theoretical aspects. Its use soon spread to other areas, especially for what we might call ‘structuredliquids’, i.e. drilling muds, cements and certain food systems — see below for a more extensive listing.Indeed, for many, the vane has now become the universal geometry of choice for ‘yield-stress’ (i.e. veryshear-thinning liquids) fluids, being easy to manufacture to reasonable tolerances, and simple to clean,see for instance [6].

3. Theory and technique development

A logical though not an historical progression in the use of the vane is first for the measurement ofthe modulus of a structured liquid or the viscosity of a Newtonian liquid, then to measure yield stressand finally steady-state flow-curves. We will review the development of theory and practice in thatorder.

3.1. The modulus of linear elastic solids and the viscosity of Newtonian liquids

Sherwood and Meeten [7] used complex variable techniques to calculate the torqueM on an infinitelylong two-bladed vane. They then computed the torque on a series ofN-bladed vanes of finite length bymeans of boundary-integral techniques, first as a function of linear elastic modulus of a linear elastic solidit was immersed in, and then — since the mathematical formulation is very similar — the torque due to(Newtonian) viscosity in creeping flow in an infinite expanse of (Newtonian) liquid. They also predictedthe effect of the ends of the vane on the torque. We may summarise their results as follows for relativelylong blades (l/a > 3) wherel is the blade length anda the radius of the circumscribing circle formed bythe ends of the blades)

_

M = A_

l + B, (1)

where_

M is theM/2πηa3Ω and_

l is thel/a. A andB are constants depending on the number of blades,as shown below

N Value ofA Value ofB

2 1 0.663 1.33 1.004 1.51 1.26 1.66 1.568 1.75 1.71


Fig. 2. Sherwood and Meeten’s [7] computed values ofB, the end-correction parameter, compared with the empirical expressionB = 2.75− 3/

√N .

They give the value ofA asA = 2−2/N . An infinite number of blades equates to a solid cylinder, and

of course gives the expected result that_

M = 2_

l for rotation of a solid cylinder in an unbounded fluid.With regard toB, Sherwood and Meeten then stated that it is a function ofN, but got no further. However,

it can be shown that the functionB = 2.75− 3/√

N gives quite a good fit to the data for their computedresults over the range of two to four, six and eight-blades, see Fig. 2.

These formulae indicate that for a four-bladed vane,A equals 1.5, andB equals 1.25. If we use a shortvane with say with a value ofl/a of 2, then the geometric constant would be 4.25. If we had assumed thatwe were dealing with a cylinder with no end effect, then we would have an equivalent value of 4, thus,giving an error of just less than 6% if we had used the long cylinder formula instead. Indeed if we wereto use a vane geometry with anl/a ratio of 1.88, we would have no error at all if we assumed that thevane was a cylinder with no end effect!

Their predictions worked very well when tested against experimental results for a Newtonian liquidand a range of vanes covered by the theory, giving results to within a few percent of the measured values,see also [8]. Of course the same theory would work for the response of a vane in an elastic solid, with therotation (in radians) replacing the rotation rate (in rad/s) and the shear modulus replacing the viscosity,if we make the reasonable assumption that the Poisson’s ratio is equal to 1/2.

The shear elasticity and yield strain were measured by Alderman, Meeten and Sherwood [9] for ben-tonite suspensions, which compared favourably with the values obtained with those using porous cylindersand a thin disc. Apart from the eight-bladed vane, the two to four and six-bladed versions gave sensiblythe same values for the modulus, and these agreed well with measurements using concentric cylinders[9]. The problems they encountered with the eight-bladed vane were attributed to the blade thickness, theeffect of which is of course accentuated. We have not considered the effect of blade thickness elsewhere,since usually it does not present a problem, apart from theoretical calculations, where an infinitely thinblade produces a singularity in the calculations. This can be overcome numerically to some extent, butthe introduction of a finite though modest thickness will also tend to elevate the problem.

3.2. Use of the vane geometry to measure yield stress

One problem that makes this area very difficult is the precise definition of yield stress (that is accepting,for the sake of argument that there is such an entity as yield stress, see [10,11]). In some cases, it appears


to be taken as the departure from linearity of the stress response in a plastic solid as the strain is increased,while in other cases it is taken as the cessation of flow in a structured liquid as the stress is decreased.Others take it as the maximum stress between these two, obviously, real materials will respond to theapplication of different stress or strain histories in different ways, and diverse results could ensue. Thisis certainly true if different geometries with different stress and strain histories are used, see Nguyen andBoger [4,13]. However, this point is outside the scope of this paper, but for a comprehensive discussionof the definition of yield stress and measurement of this property see the reviews by Barnes [11,12] andNguyen and Boger [13], see also Yoshimura et al. [14].

We will simply assume that a yield stress—, however defined — can be measured, and we are onlyinterested in how this value can be measured using a vane-like geometry.

With the vane method, the usual simple formula employed for calculating the yield stress is derivedon the basis that the yield stress acts uniformly on the side and ends of an equivalent fluid cylinderformed when a vane is rotated [3,5]. The total torque on the sides of an equivalent cylinder is 2πσ0la2

and 4πσ0a3/3 on its ends. The yield stress would then be given by

σ0 = M

2πa3

(l

a+ 2

3

)−1

(2)

Out of interest, if we compare Eq. (2) for a yield-stress fluid with Sherwood and Meeten’s correspondingtheory for a Newtonian liquid (Eq. (1)), we see that for a four-bladed vane the value 2/3, i.e.∼0.66, isreplaced by 1.2/1.51, i.e.∼0.8. Thus, the Newtonian liquid has, as we might expect, a slightly largerend correction. Also the equivalent pre-multiplier is different, so Sherwood and Meeten’s theory gives avalue 1.51 times smaller, since the flow-lines dip into the space between the vanes, and make the effectivediameter smaller.

However, Keentok [5] also suggested that the diameter of the sheared surface could be up to 5% greaterthan that determined by the circumscribed circle defined by the blade tips. This, he claimed, was measuredphotographically for some grease samples and found to be approximately correct. He and others [15]later used computer simulations of a four-bladed vane rotating in a Bingham liquid and showed that theeffective sheared radius was 2.5% greater than the vane radius, which they claimed agreed well withexperimental data on two viscoelastic automotive greases. They also used a photographic method toshow that the sheared shape was approximately circular. If this increase in the equivalent radius of thesheared cylinder is true, then it can make up to 10% difference to the final value of the yield stress. Inthis context, Yan and James [16] investigated the behaviour of Herschel-Bulkley, Bingham and Cassonfluids in a four-blade vane geometry using the FIDAP finite-element program. They found that for thesemodel liquids, the fluid between the vanes was trapped within a circular cylinder, and that ‘the shearstress was evenly distributed over the surface of the cylinder’, with the cylinder exactly defined by thevane tips. This means that the simplifying assumption that the vane behaves like a solid cylinder withoutslip is indeed valid. This finding is of course contrary to that of Keentok [5,15], but Yan and James useda more refined mesh in their computations, and they questioned Keentok’s photographic experiment,noting that little description was given. Barnes and Carnali [17], see below, found the same coincidencebetween the sheared surface and the circle formed by the vane tips in their study of very shear-thinningliquids.

We, therefore, conclude that one can simply calculate the yield stress using a vane on the basis of anequivalent solid cylinder defined by the circumscribing circle formed by the tips of the blades. This is in


fact in agreement with the much earlier work of Cadling and Odenstad who used the vane for measuringthe shear strength of soils [18]. Furthermore, this feature of the vane geometry highlights its advantage,compared to other methods, as a quick single-point determination of the yield stress.

Another characteristic of the vane method is that the vane is used simply as an attachment, which can bemade to fit an existing rheometer. Yield-stress measurement by means of the vane is often conducted at aconstant and usually low rotational rate using a rate-controlled instrument. Liddell et al. [19] pointed outthat the driving mechanism used in such instruments for running the vane could have a significant effecton the result. By comparing the behaviour of measuring systems with stiff and weak springs, they showedthat the real build-up of strain in a structured liquid is slower if the vane is driven through/against a weakspring which then takes up most of the imposed strain, and that this gave a better measure of a yield stress,since any viscous component present is minimised. The particular example they cited is a Weissenbergrheogoniometer with a spring of stiffness 1.1 N m/rad and a Haake viscometer spring some 300 timesmore compliant at 0.003 N m/rad, with the latter offering the better measurement. To give comparableresults, the Weissenberg rheogoniometer had to be driven much slower. Their ‘ideal’ response from aslow-running Haake — 0.2 rpm — is a linear increase in stress, with a clear break from linearity, eitherfollowed by a maximum value and a fall-off to a lower steady value, or else a break from linearity and alevelling off of stress to a constant value, see Fig. 3. The Weissenberg gave a non-linear stress build-upindicating quite a lot of ‘creep flow,. . . , occurring well below the yield stress’. In general, it is goodpractice to establish the suitable range for rotational rate of the vane where the maximum shear stress isessentially constant [3,9]. The maximum operating speed, which normally corresponds to a rapid increasein the stress overshoot with increasing rotational rate [9], is reasonably high for fluids having high yieldstresses [3]. For low-yield-stress fluids, errors are thus expected even if the vane is operated at the lowestspeed available in the rheometer since the maximum stress may contain some contribution due to theviscous component if the vane speed is not sufficiently low. This has led to a suggestion that the vanemethod is most suitable for measuring yield stress values greater than ca. 10 Pa [9,13]. The alternativeprocedure is to operate the vane in the constant-stress mode as demonstrated by Yoshimura et al. [14] andJames et al. [29]. In this way, the vane method becomes basically a creep test with the added advantageof no wall slip.

Fig. 3. The typical start-up response of a range of hypothetical ‘yield-stress’ materials when measured using a slowly rotatingvane, showing the various definitions of yield stress appropriate to a solid yielding at non-linearity, through to a liquid-likeequilibrium response, with an intermediate maximum stress also possible as a definition.


3.3. The use of the vane geometry to measure non-Newtonian flow-curves

Barnes and Carnali [17] concluded that for a very shear-thinning, power-law liquid (power-law index<

0.5), the vane sheared the liquid outside a circular cylinder prescribed by the blade tips, and that little orno shearing took place within this cylinder. From their numerical simulation, they also found, as expected,that the stream-lines around the vane for a Newtonian liquid were not circular, but dipped into the spacebetween the vanes. They only became circular when the power-law index of the power-law model usedwas less than about 0.5.

Their experimental end effect on a vane witha equal to 4.25 mm and a range of lengths was only2 mm for a non-Newtonian liquid. For their experimental length of 48 mm, this meant that the end effectcould be ignored. They used a gap of 1 mm only. Using Sherwood and Meeten’s Newtonian end-correctioncalculation for an infinite gap, we would expect an end correction of around 2.88 mm. The results comparewell with Meeten and Sherwood’s measured results for the modulus of a bentonite suspension [20].

Barnes and Carnali also showed that the stress distribution in the sheared liquid in the gap peakedsharply in the immediate vicinity of the vane tips (as was also shown in the calculations of Keentok et al.[15]) but was constant in all other parts of the gap, see above, and in fact this constant stress accountedfor the vast majority of the measured torque, with the local peaks accounting for very little. In theirexperimental section, they showed that for a 4.2% dispersion of Veegum PRO clay suspension and a5.5% CMC solution, the use of the vane as compared to the equivalent concentric cylinder gave the sameresult in the Newtonian region at very low stresses, but that at higher stresses, the vane reduced the amountof ‘slip’. However, as we shall see below, the outer smooth cup could still cause some slip, and in facttheir results still showed some strange effects.

Lastly, Barnes and co-workers [21] later used the vane geometry to measure the flow properties of veryshear-thinning non-Newtonian liquid products in the home and personal care area, as well as examplesin the food and bio-processing areas. They improved the simple vane geometry by the addition of aslender gauze basket inserted inside an outer cylinder (see Fig. 4), which eliminates slip there also. Withthis modification, the flow curves obtained for various shear-thinning liquids were found to exhibit theexpected smooth continuous, but precipitous, drop from a high value of viscosity to a much lower value,with no breaks in the curve, see for instance Fig. 5. They also showed that even with the vane, but withoutthe basket, a break in the curve indicating wall slip could still be seen, albeit at a higher stress [16].

One obvious limitation to the use of the vane geometry is for low-viscosity liquids, where inertial effectsbecome important, and simple concentric flow-lines becomes distorted in some way, even to the extentof vortices forming behind the blades for low-viscosity liquids (although this has not been establishedunequivocally). The extra dissipation of energy associated with these flow distortions means that theindicated viscosity would be too high. Many structured liquids drop from a very high viscosity at lowshear stress to quite a low viscosity at higher stress, but often this means that we are in this forbidden range.Fig. 6 shows the typical situation for two low-viscosity Newtonian silicone oils measured at relativelyhigh rotation rates. More work needs to be done to properly understand and characterise this limitation,so that areas where serious artefacts are introduced can be avoided.

4. General applications

The vane has become a standard way of measuring the yield stress of food systems, see [22] for acollection of useful references in this area. Steffe [22] claims that ‘overall, the vane method has much to


Fig. 4. The vane-and-basket geometry.

offer the food engineer in need of a yield stress measurement: the technique involves a simple theory thatproduces quick, reproducible results using equipment that is inexpensive and durable’.

The vane has been advocated widely by the food technology groups in the USA headed by Steffe andDaubert, see [23,24]. Indeed, there have been efforts to make the vane method a national standard formeasurement of the yield stress of food (US National Research Committee NC-136) [25].

Fig. 5. The flow curves for three concentrations of Carbopol 940 dispersions in water measured using the vane-and-basketgeometry.


Fig. 6. The normalised viscosity (measured over actual),ηm/η, vs. the quotient of rotation rate and actual viscosity,w/η, for twosilicone oils of viscosities 0.0125 Pa s (crosses) and 0.047 Pa s (triangles), respectively, measured in a small, four-bladed vanegeometry with the vane height,l = 20 mm, vane radius,a = 5 mm and an outer cylinder diameter of 12.84 mm.

5. Specific applications studied using the vane geometry

There are five general areas where the vane geometry has been frequently used to measure one oranother rheological properties. These areas are

• inorganic colloidal dispersions,• liquid-like foods,• bioengineering systems (fermentation broths, etc.),• miscellaneous dispersions, and• foams, etc.

and various examples of these are given in Tables 1–5.

Table 1Some uses of the vane geometry for inorganic colloidal dispersions, listed alphabetically

Worker(s) and reference Type of dispersion Comments

Alderman et al. [9] Bentonite Yield stressBenna et al. [26] Sodium bentonite Effect of pH on rheologyChang and Smith [27] Nuclear waste slurries Rheological characterisationFranks et al. [28] Alumna suspensions ‘Ion-specific’ yield stressJames et al. [29] Illite suspensions Yield stressLeong [30] ZrO2 Depletion interactionLiddell et al. [31] TiO2 pigment Yield stressLin et al. [32] Non-aqueous iron-oxide Rheological modelPignon et al. [33] Discotic clay Yield stressRamakrishnan et al. [34] Ceramic powders Effect of solids loading and pHYanez et al. [35] Alumna–zirconia suspensions Effect of electrolyte on rheology


Table 2Some uses of the vane geometry for food systems listed alphabetically

Worker(s) and reference Type of food system Comments

Briggs et al. [36] Frozen ice cream Yield stressDaubert et al. [37] Various spreads Measure of food spreadabilityDimonte et al. [38] Virgin yoghurt Yield stressGeraghty and Butler [39] Commercial yoghurt Used with cup in bob geometryHouska et al. [40] Fruit pectin jam Yield stressMleko and Foegeding [41] Processed cheese analogue Yield stressMissaire et al. [42] Apple pulps Yield stressPernell et al. [43] Various protein foams Yield stressRao [44] Mustard ‘Structural approach to rheology’Rao and Steffe [45] Various foods Yield stressTruong and Daubert [46] Gellan gum gels Yield stressTucker et al. [47] Modified starch suspensions Used with pulse shearometryWilson et al. [48] Molten chocolate Yield stress and flowYoo and Rao [49,50] Tomato puree Yield stress and viscosityZhang and Nguyen [51] Mayonnaise Thixotropy

Table 3Some uses of the vane geometry for bioengineering systems listed alphabetically

Worker(s) and reference Bioengineering system Comments

Leongpoi and Allen [52] Fermentation broths, ketchup, Yoghurt, and pulp suspensions Yield stressMohseni and Allen [53] Various fermentation broths Yield stressMohseni et al. [54] Various fermentation broths Yield stressPernell et al. [55] Protein foams Yield stressSvihla et al. [56] Filamentous suspensions Vane as a mixer elementTruong and Daubert [46] Soybean protein Yield stress

Table 4Some uses of the vane geometry for various dispersions listed alphabetically


Austin et al. [57] Wet-process sprayed mortars ‘Rheological performance’Haimoni and Hannant [58] Oil well cements Gel strengthIyer and Stanmore [59] Dense fly-ash slurries Yield stressLeong et al. [60] Brown coal slurries Yield stress and thixotropyNguyen and Boger [61] Bauxite residue ThixotropyPinkerton and Norton [62] Lavas from Mount Etna Newtonian above 1120CPrzewlocki [63] Brickmaking clay Shear strengthRajgelj [64] Fresh concrete mortars Effect of parametersStanmore and Page [65] Dense fly-ash slurries ‘Shear failure’Turian et al. [66] Coal–water mixtures Yield stressTurian et al. [67] Mineral slurries Settling and rheologyWardhaugh and Boger [68] Waxy crude-oil ‘Yielding behaviour’Wichmann and Riehl [69] Waterworks sludge ‘Shear strength’


Table 5Some uses of the vane geometry for various materials listed alphabetically


Arola et al. [70] Microfibrous cellulose Vane results compared with velocity field from MRIGardiner et al. [71] Aqueous foams in dry limit Yield stressRosentrater et al. [72] Corn masa by-products Yield stressZhang et al. [73] Reactive polyurethane foam ‘Modulus development’

For a very good review of the use of the vane for measuring soil strength, see reference [74], whichcontains 22 papers on all aspects of the use of the vane for soils and is well worth reading.

6. Conclusions

Vane geometries are now available as standard or special items for most rheometers or viscometers,see Fig. 1 for example, but otherwise they are easy to fabricate, and their use adds significantly to therepertoire of any general rheology laboratory. This is particularly true for the measurement of materialswhere there is reason to believe that significant slip effects might be expected, see Barnes [75].

Acknowledgements

Thanks are due to Wolfgang Marquardt of the Haake viscometer company (Gebrueder Haake, Karlsruhe,Germany) for information on the history of their vane geometry, and Mark Harris for help in collectingthe data for Fig. 6.

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