Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2013 Article ID 406018 5 pageshttpdxdoiorg1011552013406018
Research ArticleAnalysis on Nonlinear Stress-Growth Data for Shear Flow ofStarch Material with Shear Process
Jinghu Yu Dejun Ma and Hui Lu
Jiangnan University Lihu Road No 1800 Wuxi Jiangsu China
Correspondence should be addressed to Jinghu Yu jhyujiangnaneducn
Received 3 May 2013 Accepted 29 May 2013
Academic Editor Jun Wang
Copyright copy 2013 Jinghu Yu et alThis is an open access article distributed under theCreativeCommonsAttribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
The material function of liquid materials for packaging plays an important role in analysis of its mechanical behavior Themechanical behavior of material affects the packaging process in many aspects such as selection of packaging materials andpreparation of packaging method Therefore research on the material function of the liquid material is very helpful to guide thepackaging process and look into how the packaging quality and efficiency are affected by themechanical properties of materialThispaper established the material function for the starch solution under shear process With the relaxation test of the starch solutionspecimens the119866(119905) function and dumping functionwere established and verified Based on thememory function of starch solutionthe material function of starch solution was constructed and approved to be efficiently predict the mechanical behavior during theshear process Therefore such material function can be used to guide the operation on the shear flow
1 Introduction
Starches have been used for many years in the food industryand their rheological properties decide different applicationsin food products [1 2] For this reason their rheologicalbehavior has deserved increasing attention The nonlinearbehavior of starch solution plays an important role in manypackaging processes and especially it affects the packagingmaterial transmission speed and high weight measurementprecision [3 4] Analysis of the nonlinear viscoelastic behav-ior of starch solution is of great importance for their rheolog-ical characterization
The material function is the basis of the analysis on thestarch solution In order to establish its material function theconstitutive equation must be constructed according to themost suitable experiment [5] It is often found that the Lodgemodel can successfully describe the behavior of rubber-likeliquid under shear flow or elongational flow [6 7]The Lodgemodel can be expressed as follows
120590 (119905) = minusint
119905
minusinfin
119872(119905 minus 1199051015840 120574) lowast 120576 (119905
1015840) 1198891199051015840 (1)
where 120590 is the stress at the current time 119905 119872(119905 minus 1199051015840 120574) isthe memory function specific for the material and it can be
established by suitable experiment 120576(1199051015840) is the strain functiondependent on the time t and it can be defined in the specificprocess
Recently the memory function is often expressed as aproduct of the memory function for the linear behavior119866(119905) and a so-called damping function ℎ(120574) [8ndash10] Yu et al[11] established and validated a rheological model that canbe used to characterize viscoelastic properties of food gelsduring compression under small and large deformation [11]The aim of this paper is to give experimental justificationfor linear behavior 119866(119905) and the damping function ℎ(120574)Taking the starch solution as sample its material functionwas established based on the linear shear modulus 119866(119905)and damping function ℎ(120574) Through comparison of theexperimental data and the calculated shear stress by thematerial function the material function of starch solutionwas approved to be successfully describing the behavior of thestarch solution under shear flow
2 Experimental Materials and Methods
The type of modified starch is ULTRA-TEX 1 corn starchfrom National Starch Food Innovation This kind of starch
2 Mathematical Problems in Engineering
7 starch solution
Strain sweep from 00001 to 10 strain sweep step
Strain ()
0101001
1
11
10
10
10
100
01
1
10
100
100 1000 10000
100
G998400
(Pa)
G998400998400
(Pa)
120575(d
egre
es)
Figure 1 Strain sweep test from 00001 to 10 at the frequency 1
7 starch solution
Strain is 03 stress relaxation test
Time (s)
1
10
100
1000
10000
1E5
Mod
ulus
G(t)
(Pa)
0 50 100 150 200 250 300
Figure 2 Relaxation test within linear range of strain
and distilled water were used tomake different concentrationstarch solution The whole experiment was performed onthe Rheometer AR-2000 from TA instruments Ltd The conehead was installed and its angle is 28 degree The constanttest temperature is 25∘C
High shear rate and long time shear test were performedto find if the shear process affects the strain relaxation testShear rate influence on the strain can be found Thereforethememory function can be established by themany differentstrain relaxation tests
3 Memory Function for the NonlinearViscoelastic Behavior
Thememory function can characterize the mechanical prop-erty of the specific material [12] According toWagner [9 10]
for simple shear flow the generalized memory function isexpressed by
119872(119905 minus 1199051015840 1205741199051199051015840) =sdot
119872 (119905 minus 1199051015840) ℎ (1205741199051199051015840) (2)
wheresdot
119872 (119905minus1199051015840) is the linearmodulus ofmaterial under small
deformation It describes the linear relationship betweenthe strain and stress of material The nonlinearity of therheological behavior is only characterized by the dumpingfunction ℎ(120574
1199051199051015840)
For simple shear flow the well known relations for theshear stress 120590(119905) can be expressed by
120590 (119905) = int
infin
0
119872(119905 minus 1199051015840) 12057411990511990510158401198891199051015840 (3)
In order to establish the shear modulus function and thedamping function the linear range of the relationship of thestress and strainmust be foundwith strain sweep test Figure 1shows that the storage modulus1198661015840 the lost modulus 11986610158401015840 anddifferent degree delta are almost constant when the strain isless than 001 It indicates that the relationship of stress andstrain of starch solution is linear during the step in shearstrain from0 to 001Therefore in the linear viscoelastic rangethe shear relaxation modulus 119866(119905) can be given by
According to the strain sweep test result the suitablestrain relaxation test was carried out The measurement dataof relaxation test was shown in Figure 2 The strain value ofrelaxation test is 03 and it belongs to the linear viscoelasticrange of 7 concentration starch solution
The recently published paper that approved the linearmodulus function can be expressed by [13 14]
119866 (119905) = 119886119905minus119899 (5)
Take the experiment data (Figure 2) to fit the function (5)withOrigin 80 and the fitted linearmodulus function can beexpressed by
119866 (119905) = 6469095119905minus019167 (6)
The linear modulus function119866(119905) characterizes the linearproperty of material during the small deformation Withcertain deformation the relationship of stress and strain islinear and the shear modulus119866(119905) is only dependent on time119905 With the strain increasing the relationship of stress andstrain is nonlinear and shear modulus 119866(119905 120574) is dependenton time and strain The shear modulus function 119866(119905 120574) canbe expressed by [15 16]
where ℎ(120574) is a damping function and it is a function of strain120574The damping functionwas added into the shearmodulus tocharacterize the nonlinear property of material It describesthe relationship of the shear modulus and the strain
Mathematical Problems in Engineering 3
Table 1 The value of strain at t = 50 s in the different strainrelaxation test
Many measurements of the relaxation modulus were per-formed in a nonlinear shear strain range of 120574 = 4 to10 (Figure 3) where the starch solution behaves stronglynonlinear
According to the published data of damping function[17 18] the following equation can be selected as the starchsolutionrsquos damping function
ℎ (120574) = 119890minus119899120574 (9)
Therefore the relaxation modulus can be expressed asfollows
Figure 3 119866(119905 120574) curve during the stress relaxation test underdifferent strain for 03 4 20 100 300 600 respectively
7 starch solution
Shear rate sweep from 01 to 10 (flow step)Time (s)
Stra
in
Shea
r rat
e
Shea
r stre
ss (P
a)0 100 200 300 400 500 600 700 800 900 1000
0
25
5
75
10
125
15
175
20
0
25
5
75
10
125
15
175
20
0
2
4
6
8
12
10
450
400
350
300
250
200
150
100
50
0
225
Visc
osity
(Pamiddot
s)
Figure 4 Shear rate step flow test
The verified experiment was carried out and the resultwas shown in Figures 4 and 5
In the shear rate sweep test the time and shear rate areknown Therefore the strain can be calculated by shear rateand time The above parameters were taken into (14) and thepredict result was shown in Figure 5
Viscosity-shear rate curve of starch solution was shownin Figure 6
It indicates that the viscosity of starch solution willbecome thin with the shear rate increasing
The predicted results indicate that the material functionconstructed with memory function describes the flow behav-ior during the shear rate step test The shape of predicts
4 Mathematical Problems in Engineering
Calculated dataMeasurement data
Shea
r stre
ss (p
a)
Shear rate
25
20
15
10
5
00 1 2 3 4 5 6 7 8 9 10
Figure 5 Predicted result of shear stress during the shear rate sweeptest
Calculated dataMeasurement data
Shear rate
25
20
15
10
5
00 1 2 3 4 5 6 7 8 9 10
Visc
osity
(Pamiddot
s)
Figure 6 Viscosity-shear rate curve
line based on the material function was very similar to theshape of measured data lineWhen the shear rate increases toinfinite both the predicted data and test data are close to thesame value
5 Conclusion
The memory function of starch solution can be constructedby the shear relaxation test Based on the memory functionthe material function of starch solution was established topredict the shear stress and viscosity during the steady shearflow The predicted result shows that the material functioncan be used to describe the behavior of starch solution duringthe shear process
Acknowledgment
This work was supported by the Fundamental ResearchFunds for the Central Universities under Grant noJUSRP11203
References
[1] D Eidam W M Kulicke K Kuhn and R Stute ldquoFormationof maize starch gels selectively regulated by the addition ofhydrocolloidsrdquo Starch vol 47 pp 378ndash384 1995
[2] L Quintieri A Monteverde and L Caputo ldquoChanges inprolamin and high resistant starch composition during the pro-duction process of Boza a traditional cereal-based beveragerdquoEuropean FoodResearch andTechnology vol 235 no 4 pp 699ndash709 2012
[3] L Duo and G Dan ldquoImplementing high weight measurementprecision in package machines by using 8031 single chip micro-computerrdquo Journal of Tianjin University of Commence vol 4 pp8ndash14 1994
[4] C Luo ldquoThe calculation of the solid conveying volumetric ratioflow rate of the food extruderrdquo Packaging and Food Machineryvol 26 no 2 pp 30ndash32 2008
[5] J F Steffe Rheological Methods in Food Process EngineeringFreeman Press East Lansing Mich USA 1996
[6] A S Lodge Elastic Liquids Academic Press London UK 1964[7] A S Lodge and J Meissner ldquoComparison of network theory
predictions with stresstime data in shear and elongation for alow-density polyethylene meltrdquo Rheologica Acta vol 12 no 1pp 41ndash47 1973
[8] M Sugimoto Y Masubuchi J Takimoto and K KoyamaldquoMelt rheology of polypropylene containing small amounts ofhigh molecular weight chain I Shear flowrdquo Journal of PolymerScience B vol 39 no 21 pp 2692ndash2704 2001
[9] M H Wagner ldquoAnalysis of time-dependent non-linear stress-growth data for shear and elongational flow of a low-densitybranched polyethylene meltrdquo Rheologica Acta vol 15 no 2 pp136ndash142 1976
[10] M H Wagner ldquoPrediction of primary normal stress differencefrom shear viscosity data using a single integral constitutiveequationrdquo Rheologica Acta vol 16 no 1 pp 43ndash50 1977
[11] J H Yu P H S Santos and O H Campanella ldquoA study tocharacterize the mechanical behavior of semi-solid viscoelasticsystems under compression chewing case study of agar gelrdquoJournal of Texture Studies vol 43 no 6 pp 459ndash467 2012
[12] J D Ferry Viscoelastic Properties of Polymers John Wiley ampSons New York NY USA 1980
[13] K Osaki ldquoOn the damping function of shear relaxation modu-lus for entangled polymersrdquo Rheologica Acta vol 32 no 5 pp429ndash437 1993
[14] Q Zheng W Wang Q Yu J Yu L He and H Tan ldquoNon-linear viscoelastic behavior of styrene-[ethylene-(ethylene-propylene)]- styrene block copolymerrdquo Journal of PolymerScience B vol 44 no 9 pp 1309ndash1319 2006
[15] F A Morrison Understanding Rheology Oxford universitypress New York NY USA 2001
[16] W Wang Z Lu Y Cao J Chen J Wang and Q ZhengldquoInvestigation and prediction on the nonlinear viscoelasticbehaviors of nylon1212 toughened with elastomerrdquo Journal ofApplied Polymer Science vol 123 no 3 pp 1283ndash1292 2012
Mathematical Problems in Engineering 5
[17] H Watanabe T Sato K Osaki et al ldquoRheological images ofpoly(vinyl chloride) gels 4 Nonlinear behavior in a critical gelstaterdquoMacromolecules vol 31 no 13 pp 4198ndash4204 1998
Figure 1 Strain sweep test from 00001 to 10 at the frequency 1
7 starch solution
Strain is 03 stress relaxation test
Time (s)
1
10
100
1000
10000
1E5
Mod
ulus
G(t)
(Pa)
0 50 100 150 200 250 300
Figure 2 Relaxation test within linear range of strain
and distilled water were used tomake different concentrationstarch solution The whole experiment was performed onthe Rheometer AR-2000 from TA instruments Ltd The conehead was installed and its angle is 28 degree The constanttest temperature is 25∘C
High shear rate and long time shear test were performedto find if the shear process affects the strain relaxation testShear rate influence on the strain can be found Thereforethememory function can be established by themany differentstrain relaxation tests
3 Memory Function for the NonlinearViscoelastic Behavior
Thememory function can characterize the mechanical prop-erty of the specific material [12] According toWagner [9 10]
for simple shear flow the generalized memory function isexpressed by
119872(119905 minus 1199051015840 1205741199051199051015840) =sdot
119872 (119905 minus 1199051015840) ℎ (1205741199051199051015840) (2)
wheresdot
119872 (119905minus1199051015840) is the linearmodulus ofmaterial under small
deformation It describes the linear relationship betweenthe strain and stress of material The nonlinearity of therheological behavior is only characterized by the dumpingfunction ℎ(120574
1199051199051015840)
For simple shear flow the well known relations for theshear stress 120590(119905) can be expressed by
120590 (119905) = int
infin
0
119872(119905 minus 1199051015840) 12057411990511990510158401198891199051015840 (3)
In order to establish the shear modulus function and thedamping function the linear range of the relationship of thestress and strainmust be foundwith strain sweep test Figure 1shows that the storage modulus1198661015840 the lost modulus 11986610158401015840 anddifferent degree delta are almost constant when the strain isless than 001 It indicates that the relationship of stress andstrain of starch solution is linear during the step in shearstrain from0 to 001Therefore in the linear viscoelastic rangethe shear relaxation modulus 119866(119905) can be given by
According to the strain sweep test result the suitablestrain relaxation test was carried out The measurement dataof relaxation test was shown in Figure 2 The strain value ofrelaxation test is 03 and it belongs to the linear viscoelasticrange of 7 concentration starch solution
The recently published paper that approved the linearmodulus function can be expressed by [13 14]
119866 (119905) = 119886119905minus119899 (5)
Take the experiment data (Figure 2) to fit the function (5)withOrigin 80 and the fitted linearmodulus function can beexpressed by
119866 (119905) = 6469095119905minus019167 (6)
The linear modulus function119866(119905) characterizes the linearproperty of material during the small deformation Withcertain deformation the relationship of stress and strain islinear and the shear modulus119866(119905) is only dependent on time119905 With the strain increasing the relationship of stress andstrain is nonlinear and shear modulus 119866(119905 120574) is dependenton time and strain The shear modulus function 119866(119905 120574) canbe expressed by [15 16]
where ℎ(120574) is a damping function and it is a function of strain120574The damping functionwas added into the shearmodulus tocharacterize the nonlinear property of material It describesthe relationship of the shear modulus and the strain
Mathematical Problems in Engineering 3
Table 1 The value of strain at t = 50 s in the different strainrelaxation test
Many measurements of the relaxation modulus were per-formed in a nonlinear shear strain range of 120574 = 4 to10 (Figure 3) where the starch solution behaves stronglynonlinear
According to the published data of damping function[17 18] the following equation can be selected as the starchsolutionrsquos damping function
ℎ (120574) = 119890minus119899120574 (9)
Therefore the relaxation modulus can be expressed asfollows
Figure 3 119866(119905 120574) curve during the stress relaxation test underdifferent strain for 03 4 20 100 300 600 respectively
7 starch solution
Shear rate sweep from 01 to 10 (flow step)Time (s)
Stra
in
Shea
r rat
e
Shea
r stre
ss (P
a)0 100 200 300 400 500 600 700 800 900 1000
0
25
5
75
10
125
15
175
20
0
25
5
75
10
125
15
175
20
0
2
4
6
8
12
10
450
400
350
300
250
200
150
100
50
0
225
Visc
osity
(Pamiddot
s)
Figure 4 Shear rate step flow test
The verified experiment was carried out and the resultwas shown in Figures 4 and 5
In the shear rate sweep test the time and shear rate areknown Therefore the strain can be calculated by shear rateand time The above parameters were taken into (14) and thepredict result was shown in Figure 5
Viscosity-shear rate curve of starch solution was shownin Figure 6
It indicates that the viscosity of starch solution willbecome thin with the shear rate increasing
The predicted results indicate that the material functionconstructed with memory function describes the flow behav-ior during the shear rate step test The shape of predicts
4 Mathematical Problems in Engineering
Calculated dataMeasurement data
Shea
r stre
ss (p
a)
Shear rate
25
20
15
10
5
00 1 2 3 4 5 6 7 8 9 10
Figure 5 Predicted result of shear stress during the shear rate sweeptest
Calculated dataMeasurement data
Shear rate
25
20
15
10
5
00 1 2 3 4 5 6 7 8 9 10
Visc
osity
(Pamiddot
s)
Figure 6 Viscosity-shear rate curve
line based on the material function was very similar to theshape of measured data lineWhen the shear rate increases toinfinite both the predicted data and test data are close to thesame value
5 Conclusion
The memory function of starch solution can be constructedby the shear relaxation test Based on the memory functionthe material function of starch solution was established topredict the shear stress and viscosity during the steady shearflow The predicted result shows that the material functioncan be used to describe the behavior of starch solution duringthe shear process
Acknowledgment
This work was supported by the Fundamental ResearchFunds for the Central Universities under Grant noJUSRP11203
References
[1] D Eidam W M Kulicke K Kuhn and R Stute ldquoFormationof maize starch gels selectively regulated by the addition ofhydrocolloidsrdquo Starch vol 47 pp 378ndash384 1995
[2] L Quintieri A Monteverde and L Caputo ldquoChanges inprolamin and high resistant starch composition during the pro-duction process of Boza a traditional cereal-based beveragerdquoEuropean FoodResearch andTechnology vol 235 no 4 pp 699ndash709 2012
[3] L Duo and G Dan ldquoImplementing high weight measurementprecision in package machines by using 8031 single chip micro-computerrdquo Journal of Tianjin University of Commence vol 4 pp8ndash14 1994
[4] C Luo ldquoThe calculation of the solid conveying volumetric ratioflow rate of the food extruderrdquo Packaging and Food Machineryvol 26 no 2 pp 30ndash32 2008
[5] J F Steffe Rheological Methods in Food Process EngineeringFreeman Press East Lansing Mich USA 1996
[6] A S Lodge Elastic Liquids Academic Press London UK 1964[7] A S Lodge and J Meissner ldquoComparison of network theory
predictions with stresstime data in shear and elongation for alow-density polyethylene meltrdquo Rheologica Acta vol 12 no 1pp 41ndash47 1973
[8] M Sugimoto Y Masubuchi J Takimoto and K KoyamaldquoMelt rheology of polypropylene containing small amounts ofhigh molecular weight chain I Shear flowrdquo Journal of PolymerScience B vol 39 no 21 pp 2692ndash2704 2001
[9] M H Wagner ldquoAnalysis of time-dependent non-linear stress-growth data for shear and elongational flow of a low-densitybranched polyethylene meltrdquo Rheologica Acta vol 15 no 2 pp136ndash142 1976
[10] M H Wagner ldquoPrediction of primary normal stress differencefrom shear viscosity data using a single integral constitutiveequationrdquo Rheologica Acta vol 16 no 1 pp 43ndash50 1977
[11] J H Yu P H S Santos and O H Campanella ldquoA study tocharacterize the mechanical behavior of semi-solid viscoelasticsystems under compression chewing case study of agar gelrdquoJournal of Texture Studies vol 43 no 6 pp 459ndash467 2012
[12] J D Ferry Viscoelastic Properties of Polymers John Wiley ampSons New York NY USA 1980
[13] K Osaki ldquoOn the damping function of shear relaxation modu-lus for entangled polymersrdquo Rheologica Acta vol 32 no 5 pp429ndash437 1993
[14] Q Zheng W Wang Q Yu J Yu L He and H Tan ldquoNon-linear viscoelastic behavior of styrene-[ethylene-(ethylene-propylene)]- styrene block copolymerrdquo Journal of PolymerScience B vol 44 no 9 pp 1309ndash1319 2006
[15] F A Morrison Understanding Rheology Oxford universitypress New York NY USA 2001
[16] W Wang Z Lu Y Cao J Chen J Wang and Q ZhengldquoInvestigation and prediction on the nonlinear viscoelasticbehaviors of nylon1212 toughened with elastomerrdquo Journal ofApplied Polymer Science vol 123 no 3 pp 1283ndash1292 2012
Mathematical Problems in Engineering 5
[17] H Watanabe T Sato K Osaki et al ldquoRheological images ofpoly(vinyl chloride) gels 4 Nonlinear behavior in a critical gelstaterdquoMacromolecules vol 31 no 13 pp 4198ndash4204 1998
Many measurements of the relaxation modulus were per-formed in a nonlinear shear strain range of 120574 = 4 to10 (Figure 3) where the starch solution behaves stronglynonlinear
According to the published data of damping function[17 18] the following equation can be selected as the starchsolutionrsquos damping function
ℎ (120574) = 119890minus119899120574 (9)
Therefore the relaxation modulus can be expressed asfollows
Figure 3 119866(119905 120574) curve during the stress relaxation test underdifferent strain for 03 4 20 100 300 600 respectively
7 starch solution
Shear rate sweep from 01 to 10 (flow step)Time (s)
Stra
in
Shea
r rat
e
Shea
r stre
ss (P
a)0 100 200 300 400 500 600 700 800 900 1000
0
25
5
75
10
125
15
175
20
0
25
5
75
10
125
15
175
20
0
2
4
6
8
12
10
450
400
350
300
250
200
150
100
50
0
225
Visc
osity
(Pamiddot
s)
Figure 4 Shear rate step flow test
The verified experiment was carried out and the resultwas shown in Figures 4 and 5
In the shear rate sweep test the time and shear rate areknown Therefore the strain can be calculated by shear rateand time The above parameters were taken into (14) and thepredict result was shown in Figure 5
Viscosity-shear rate curve of starch solution was shownin Figure 6
It indicates that the viscosity of starch solution willbecome thin with the shear rate increasing
The predicted results indicate that the material functionconstructed with memory function describes the flow behav-ior during the shear rate step test The shape of predicts
4 Mathematical Problems in Engineering
Calculated dataMeasurement data
Shea
r stre
ss (p
a)
Shear rate
25
20
15
10
5
00 1 2 3 4 5 6 7 8 9 10
Figure 5 Predicted result of shear stress during the shear rate sweeptest
Calculated dataMeasurement data
Shear rate
25
20
15
10
5
00 1 2 3 4 5 6 7 8 9 10
Visc
osity
(Pamiddot
s)
Figure 6 Viscosity-shear rate curve
line based on the material function was very similar to theshape of measured data lineWhen the shear rate increases toinfinite both the predicted data and test data are close to thesame value
5 Conclusion
The memory function of starch solution can be constructedby the shear relaxation test Based on the memory functionthe material function of starch solution was established topredict the shear stress and viscosity during the steady shearflow The predicted result shows that the material functioncan be used to describe the behavior of starch solution duringthe shear process
Acknowledgment
This work was supported by the Fundamental ResearchFunds for the Central Universities under Grant noJUSRP11203
References
[1] D Eidam W M Kulicke K Kuhn and R Stute ldquoFormationof maize starch gels selectively regulated by the addition ofhydrocolloidsrdquo Starch vol 47 pp 378ndash384 1995
[2] L Quintieri A Monteverde and L Caputo ldquoChanges inprolamin and high resistant starch composition during the pro-duction process of Boza a traditional cereal-based beveragerdquoEuropean FoodResearch andTechnology vol 235 no 4 pp 699ndash709 2012
[3] L Duo and G Dan ldquoImplementing high weight measurementprecision in package machines by using 8031 single chip micro-computerrdquo Journal of Tianjin University of Commence vol 4 pp8ndash14 1994
[4] C Luo ldquoThe calculation of the solid conveying volumetric ratioflow rate of the food extruderrdquo Packaging and Food Machineryvol 26 no 2 pp 30ndash32 2008
[5] J F Steffe Rheological Methods in Food Process EngineeringFreeman Press East Lansing Mich USA 1996
[6] A S Lodge Elastic Liquids Academic Press London UK 1964[7] A S Lodge and J Meissner ldquoComparison of network theory
predictions with stresstime data in shear and elongation for alow-density polyethylene meltrdquo Rheologica Acta vol 12 no 1pp 41ndash47 1973
[8] M Sugimoto Y Masubuchi J Takimoto and K KoyamaldquoMelt rheology of polypropylene containing small amounts ofhigh molecular weight chain I Shear flowrdquo Journal of PolymerScience B vol 39 no 21 pp 2692ndash2704 2001
[9] M H Wagner ldquoAnalysis of time-dependent non-linear stress-growth data for shear and elongational flow of a low-densitybranched polyethylene meltrdquo Rheologica Acta vol 15 no 2 pp136ndash142 1976
[10] M H Wagner ldquoPrediction of primary normal stress differencefrom shear viscosity data using a single integral constitutiveequationrdquo Rheologica Acta vol 16 no 1 pp 43ndash50 1977
[11] J H Yu P H S Santos and O H Campanella ldquoA study tocharacterize the mechanical behavior of semi-solid viscoelasticsystems under compression chewing case study of agar gelrdquoJournal of Texture Studies vol 43 no 6 pp 459ndash467 2012
[12] J D Ferry Viscoelastic Properties of Polymers John Wiley ampSons New York NY USA 1980
[13] K Osaki ldquoOn the damping function of shear relaxation modu-lus for entangled polymersrdquo Rheologica Acta vol 32 no 5 pp429ndash437 1993
[14] Q Zheng W Wang Q Yu J Yu L He and H Tan ldquoNon-linear viscoelastic behavior of styrene-[ethylene-(ethylene-propylene)]- styrene block copolymerrdquo Journal of PolymerScience B vol 44 no 9 pp 1309ndash1319 2006
[15] F A Morrison Understanding Rheology Oxford universitypress New York NY USA 2001
[16] W Wang Z Lu Y Cao J Chen J Wang and Q ZhengldquoInvestigation and prediction on the nonlinear viscoelasticbehaviors of nylon1212 toughened with elastomerrdquo Journal ofApplied Polymer Science vol 123 no 3 pp 1283ndash1292 2012
Mathematical Problems in Engineering 5
[17] H Watanabe T Sato K Osaki et al ldquoRheological images ofpoly(vinyl chloride) gels 4 Nonlinear behavior in a critical gelstaterdquoMacromolecules vol 31 no 13 pp 4198ndash4204 1998
Figure 5 Predicted result of shear stress during the shear rate sweeptest
Calculated dataMeasurement data
Shear rate
25
20
15
10
5
00 1 2 3 4 5 6 7 8 9 10
Visc
osity
(Pamiddot
s)
Figure 6 Viscosity-shear rate curve
line based on the material function was very similar to theshape of measured data lineWhen the shear rate increases toinfinite both the predicted data and test data are close to thesame value
5 Conclusion
The memory function of starch solution can be constructedby the shear relaxation test Based on the memory functionthe material function of starch solution was established topredict the shear stress and viscosity during the steady shearflow The predicted result shows that the material functioncan be used to describe the behavior of starch solution duringthe shear process
Acknowledgment
This work was supported by the Fundamental ResearchFunds for the Central Universities under Grant noJUSRP11203
References
[1] D Eidam W M Kulicke K Kuhn and R Stute ldquoFormationof maize starch gels selectively regulated by the addition ofhydrocolloidsrdquo Starch vol 47 pp 378ndash384 1995
[2] L Quintieri A Monteverde and L Caputo ldquoChanges inprolamin and high resistant starch composition during the pro-duction process of Boza a traditional cereal-based beveragerdquoEuropean FoodResearch andTechnology vol 235 no 4 pp 699ndash709 2012
[3] L Duo and G Dan ldquoImplementing high weight measurementprecision in package machines by using 8031 single chip micro-computerrdquo Journal of Tianjin University of Commence vol 4 pp8ndash14 1994
[4] C Luo ldquoThe calculation of the solid conveying volumetric ratioflow rate of the food extruderrdquo Packaging and Food Machineryvol 26 no 2 pp 30ndash32 2008
[5] J F Steffe Rheological Methods in Food Process EngineeringFreeman Press East Lansing Mich USA 1996
[6] A S Lodge Elastic Liquids Academic Press London UK 1964[7] A S Lodge and J Meissner ldquoComparison of network theory
predictions with stresstime data in shear and elongation for alow-density polyethylene meltrdquo Rheologica Acta vol 12 no 1pp 41ndash47 1973
[8] M Sugimoto Y Masubuchi J Takimoto and K KoyamaldquoMelt rheology of polypropylene containing small amounts ofhigh molecular weight chain I Shear flowrdquo Journal of PolymerScience B vol 39 no 21 pp 2692ndash2704 2001
[9] M H Wagner ldquoAnalysis of time-dependent non-linear stress-growth data for shear and elongational flow of a low-densitybranched polyethylene meltrdquo Rheologica Acta vol 15 no 2 pp136ndash142 1976
[10] M H Wagner ldquoPrediction of primary normal stress differencefrom shear viscosity data using a single integral constitutiveequationrdquo Rheologica Acta vol 16 no 1 pp 43ndash50 1977
[11] J H Yu P H S Santos and O H Campanella ldquoA study tocharacterize the mechanical behavior of semi-solid viscoelasticsystems under compression chewing case study of agar gelrdquoJournal of Texture Studies vol 43 no 6 pp 459ndash467 2012
[12] J D Ferry Viscoelastic Properties of Polymers John Wiley ampSons New York NY USA 1980
[13] K Osaki ldquoOn the damping function of shear relaxation modu-lus for entangled polymersrdquo Rheologica Acta vol 32 no 5 pp429ndash437 1993
[14] Q Zheng W Wang Q Yu J Yu L He and H Tan ldquoNon-linear viscoelastic behavior of styrene-[ethylene-(ethylene-propylene)]- styrene block copolymerrdquo Journal of PolymerScience B vol 44 no 9 pp 1309ndash1319 2006
[15] F A Morrison Understanding Rheology Oxford universitypress New York NY USA 2001
[16] W Wang Z Lu Y Cao J Chen J Wang and Q ZhengldquoInvestigation and prediction on the nonlinear viscoelasticbehaviors of nylon1212 toughened with elastomerrdquo Journal ofApplied Polymer Science vol 123 no 3 pp 1283ndash1292 2012
Mathematical Problems in Engineering 5
[17] H Watanabe T Sato K Osaki et al ldquoRheological images ofpoly(vinyl chloride) gels 4 Nonlinear behavior in a critical gelstaterdquoMacromolecules vol 31 no 13 pp 4198ndash4204 1998
[17] H Watanabe T Sato K Osaki et al ldquoRheological images ofpoly(vinyl chloride) gels 4 Nonlinear behavior in a critical gelstaterdquoMacromolecules vol 31 no 13 pp 4198ndash4204 1998
