Comparison of methods to measure yield stress of soft
solids
M.Castro,a)D.W.Giles,and C.W.Macosko
Department of Chemical Engineering and Materials Science,
University of Minnesota,Minnesota55455
T.Moaddel
Unilever Rearch and Development,Trumbull,Connecticut06611 (Received27March2009;final revision received22September2009;
published25January2010͒
Synopsis
Many interesting industrial materials are highly viscous or ,soft solids.Their complexity,proceeding from heterogeneous structures,often reveals interesting rheological properties.T
heir processing requires the determination of rheological parameters such as viscosity, modulus,and yield stress value.We compare three methods to measure the yield stress of one particular soft solid ,concentrated surfactant systems,models for bar soap.One method is bad on orifice die extrusion and us the Benbow–Bridgwater equation.Two methods ud a rotational rheometer:in one,dynamic͑small strain sinusoidal oscillation͒experiments were performed as a function of increasing strain amplitude with rrated parallel plate geometry.The maximum in the elastic stress curve was ud to estimate the yield stress.The other method using the rotational rheometer,which we call strand shearing,involves the u of a newfixture designed to grip the samples that were too stiff for rrated plates but too soft for traditional solids fixtures.In this method,the maximum of a plot of stress versus time at a constant shear rate is taken as the yield stress.The advantages and limitations of the techniques are discusd and applied to our particular soap model system.
©2010The Society of Rheology.͓DOI:10.1122/1.3248001͔
洗衣服去I.INTRODUCTION
Many uful materials are highly viscous systems,often called soft solids.Such ma-terials can be found in ceramics manufacturing,food processing͓Gray and Chinnaswamy ͑1995͔͒͑e.g.,food paste-ram e
xtrusion and chocolate cold-extrusion͓Chen and Mackley ͑2006͔͒͒,or cosmetics formulation͓Spitz͑1990͒;Burke͑2005͒;Hill͑2004͔͒.The rheo-
logical properties of such materials influence their manufacture and utilization.Among the rheological properties of the materials,the yield stress value is of great importance, especially for process such as extrusion and forming.Soap bar manufacture involves
a͒Author to whom correspondence should be addresd.Prent address:Materials Engineering Lab.of Brittany ͑LIMATB͒,European University of Brittany͑UEB͒,Rue Saint Maude,56321Lorient,France;electronic mail: mickael.castro@univ-ubs.fr
©2010by The Society of Rheology,Inc.
J.Rheol.54͑1͒,81-94January/February͑2010͒0148-6055/2010/54͑1͒/81/14/$30.00
81
好听的军歌
flowing,cooling,and stamping a molten mixture of surfactants and water ͑and additives such as perfumes ͒.In the production of the soap bars,the yield stress of the mixture at the various temperatures can affect processability and the ability to form bars at the desired rate and quality.The
yield stress should fall within some range to allow particular process steps to work.This paper describes methods to practically measure the yield stress of the materials,which fall within a range of softness or hardness that caus difficulty with wall slip and with traditional methods to grip samples in rheometers.In this study,we compare different techniques to rapidly measure the yield stress of lf-supported soft ,concentrated surfactant systems:͑1͒orifice die capillary rheometry bad on the analysis of Benbow and Bridgwater ͑1993͒,͑2͒rotational rheometry with rrated plates and sinusoidal oscillation experiments at increasing strain amplitudes,and ͑3͒rotational rheometry with a new strand shearing technique using a novel fixture design.II.MATERIALS AND METHODS
A.Materials
The model system consists of a blend of three pure surfactants ͑sodium salts of lauric,oleic,and stearic acids ͒and distilled water ͑cf.Table I ͒.The surfactants were purchad from TCI America-Japan and ud as received.
B.Preparation
Prior to mechanical mixing,the three surfactants ͑sodium stearate,laurate,and oleate ͒were pre-mixed t
ogether in a beaker.The mass ratio between the three components was kept constant in all the experiments here ͑stearate:laurate:oleate 3:1:3͒.Distilled water was added to the blend in different amounts and further mixed with a glass rod.Table II summarizes the sample compositions.The nomenclature “SLOW”has been adopted to identify our samples.The number following SLOW refers to the water level of the ,SLOW10refers to SLOW sample with 10%water.The pre-mixed compo-nents were then further procesd with a small scale twin screw extruder,mixed at 45°C for 45min,as described in a previous work by Mongondry et al.͑2006͒.The screw speed was t at 100rpm.The average shear rate was estimated to be 50s −1͓Maric and Macosko ͑2001͔͒.After mixing,samples were extruded through a 1mm diameter die and
感冒英语TABLE I.Materials ud to prepare paste.Chemical formula
长白山旅游攻略
CAS No.Purity ͑%͒Sodium laurate
CH 3͑CH 2͒10COONa 629-25-4Min.97.0Sodium oleate
CH 3͑CH 2͒7CH:CH ͑CH 2͒7COONa
143-19-1Min.95.0Sodium stearate CH 3͑CH 2͒16COONa 822-16-2Min.95.0
荠菜花煮鸡蛋TABLE II.Sample formulations ͑wt %͒.
SLOW 10
SLOW 13SLOW 17S tearate
38.33735.4L aurate
13.51312.5O leate
38.33735.4W ater 9.91316.7
cad镜像82
CASTRO et al.
collected directly in a glass vial and aled to prevent water evaporation.Water content was checked after mixing using thermogravimetric analysis ͑TGA ͒.
C.Capillary rheometry
1.Background
Using capillary extrusion,Benbow and Bridgwater ͑1993͒developed an analysis to measure the rheological properties of pastes.Since then other authors,Horrobin and Nedderman ͑1998͒,Bates and Bridgwater ͑2000͒,Domanti et al.͑2002͒,or Domanti and Bridgwater ͑2004͒for example,have ud this analysis.Figure 1illustrates the esntial parts in the system.The model consists of an extruder with a square ͑180°͒entry die,a circular barrel,and die of diameters D 0and D ,respectively.The paste is forced by a piston through the die and the pressure drop is recorded.In practice,for square entry geometries,stagnant zones are formed in the entry region,above the die,as shown in Fig.1.
In developing their analysis technique,they first considered the work done by the extrusion pressure on a paste of initial cross-ctional area A 0and initial length l 0in a linear ,uniaxial yield stress.Considering a constant volume,a zero length die ͑orifice die ͒,and a plastic behavior,they obtained the following equation for the uniaxial yield stress :
P =2ln D 0D .͑1͒
This equation describes the pressure that is required to deform the paste from an original diameter D 0to a final diameter D .In performing the experiments,they found that pres-sure exhibits some rate dependence.Thus,to fit their data,they ud =0+␣V n ,where they defined 0as the bulk yield stress of paste at low velocity and ␣and n being
the
FIG.1.Notation for paste extrusion through an orifice die.
83
YIELD STRESS OF SOFT SOLIDS
bulk velocity factor and exponent,respectively.Hence,replacingin Eq.͑1͒with the expression describing the rate dependence,gives
P=2͑0+␣V n͒ln D0
D
.͑2͒
Here,0,␣,and n can be regarded as material constants,assumed to be independent of die geometry and extrusion rate.And so,using Eq.͑2͒,the extensional yield stress0can be estimated from an orifice die extrusion experiment and converted into a shear stress0 following V on Mis criterion which states that
0=0
ͱ3.͑3͒
Some authors have questioned the rate dependence of the yield stress in the Benbow–Bridgwater model.For instance,Zheng et al.͑1992͒investigated the extrusion of Herschel–Bulkley materials through a square entry die and concluded that an apparent shear rate,equal to͑V/D͒,should be ud in place of the extrudate velocity͑V͒in Eq.͑2͒.They obrved that the coefficient n ud in Eq.͑2͒is equal to the power law index and eventually that the coefficient␣is a function of both the power law index and the
consistency.They did not pursue any further comparisons between the two models. Blackburn͑1995͒highlighted the fact that in the Benbow–Bridgwater model,the velocity was being ud to reprent a shear rate,which is dimensionally inconsistent.The author propod a rate dependence bad on the product of the velocity to die diameter ratio raid to some power and the barrel to die diameter ratio raid to some power.More recently,Basterfield et al.͑2005͒developed an analytical model for orifice extrusion. They ud a Herschel–Bulkley material and considered theflow as being predominantly extensional,as a result of the convergence of theflow clo to the die entranc
e.As such they expresd the Herschel–Bulkley relation in uniaxial form=0+k u˙n,whereand ˙are the effective uniaxial stress and strain rate and0and k u are the uniaxial yield stress andflow consistency.The authors developed this model and compared to the Benbow–Bridgwater equation.They ended with the following expression:
P=20ln D0
D
+Ak uͩ2V D
ͪnͩ1−ͩD D
ͪ3nͪ,͑4͒
with
A=2
3n
͑sinmax͑1+cosmax͒͒n,͑5͒
wheremax is the maximum cone angle formed by the static zones.They demonstrated that the coefficient A shows a very small nsitivity tomax which was arbitrarilyfixed at max=45°.They have shown that this expression is capable of describing experimental
data as accurately as Eq.͑2͒.Both gave identical results for the value of the yield stress 0.However,their model Eq.͑4͒,contrary to Eq.͑2͒,includes only dimensionally con-sistent parameters,in particular,theflow consistency k u.In this report,we focus on the converted yield stress value͑0͒,obtained from Eqs.͑2͒and͑3͒.Using Eq.͑4͒,the same yield stress value is calculated.The power law index n andflow consistency k u of Eq.͑4͒are not further discusd in this paper.
84CASTRO et al.
2.Orifice extrusion
Orifice extrusion was performed with a capillary rheometer ͑Goettfert,Visco tester 1500͒tup with 0.5,1,and 2mm diameter orifice dies ͑die length clo to zero ͒.The 12mm diameter barrel was filled manually.Experiments were made from 25to 100°C.The piston velocity was t between 0.005and 1
mm s −1.Pressure was recorded just above the die entry.Considering the high yield stress of our materials and in order to correctly record the pressure,silicone grea was ud to fill the gap between the channel and the pressure transducer.In order to illustrate the static region at the die exit,the barrel was filled with uncolored sample and three stripes of colored sample as depicted in Fig.2.The piston velocity was t at 3mm s −1and the temperature was 45°C.As the last colored stripe began to exit the 0.5mm diameter die,the piston was stopped.To visualize the static region,the remaining sample was removed from the barrel and cut longitudinally into two pieces,as shown in Fig.2.
D.Rotational rheometry
Nguyen and Boger ͑1992͒reviewed the yield stress and techniques ud to measure it.We ud two techniques with rotational rheometers:one using sinusoidal oscillations and the other using startup of steady shearing.
1.Sinusoidal oscillation experiment
One way to measure the yield stress is to u dynamic strain or stress measurements with a rotational rheometer ͓Nguyen and Boger ͑1992͒;Walls et al.͑2003͔͒.According to Walls et al.͑2003͒,this tec
hnique has veral advantages including the capability to u different plate geometries such as rrated plates ͑required for our system ͒,in addition to providing the viscoelastic properties of our materials from which further description can be gained in addition to a measure of the yield stress.Two different ways of using dynamic measurements to measure yield stress include:
-Taking the maximum in the plot of the in-pha stress component 0=␥0G 0Јversus ␥0͓Yang et al.͑1986͒;Youssry et al.͑2008͔͒.-Obtaining the cross over point of the elastic ͑G Ј͒and viscous ͑G Љ͒moduli by increasing the stress amplitude ͓Shih et al.͑1999͔͒.In our study,the maximum of
the FIG.2.Static zones visualization.͑a ͒Sketch of the stripes before extrusion.͓͑b ͒and ͑c ͔͒Picture of the sample after extrusion ͑longitudinal cut ͒.
85启发性教育>张家庭
YIELD STRESS OF SOFT SOLIDS
