du x Theory Viscosity is a measure of resistance to flow. [1] Figure 1 illustrates this. F A d y

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1 F Compariso of differet methods to characterize the rheological behaviour of complex foods Master Thesis i Chemical Egieerig, Lud Uiversity, 200 Aette Juldorf Abstract I this article the viscosity is measured for a simple Newtoia fluid ad complex shear-thiig fluids with cocetric cyliders, mixers ad a capillary viscometer. The Newtoia fluid is White Syrup ad the complex fluids are tomato paste ad a model suspesio similar to tomato paste. The results show that it is difficult dealig with fluids cotaiig fibres. The tomato paste gave varyig results, both whe comparig all the viscometers as whe comparig differet measurig occasios. The reasos for the varyig results were probably due to the effect of wall shearig ad wall slip o the fluids. Besides the orietatio of the fibres ad air bubbles i the fluids probably iflueced the results. The best results from the capillary viscometer were those made with the shortest ad widest capillaries. A sythetic model fluid cosistig of xatha gum, starch ad fibres was developed. This model fluid showed the same behaviour as tomato paste, as far as they could be compared due to the varyig results of tomato paste. Itroductio The aim of this thesis was to measure the viscosity of tomato paste with differet viscometers i order to be able to choose the best ad most reliable method for the viscosity measuremet. Aother goal was to try to make a model fluid, which should have the same properties as tomato paste. The model fluid should preferably be able to be reproduced ad used istead of tomato paste. The traditioal viscometers such as the cocetric cylider ad coe ad plate are ot suitable to use whe measurig the viscosity of fluids cotaiig fibres. The process idustry though do ot oly eed the viscosity values of simple Newtoia fluids but also of all fluids cotaiig for istace fibres ad suspeded particles, which are commo i the food idustry. The viscosities of these products are importat whe desigig process equipmet such as heat exchagers, pumps ad agitators so that they are ot oversized. Theory Viscosity is a measure of resistace to flow. [] Figure illustrates this. d y Figure A y du x x Two plates with the area A cotai a thi layer of fluid. The bottom plate does ot move, while the top plate is forced to move because of the force F [N]. The shear stress is defied as F A [N/m 2 ]. The upper plate is movig with the velocity du x [m/s]. The shear rate is defied as the velocity gradiet du x dy [s - ]. If the shear stress ad the shear rate are kow the dyamic viscosity ca be calculated as [Pa s]. This type of viscosity is called either shear viscosity or absolute viscosity. The absolute viscosity is maily depedet o shear rate, the time at which it has bee sheared ad temperature. [2] Fluids ca be divided i two groups, Newtoia ad o-newtoia fluids. Newtoia fluids are simple fluids for which the viscosity does ot vary with shear rate. The oly stress geerated is the shear stress ad if the shearig is stopped the viscosity is costat ad the shear stress falls to zero. All fluids that do ot follow the behaviour metioed above are o-newtoia. No- Newtoia fluids ca be divided ito timedepedet fluids, time-idepedet fluids ad viscoelastic fluids. These groups also have subgroups. This thesis will study the behaviour of tomato paste, which is a time-idepedet fluid. Time-idepedet fluids ca either follow the Ostwald de Waele model, also called the power law or be Bigham plastic. The power

2 law, Equatio, follows the behaviour of tomato paste. du x K [N/m 2 ] (Equatio ) dy The factor K [Pa s ] is the cosistecy idex or power law coefficiet ad [-] is the power law expoet. For Newtoia flow is equal to oe ad K equals the viscosity. For shear-thiig fluids is less tha oe while it is bigger tha oe for shear-thickeig fluids. [] [2] Havig particles i a fluid will affect its viscosity. It is ot uusual for wall-slip to occur if there are particles i the fluid. The viscosity chages with cocetratio. Decreasig the particle size will usually icrease the viscosity. Suspesios with a broader size distributio usually have a lower viscosity sice the smaller particles ca fit ito the gaps betwee the bigger oes. The thickeig effect of particles follows the descedig order: rods > plates > cubes/grais > spheres, if addig the same phase volume ad cosiderig their shape. [] [] There are two differet categories of istrumets measurig the rheological behaviour; rotatioal type ad tube type. The viscometers used i this thesis are cocetric cyliders ad mixers, which are of the rotatioal type, ad the high pressure capillary is a tube type viscometer. Capillary viscometers are the most commoly used istrumet for measurig viscosity because of its simplicity, low cost ad accuracy. There are two differet set ups for the cocetric cylider, either is the bob rotatig ad the cup statioary or is the bob statioary ad the cup rotatig. The distace betwee the cup ad cylider should be arrow but there might be problems if the particles are larger tha the gap. [] Mixer viscometers are useful to food egieerig for complex fluids, which are associated with slip, time-depedet behaviour, large particles ad particle settlig. Examples of mixers are the paddle ad helix. [4] [] Equipmet ad materials All viscosity measuremets performed with the rotatioal viscometer was carried out with a Physica MC rheometer. The measurig istrumets used were three cocetric cyliders; Z2 DIN (4 mm), Z DIN (2 mm) ad Z4 DIN (4 mm), oe helix ad oe paddle. The highpressure capillary viscometer was equipped with eight differet capillaries. The Newtoia fluids used for calibratio was Viscosity Referece Stadard oil D 000 ad White Syrup (Daisco Sugar AB). The tomato paste was of the brad Golde Pheasat. The model that seemed to be most equal to tomato paste was a mixture of 2% Keltrol xatha gum (CPKelco), 0.% Prejel VA70 S (AVEBE Stadex), % fibres (Fibrex, Daisco Sugar AB) ad 86.% water. Results ad discussio Three differet fluids have bee evaluated with three types of viscometers. The first fluid used was the White Syrup, which was meat to work as a kid of referece. Due to the fact that if syrup did ot give ay good results either would the other two fluids sice the tomato ad model fluid are of more complicated ature. The measuremets started with the capillary viscometer, the the cocetric cylider viscometers were used ad fially the samples were evaluated with the mixer viscometers. The tomato paste ad the model fluid had to be pumped ito the vessel because of their cosistecy. This meat that there might get some water i the sample sice the pump had to start with pumpig water to be able to pump the more hard flowig fluids. Sice tomato paste was measured at four differet occasios there might be a differet amout of water i the sample at each occasio. Capillary viscometer K ad are calculated from collected data. For time-idepedet fluids i lamiar flow, i a tube, the followig equatio ca be used. p r 2 L ' 4 Q K' r p r 2 L 4 Q r If the logarithm of logarithm of is plotted versus the the the ad K values ca be determied. For power law fluids ' ad K' K. [4] 4 The values were as they should be, very close to oe for White Syrup. Ay varyig results might be because of the great temperature depedece of White Syrup. The tomato paste was measured at four differet days. The days will i this thesis be referred to as differet occasios. The results of oe of the 2

3 occasios ca be studied i Figure 2 ad Table. The ad K values differ both betwee the capillaries ad amog the differet occasios. The values caot be compared as lookig at oly or K. They are obtaied i pair ad have to be compared together. The viscosity has bee calculated ad by studyig these values the ad K ca be compared. The viscosity is always decreasig as the shear rate is icreased ad this shows that tomato paste is a shear-thiig fluid. 000 dpr/(2l) (Pa) Q/(pi*r^) (/s) L=, r=0,004 L=,, r=0,004 L=,, L=,, r=0,002 L=, r=0,002 r=0,00 Figure 2 Usig the power law to get ad K for the capillaries for tomato paste. L (m) r (m) (-) K (Pa s^) shear rate (/s) viscosity (Pa s) Table The ad K values as well as the viscosity for differet shear rates. The results of the model fluid were similar to those of tomato paste. Cocetric cylider viscometer All the fluids were measured with the three measurig systems, Z2 DIN (4 mm), Z DIN (2 mm) ad Z4 DIN (4 mm), after the fluids hade passed through the capillaries several times. The viscosity of White Syrup was costat whe raisig the shear rate. The value was very close to oe for Z ad Z4 while Z2 was ot suited to measure syrup. Tomato paste has bee measured for several occasios with varyig results each time. The results also kept chagig durig the day util the tomato reached some kid of equilibrium after a umber of tests. This occurred eve though the tomato paste hade already bee mechaically worked up i the capillary viscometer. The reaso is probably that the fibres will orietate themselves alog the flow or that wall-slip has occurred. Oe reaso why the results vary betwee the days may be differet amouts of water i the fluid. The model fluid showed similar results to those of the tomato paste. Mixer viscometers For White Syrup the helix ad paddle gave results that correspoded with the results give for the cocetric cylider. The reaso that the results show similar results for White Syrup but ot for tomato paste ad the model fluid is that the mixers have bee calibrated with Viscosity Stadard Oil which is Newtoia. The results from the helix ad paddle are therefore ot correspodig to the results from the cocetric cyliders for o-newtoia fluids. Because of this a costat k ca be evaluated which is a mixer viscometer costat havig uits of /rev. [4] Agai the results of the tomato paste ad the model fluid were differet from oe measuremet to aother. The results of two occasios for tomato paste ca be see i Table 2 ad the results of the model fluid are show i Table. If the k values for tomato paste are compared to those of the model fluid it is hard to say if the model fluid ca be approved sice the values of tomato are so varyig. System (-) K (Pa s ) k' (/rev) Occasio helix helix paddle paddle Table 2, K ad k values for tomato paste at two occasios. System (-) K (Pa s^) k' (/rev) helix paddle Table, K ad k values for model fluid.

4 Pressure quotiet The results of the cocetric cylider viscometer was compared to the results from the capillary viscometer by defiig a pressure quotiet quotiet calculated pressure differece for capillary viscometer with ad K obtaied from rotatioal viscometer read pressure differece from capillary viscometer The cocetric viscometer, Z DIN (2mm), was used as referece. Its viscosity, ad K values at the correct temperature were used to calculate the pressure differece for the capillary viscometer. The formulas used were Newtoia fluid: p D L No Newtoia fluid: 2 Q 4 D p D 2 Q K 4 L 4 D The results were preseted by plottig the pressure quotiets versus the pressure for the differet capillaries. The results of White Syrup ca be see i Figure. The quotiets are ufortuately ot oe, which they should have bee for a Newtoia fluid. cdp/dp (-),4,2 0,E+0 0 2,E+0 4,E+0 dp (Pa) 6,E+0 L=, r=0.004 L=, r=0.002 L=., r= L=., r=0.004 L=, r=0.002 L=., r=0.004 Figure Pressure quotiets versus pressure for White Syrup Tomato paste had very differig results from oe occasio to aother ad betwee the differet capillaries. The results from oe occasio ca be see i Figure 4. The best results are the oes made with the largest radius ad shortest legth of the capillary. The reaso is probably that there will be more wall shearig, possibilities for wall slip ad ifluece of the fibres i the loger capillaries. This theory ca also be applied to why the larger diameter gives the best results. cdp/dp 2,6 2,2,8,4 0, dp(pa) L=, r=0,004 L=,, r=0,004 L=,, L=,, r=0,002 L=, r=0,002 r=0 00 Figure 4 Pressure quotiets versus pressure for tomato paste with =0.2 ad K=09.2. The results of the model fluid look similar to those of the tomato paste. Also here are the best results the oes from the capillaries with the largest radius ad the shortest legth. If lookig at Figure it ca be see that it does ot matter i which order the capillaries are used. The test was started ad fiished with the same capillary ad these measuremets gave the same results, which meas that the fluid is ot oticeable broke dow by the capillary viscometer. cdp/dp,8,4 0, dp(pa) L=, r=0,004 L=,, r=0,004 L=, r=0,002 L=,, r=0,002 L=,, r=0,00 Figure Pressure quotiets versus pressure for model fluid with =0.24 ad K=86. The reaso that the pressure quotiet differs from oe might be Pressure losses due to etrace effects. Differet ad K values achieved with the rotatioal viscometer. Differet shear rate itervals. Temperature depedecy. Not so accurate measuremets. The complicated behaviour of the fluids cotaiig fibers. Coclusios It is complicated dealig with fluids cotaiig fibres. The results of these fluids varied both betwee differet samples of the same fluid ad betwee measuremets performed just after each other o the same sample. The reasos for the varyig results were probably because of the effect wall shearig ad wall slip had o the fluids ad also orietatio of the fibres ad air bubbles i the fluids. 4

5 If comparig the capillary viscometer to Z DIN the best results were achieved with the capillaries havig the largest diameter ad the shortest legth. The helix ad paddle must be calibrated for the type of fluid they are goig to measure if the results shall be compared with the results of the cocetric cyliders or the capillary viscometer. If they are ot calibrated a costat k ca be calculated, which ca be used to compare the same sort of fluids for a specific system. It was hard to tell if the model fluid could replace tomato paste sice the tomato paste showed so varyig results. The results betwee the tomato ad the model did ot differ more tha the results of tomato paste itself. The aim withi this thesis was to fabricate a model that ca replace tomato paste, could seem to be fulfilled. Nomeclature A Area [m 2 ] D Diameter [m] F Force [N] L Legth [m] K Costistecy idex [Pa s ] k Metzer-Otto parameter [/rev] Power law expoet [-] p Pressure [Pa] Q Volumetric flow rate[m /s] r Radius [m] Shear rate [s - ] Viscosity [Pa s] Shear stress [N/m 2 ] Refereces [] Bares H. A., Hutto J. F., Walters K., A itroductio to Rheology, 989. [2] Perry Robert H, Gree Do W., Perry s Chemical Egieer s Hadbook, 4 th editio, 997, chapter 6. [] Bares Howard A., Viscosity, Istitute of No-Newtoia Fluid Mechaics, Uiversity of Wales, [4] Steffe James F., Rheological Methods i Food Process Egieerig, 992. [] Eriksso Igrid, Utvärderig av e helixspidel för viskositetsmätigar på flytade partikulära livsmedel, Departmet of Chemical Egieerig, 200. Ackowledgemets This Master Thesis was made as a co-operatio betwee Tetra Pak ad the Departmet of Chemical Egieerig at Lud Uiversity. I would like to thak my supervisors Ulf Bolmstedt (Tetra Pak) ad Aders Axelsso (Departmet of Chemical Egieerig) for their guidace ad help throughout the work.