ࡱ> 1 &'()*Oh+'0 4 DP l x  @Physical properties of concentrated solutions of soluble coffeehys vsobolikprosobsob Normal.dotoPC-418d9-4Microsoft Word 8.0 @@#@.#@NRK%m #A՜.+,D՜.+,l( hp|   c!O1 @Physical properties of concentrated solutions of soluble coffee Title 6> _PID_GUIDAN{082451D9-0B04-11D4-9133-00C04F32355E}Viscosity and electrical conductivity of concentrated solutions of soluble coffee V.Sobolk 1, V.Tovcigrecko 2, M.Delgado1, R.}itn 3, K.Allaf 1 1 LMTAI, University of La Rochelle, Av. Michel Crepeau, 17042 La Rochelle, France e-mail: vsobolik@univ-lr.fr, kallaf @univ-lr.fr 2 Institute of Chemical Process Fundamentals, Academy of Sciences of the Czech Republic, Rozvojov 135, 16502 Prague 6, e-mail: tovcigrecko@icpf.cas.cz 3 Institute of Process Engineering, Czech Technical University, Technick 4, 16000 Prague 6, e-mail: zitny@fsid.cvut.cz Abstract Viscosity of concentrated solutions (w = 0.5-0.8) of soluble coffee was measured in the temperature range 25 - 95C. After homogenisation, the rheological behaviour was found to be Newtonian. The viscosity was correlated by a five parameter function of concentration and absolute temperature. Specific electrical conductivity of coffee solutions in water (w = 0 - 0.8) was measured in the temperature range 25  72C. A seven parameter model based on the assumption that the solution is composed of a partially dissociated species and water describes very well the measured data. Modified Casteel-Amis model equation has been identified for comparison. The conductivity dependence on concentration exhibits maxima which are the more shifted towards higher concentrations the higher is the temperature. Introduction Coffee is composed of more than 700 components. Purine alkaloids (caffeine etc.), minerals, bases, chlorogenic acids, lipids, aliphatic acids and carbohydrates (arabinose, sucrose etc.) and amino acids (tryptophan) are some of them [1]. The data on physical properties of the aqueous solutions of soluble coffee are scarce although the world production is very important and the coffee extracts enjoy extensive consumer market. The manufacturers guard probably the confidentiality of processing. We have found only one paper [2] which deals with the viscosity of aqueous coffee solutions. In this paper, the viscosity, surface tension, thermal conductivity, index of refraction and the freezing curves were measured in the solutions with coffee mass fraction 00.5. Different mixtures were examined of several coffee sorts prepared either by freeze drying (Vox Mocca, Vox Robusta) or by spray drying (Nescaf Gold, Maxwell Exquisit). As the paper [2] is written in Czech, the most important results are summarised in the following paragraphs. The dependence of the refractivity index on the coffee mass fraction w was expressed by the relation: At w=0.5, the refractivity indexes of the coffee and sucrose are about 1.44 and 1.42, respectively. It is difficult to measure the refractivity index of more concentrated coffee solutions because the dark brown colour hinders in scale observation. The density was calculated from the density of water rW and the true density of the solid coffee rC: where rW = 1000 - 0.036T - 0.004T 2 and rC= 1654 - 1.79T - 0.0063 T 2. The difference in the densities of the coffee and sucrose is about 1% at w=0.5. The flow curves were measured by a rotational viscometer Haake. The rheological behaviour was characterised as slightly pseudoplastic and thixotropic. The values of the limiting viscosity h( are also given, i.e. the values which did not change with increasing shear rate. The viscosity increased non recoverably when the solution was stored for a longer time. This fact was explained by swelling of high molecular substances which are present in the coffee. Weisser did not found any important difference in viscosity of different sort of coffee prepared either by spray drying or by freeze drying. Due to presence of surface active substances, the surface tension of coffee solutions was found to be smaller than that one of water. For w > 0.1, the surface tension was equal to 0.042 N.m-1 at 20C and 0.037 N.m-1 at 40C. The thermal conductivity of coffee solutions was found to be the same as the conductivity of sucrose solutions. It was described by the relation: Intensification of soluble coffee production requires the treatment of more concentrated solutions. The present paper focuses on the properties, which are important for ohmic heating and treatment of highly concentrated coffee solutions, i.e. viscosity and electric conductivity. The coffee studied was a freeze dried mixture of 65% coffee arabica (Colombia) and 35 % coffee robusta (Brazil), sold under the mark Caf filtr by Carrefour (France). 1 Viscosity The dependencies of shear stress on shear rate [3] were measured in a controlled rate viscometer Rheotest II, (VEB Prfgerte, Medingen, Germany). Two different geometry were used consisting of one external cup with a diameter of 40 mm and two internal cylinders, S1 and S2 with diameters 39.2 and 37.6 mm and a length of 72 mm. The temperature of the external cup and hence of the sample was controlled by a water circulator. Solutions with coffee mass fraction w=0.5  0.8 in tap water were examined in a temperature range of 2595C. The samples with the lower concentrations, w<0.75, were prepared in a glass beaker whereas the more concentrated samples were mixed directly in the viscometer cup. The preparation was similar in both cases. The dry coffee was poured into water with a temperature of 25C. The sample was then agitated with a glass bar and heated to 70C. The stainless steel viscometer cup was preheated to 60C before it was filled with a prepared sample. The cup was then pressed onto the measuring cylinder. A thin plastic disc covered the sample surface with the aim to diminish water evaporation. By means of the external cup, the sample was then cooled to the low temperature at which the viscosity measurements started. The torque was measured at shear rates going from the minimum to the maximum one and reverse. The temperature was then increased to the next one and measurements were done at increasing and then decreasing shear rate. After reaching the maximum temperature of 95C, the measurements were repeated at decreasing temperature steps. The measurements of one sample took about 4 hours. The flow curves measured immediately after the sample preparation, i.e. in the series with increasing temperature, exhibited slightly pseudoplastic behaviour with the flow index of about 0.9 and a higher apparent viscosity than the curves measured some time later after passing the maximum temperature of 95C. The latter curves exhibited Newtonian behaviour. An example of primary data is shown in Fig.1. This difference in flow behaviour can be explained by the presence either of larger molecules or of solid particles during the first phase. The concentrated solution of coffee extract needs a higher temperature (90-95C) or a longer exposition to shear rate to become homogeneous or to destroy the large molecules. The data presented in this paper correspond to the viscosity measured in the second phase after passing 95C. The measurements were done until the maximum shear rates shown in Fig.2. The range of the shear rate applied in the measurements lies below the corresponding lines. For example the dotted area represents the range for w = 0.8. The shear rate was limited either by the maximum rotational rate or by the maximum torque, which can be achieved in the viscometer. For w = 0.5, this limit was the maximum shear rate generated by the largest cylinder S1 (smallest gap). The value of the shear rate in this case is equal to 1574 s-1. For the solutions with higher viscosity, w>0.5, the limiting factor was the maximum torque and the smaller cylinder S2 (larger gap) has to be used. For this geometry, the maximum shear rate is equal to 455 s-1 . The viscosity dependence on the absolute temperature and concentration is shown in Fig.3. For w((0.5-0.8), the viscosity was fitted by the relation  The maximum error of viscosity evaluation using this relation was estimated to be less then 15 %. The viscosity measured by Weisser [2] for w = 0.5 is shown by the open diamond symbols. It does not exhibit great deviations from our measurements. For 60C, we determined 0.019 Pa.s whereas Weisser has found 0.024 Pa.s. This quite good agreement confirms the conclusion of paper [2] that the viscosity is almost independent of the coffee sort and its treatment. With the aim to extend the range of viscosity dependence also for low concentrations, w ((0-0.5), the results of paper [2] are shown in Fig. 4. The best fit of these data is by the relation 2 Specific electrical conductivity 2.1 Model design Specific electric conductivity of electrolytes ( [S.m-1] depends upon concentration, mutual interactions and mobility of ions. It is known that increasing viscosity decreases conductivity, nevertheless our attempt to correlate viscosity and conductivity of the coffee solutions failed totally. Some theoretical results originated from Debye-Hckel theory can be applied for weak electrolytes [4], but for concentrated electrolytes empirical models, e.g. normal distribution of ((() or models of the form ((()=a(() exp[b(()], are usually preferred[5]. A new empirical model describing the temperature and concentration dependency of specific electrical conductivity is based on the idea, that the coffee solution is composed of water having conductivity (w [S.m-1], dissociated coffee species with conductivity (c and non dissociated species which is an insulator. It is assumed than the amount of dissociated species is proportional to the mass fraction of coffee, (, and also to the mass fraction of water, 1-(,  EMBED Equation.2  EMBED Equation.2 . (6) Experiments indicate that the conductivity of concentrated coffee depends strongly on temperature and therefore we shall assume linear relationship for approximation of (c(T), while temperature dependency of tap water will be neglected in view of the fact, that (w is very small. Combining specific electrical conductivity of three components (non dissociated species insulator, water, and dissociated species) according to a simple model of parallel resistors, we obtain  EMBED Equation.2  (7) This model is not able to describe the experimental data properly with a constant exponent m which must be considered as a function of temperature and concentration, m(T,(). The following quite empirical Eq.(8) will be used for processing data, exhibiting a slight change of trends at concentration (c  EMBED Equation.2  . (8) The resulting model is rather complicated 7-parametric relation  EMBED Equation.2   EMBED Equation.2  (9) The proposed model (9) will be compared with the Casteel-Amis equation for ((c, T) modified by Diego [5] by inclusion of temperature. The Diego's model is based on fitting of maximum conductivity (max at the corresponding concentration cmax . The following Eq.(10) differs from the original Diego's model only by replacing concentration c with the mass fraction (:  EMBED Equation.2 . (10) The modified Casteel-Amis equation has 6 parameters, (max0, (max1, (max0, (max1, x, y and only two of them, (max0, (max1, are linear. In view of the fact, that the predicted conductivity equals zero for (=0, the model (10) cannot describe the conductivity of pure water. 2.2 Experimental results and model identification The specific electrical conductivity was measured by the conductivity probe LF 340 TetraCon 325/S, (Wissenschaftlich-Technische Werkstatten GmbH, Weilheim, Germany) suitable for highly viscous materials and pastes. The probe is composed of four graphite electrodes and a thermometer embedded in an epoxy casing. The electrodes are flush mounted in an axial groove. Dimensions of the probe and the amount of coffee sample follow from Fig.5. The samples were prepared by mixing the coffee extract with a cold tap water in a beaker which was then immersed in water heated to 80C. The homogenous sample was then filled into a small cylindrical glass cup and the probe was immersed into the sample. The temperature of the cup was controlled by a water circulator. The measurements started at the low temperature (25C) and continued until 72C. The range of temperature and concentration is shown in Fig.6. Approximately 50 values of the conductivity were recorded for each concentration at different temperatures. The simplest approach of modelling is based upon the quadratic approximation of temperature dependence evaluated separately for each measured concentration (i (i (T) = p0i + p1iT + p2iT2 (11) Identification of the coefficients p0i, p1i, p2i by linear regression was done with a relative standard deviation smaller than 1.5%. The results are summarised in Tab.1. Parameters of model (9), (c0, (c1, (w, a, b, c, (c, were identified by nonlinear regression (in house program XREGA), minimising sum of squares of deviations from 542 observation points (Ti, ( i , (i), see Tab.2. Interpretation and reliability of more or less empirical model with such a high number of parameters is always questionable, however, confidence intervals of all parameters calculated from covariance matrix are sufficiently narrow (see Tab.2) and some predicted values can be verified directly: For example (w=0.05 S.m-1 corresponds rather well to the electric conductivity of tap water (~0.043 S.m-1 at 500C) and ( c=0.454 visually fits the mass fraction characterising sudden change of trends at higher temperatures, see Fig.7. All parameters have correct sign, and for example the negative sign of the parameter c ensures not only a progressive increase of conductivity with temperature at a constant (, but also an observed mild shift of maxima ((() towards higher concentration with increasing temperature. It seems that physical relevance of parameters would allow a slight extrapolation of conductivity to higher temperatures, may be up to 900C. Exactly the same procedure and primary data were used for identification of modified Casteel-Amis model (10), and results are presented also in the Tab 2. This model approximates experimental data rather well, describes all trends, confidence intervals of parameters are acceptable, nevertheless basic statistics of errors are significantly worse in comparison with the suggested model (9). Adding the term (w(1-() to the model (10) had no significant influence upon the standard deviation (in fact unbiased estimate was slightly higher, (=0.099 S.m-1, because the number of parameters had been increased from six to seven). 3 Conclusions Immediately after preparation of the coffee solution, its rheological behaviour was slightly pseudoplastic with a flow index about0.9. After some time of the shear application in the viscometer and passing a temperature of 95C, the coffee solutions became Newtonian in the range of measured shear rates (10( g ( 1574 s-1). The viscosity dependence on temperature and concentration was described by a five parameter relation. The estimated error of viscosity measurements was about 15%. It is not bad result with respect to the inherent experimental difficulties with handling concentrated coffee solutions (swelling, caramelisation, evaporation etc.). Quite good agreement with the viscosity data measured by Weisser [2] confirmed that the coffee viscosity does not depend much on the coffee sort and the way of the coffee drying and treatment. The specific electrical conductivity was described by a seven parameter model based on the idea that the amount of dissociated coffee molecules is proportional to the coffee mass fraction and water mass fraction. This model describes the conductivity with a standard deviation of 0.062 [S.m-1] which is much lower than the standard deviation of the modified Casteel-Amis model ((=0.098 S.m-1). The specific electrical conductivity exhibits maxima at concentrations about w=0.35. The higher temperature the greater is the shift of the maximum towards higher concentration. The maximum electric conductivity of coffee solution is about 40 times higher then the conductivity of tap water at the same temperature. The viscosity and specific electrical conductivity data obtained in this article render possible the design of apparatuses for the treatment of highly concentrated coffee extracts. Acknowledgements: This research has been subsidized by the Research project of Ministry of Education of the Czech Republic J04/98:21220008. References: Caffeine, coffee, and health. (Ed. Silvio Garattini),: Raven Press, New York, 1993. Weisser H.: Measurements of physical properties of solutions of coffee extract (in Czech), PotravinYsk a chladc technika 3, 136-138 (1972). Bird R.B., Armstrong R.C., Hassager O.: Dynamics of polymeric liquids, Volume 1 Fluid mechanics, John Wiley & Sons, 1987. Koryta J. et al: Theory of electrolytes (in Czech), CSAV, No.7, Academia Praha, 1976. De Diego A., Madariaga J.M., Chapela E.: Empirical model of general application to fit ((, c, T) experimental data from concentrated aqueous electrolyte solutions, Electrochemica Acta, Vol.42, No.9, pp.1449-1456, (1997) Notation a, b, c parameters in Eqs.(8 and 9) k number of model parameters nD20 refraction index (yellow Na light at 20oC) N number of data pji parameters in Eq.(11) R correlation coefficient, T temperature [C] x, y parameters of modified Casteel-Amis model, Eq.(10), [-] g shear rate [s-1] k specific electrical conductivity [S.m-1] mean value specific electrical conductivity [S.m-1] kij parameters in Eqs.(9) l thermal conductivity [W.m-1.C-1] m viscosity [Pa.s] r density [kg.m-3] w coffee mass fraction [kg dry coffee/ kg solution] s standard deviation [S.m-1] , t shear stress [Pa] Figure captions Fig.1 Flow curves of coffee solutions, w=0.7, at 40C measurements immediately after sample preparation measurements after 2 hours after passing 95C Fig.2 Range of measured shear rates Fig.3 Dependence of viscosity on temperature and concentration for concentrated coffee solutions w : - 0.5, - 0.6, - 0.66, - 0.7, - 0.74, - 0.8,  - data [2] for w =0.5 Fig.4 Dependence of viscosity on temperature and concentration for coffee solutions with low concentration [2] w : - 0, - 0.1, - 0.2, - 0.3, - 0.4, - 0.5 Fig.5 Experimental set-up for conductivity measurements a) front view, b) cut of side view 1 conductivity probe, 2 electrodes, 3 cup, 4 cap, 5 - sample. Dimensions are in millimetres. Fig.6 Range of measured specific electrical conductivity Fig.7 Specific electrical conductivity as function of mass fraction and temperature T: - 30, - 40, - 50, - 60, - 70C Small open rectangles stand for temperatures which differ by 1 and 2C from the rated temperatures. Full lines represent Eq.(9). Tab.1 Coefficients of quadratic approximation (11) of specific electrical conductivity ki[S.m1], measured within the temperature range 25 to 72 C. i( p0i [S.m-1]p1i [S.m-1.C-1]p2i [S. m-1.C-2]101.48E-57.20E-71.70E-1020.021.33E-15.25E-36.00E-6 30.053.07E-11.28E-21.40E-540.104.22E-11.90E-21.90E-550.205.88E-12.87E-24.70E-560.305.47E-13.13E-27.80E-570.404.81E-12.96E-21.21E-480.502.73E-11.92E-21.49E-490.609.02E-29.71E-31.47E-4100.701.79E-21.20E-39.20E-5110.80-4.10E-59.39E-71.18E-8  Tab.2 Identifications of the model (9) and the modified Castel-Amis model (10) for the specific electrical conductivity of coffee (minimisation of standard deviation for N=542 observation points, within the range T((25C, 72C) and ( ((0, 0.8)) Parameters of model (9)Values and confident. intervalsParameters of model (10)Values and confident. intervals(c0 [S.m-1]5.833 (0.5(max0 [S.m-1]0.3606 (0.140(c1 [S.m-1.C-1]0.2439 (0.01(max1 [S.m-1.C-1]0.04198 (0.0028a1.731 (0.11(max00.2667 (0.020b2.648 (0.16(max1 [C-1]0.000678 (0.00034c [C-1]-0.0111 (0.0012x0.4055 (0.111(w [S.m-1]0.0503 (0.0005y-9.941 (1.06(c0.454 (0.01s [S.m-1]0.0621s [S.m-1]0.0982R0.9975R0.9936  Fig.1 Sobolik et al.  Fig.2 Sobolik et al.  Fig.3 Sobolik et al.  Fig.4 Sobolik et al.  Fig.5 Sobolik et al.  Fig. 6 Sobolik et al.  Fig.7 Sobolik et al. 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Normal_c75%/Normal_c75%_up0Normal_c75%-down1Normal_cafe_04_00(2#Normal_cafe_04_00_A.xls Graphique 1(3#Normal_cafe_04_00_A.xls Graphique 24Normal_cafe-30-12-995 Normal_F85_756dGraph3 v|c=50% &v60% 965% q70% c=75% C=80% gmaxVT=70oC ZFig1 Fig2!! 2$ solver_adj;    solver_adj:" solver_cvgMbP? solver_drv  solver_drv solver_est  solver_est solver_itrd  solver_itrd solver_lin  solver_lin solver_neg solver_num  solver_num solver_nwt  solver_nwt  solver_opt:    solver_opt:" solver_preư>" solver_preư> solver_scl  solver_scl solver_sho  solver_sho solver_timd  solver_timd" solver_tol?" solver_tol? solver_typ  solver_typ solver_val  solver_vald       /$rB]"I<9k_izaB]"I<9k_( 3  @@ IDate21.09.99Smpl.:CAFEFILTRESpec.:VODATemp.:upTAveragedownT Viscometer:Rheotest1688/S1C%Knspdalfgam[1/s]tau[Pa]h[mPas]9a10a11a12afrom 958aDate:1688/S211b12b6a7a12.3F19.0F12.0F18.2F11.4F11.0F17.8F14.3F14.6F5a17.3F27F42.6F26.5F17.2F12.2F19.9F35.3F34.4F20.1F20.2F35.8F3a4a11.3F19.4F30.4F49.5F70.9F49.3F30.0F68.0F41.3F23.0F24.2F43.0F70.6Ftime62.6F41.0F24.6F15.3F2a1a16.0F25.3F64.2F98.0F55.9F34.2F11.9F19.5F35.0F57.4F101.0F t= K *g ^ n  70oC  to 95oC R2h[mPas] t-modl[Pa]to 70oC  gmaxgminTC25.0Cupto 90Cdown30.0C40.0C50.0C60.0C70.0C80.0C90.0C12.5F22.1F21.0F from90 to25oC15.0F26.0F14.5F17.4F30oC11.6F20.0F11.5F11.2F40oC12.8FR2.h[mPas]/from90oC12gmin4gmax4ToCR282.0F52.2F30.7F19.2F11.1F81.1F88.0F57.3F21.2F13.0F13.7F37.2F60.1F89.5F71.0F44.8F29.0F17.0F11.8F18.0F30.3F45.7F70.1F84.0F53.7F30.6F19.7F20.4F32.8F54.0F64.5F23.9F25.0F41.2F56.8F59.0F36.0F20.8F12.9F 16:0000000713.3F20.5F34.0F54.2F95.3F95.0C72.6F40.6F25.4F15.9F26.4F42.4F72.2Fto 90oC  last three pointstmaxh[mPas]10.0F17.5F28.6F50.1F80.0F78.4F48.4F27.6F16.8F9.8F97.0F33.5F61.0F100.3F72.8F43.2F27.0F15.4F16.2F28.0F74.0F76.0F14.9F26.8F43.8F77.4F92.2F54.6F90.4F60.6F37.0F13.2F38.0F62.0F48.8F10.5F21.3F33.6F55.2F57.1F32.2F19.8F32.6F56.9F90.1C27.2F18.4F29.8F18.3F18.5F95.1C23.2F23.8Fto 50oC  to 60oC  to 80oC  delta^2 t-modl[Pa]20.3F13.9F24.4F24.3F14.0F40oC  h[mPas]|to 40oC  t50oC  tau-model14.2F60oC  80oC   90oC   95oC  Last three points16.5F26.1F43.6F67.0F43.3F25.8F17.7F31.5F52.8F95.0F53.3F32.0F10.8F22.7F59.3F59.6F22.2F24.0F72.0F43.5F13.5F10.6F18.7F21.4F12.1Fh[mPas]27.8F71.3F15.5F21.8F36.3F30oC  9;5413.6F23.7F38.3F99.2F99.0F64.0F23.3Fto 30oC  33.0F59.1F97.1F96.3F58.3F12.7F34.7F54.3F88.2F53.5F34.3F28.5F47.0F83.0F46.6F28.3F20.6F53.4F53.0F32.1F14.7F24.5FdoluJT ZTP TiT_U lQUGeUlUVqEV;VuV SWI W W#XmXcXX?Y5YuYDZFZ<ХZZ4%[e[[[`[&\\ \d]Z h] %-] 0^& x^n x^  _ xL_B _ Н046lT00e00wwzm00r E000rrt߿0rlte0p solver_valrcentagee_ visޝ0Űp0X{ 0T0\ZFƁT0LZFt46h6--H`EHrza dpd{0cT0t $pd{0cT0zaz0p|pB]"d{0cT0}0RT0ppPz0p%0` 0 ~ ~I*0 T IDate21.09.99Smpl.:CAFEFILTRESpec.:VODATemp.:upTAveragedownT Viscometer:Rheotest1688/S1C%Knspdalfgam[1/s]tau[Pa]h[mPas]9a10a11a12afrom 958  "`teDotes<~?<~?3` wHbTd<( 3f3f3 d  d 3 B#CDE6F"A@6\#W#@`5%x f ] `hrr d 0$S  @>L]$SL! <w = 0.5<$xx d 6S  @]S! < 0.6<xx d 6S  @ z j ]SL" < 0.8<xx d 6dT  @^0]dTX# < 0.65< xx d 6T  @O} sm ]T# < 0.7<xx d 6@U  @$z  ]@U@ < 0.75< 还33d  3Q:'  0.5Q ;(0Q ;(0Q3_  NM   <4E4  3Q:'  0.6Q ;(0Q ;(0Q3_  NM  !!<4E4  3Q:'  0.65Qi ;(0Q ;(0Q3_  NM  ""<4E4  3Q:'  0.7Qi ;(0Q ;(0Q3_  NM  ##<4E4  3Q:'  0.75Qi ;(0Q ;(0Q3_  NM  $$d4E4  3Q:'  0.8Qi ;(0Q ;(0Q3_  NM  %%<4E4D$% M 3O&Q4$% M 3O&Q4FA\M 3O: 3*4@4@4@ #M&43*??.N#M&4%  gTM 3Ov0"&PQ T, C'4% IIrM 3OI[,%&PQ g, s-1'4523   43d" 3_ M NM  MM<4444 e9@9@9@9@9@9@>@>@>@>@>@>@D@D@D@D@D@D@I@I@I@I@I@I@N@N@N@N@N@N@33333SQ@33333SQ@33333SQ@33333SQ@33333SQ@33333SQ@T@T@T@T@T@T@V@V@V@V@V@V@W@W@W@W@W@W@e@Gzn|@@Gzn|@Qo@@Gzn|@Gzn|@Zd;U@@Gzn|@Gzn|@?1zj@Zd;U@$@@Gzn|@Gzn|@Gzn|@{Okyg@an|M:@@Gzn|@Gzn|@Gzn|@Gzn|@L8aS@@Gzn|@Gzn|@Gzn|@Gzn|@Qo@@Gzn|@Gzn|@Gzn|@Gzn|@Gzn|@@Gzn|@Gzn|@Gzn|@Gzn|@Gzn|@e> Gz   dMbP?_*+%&A Page &PMSecretariatw 3dXgO$dPage personnalise 1XCCPage personnalise 2XCCPage personnalise 3XCC" dX??U } $ 7T0 ;16      82  "         " w ;w  g T0 _Date:~ ``@77___a bDate c21.09.99 7777_Smpl.: _CAFE_FILTRE~ d?_Spec.: _VODA~ e?a777777"7777777a777777 fTC gK gnhR2.ih[mPas] j7 kTC  lK  mn nR2 oh[mPas]/  77p25.0Cqb('?q*s?qx#?r/XWR@ suptto 90Cu25.0C vx&1? wM(D!? wr)? xG\@  ?uptto 90Cyz0|?z <.9?zu?zHP?9eP@ |down7D7^^~7740.0CqE?qoŏ1?qgj+?; !B@ sup740.0C vا? wz{U? w9? x`J@  77 y z£#֢? zgCV? z`$@M-? V ? ? rB)48@ sup 7 50.0C v?W[? wc? Zڊ? &ZpfrA@ 7 y ,)W? l/Z? ׆q? :@ |down 777 60.0C s? NbX9? ׆q? R k0@ sup 7 60.0C v&? ǵb? w? x4۽7@ 77 y b? v? 8EGr? (92@ |down 77770.0CiUMu?+5{?j?G Մ̔)@ sup770.0C v#? wY? w*? xloF1@  77y^T?K?N`?`h +@ |down777780.0C~Tˆ?{Nz?J_{f?gr#@ sup780.0C vJ8? wo%;6? w6? .h*@ 77777 7ym?D$]3?5?m$@ |down7D7^^~77777790.0C8d`?s?L2r?Ȝ@ up90.0C vK8|? wN? wy@e? x º'%@ 77777*777777b77777*7777777777__Date:~ `@77___  last three points 77777__Smpl.: _CAFE_FILTRE~ d?_Spec.: _VODA~ e? K  n  TC  K  n gmin4gmax4*tmaxh[mPas]__Temp.:t25.0C}to 90C____0H6bȲ?%DDD ~  ? 25.0C 7A`в? &S? A@q6A+@/XWR@ sup__ Viscometer:_Rheotest_1688/S1____  Oe? z6>W? A@q6A+`a@{N?۩U@ |down time _spd _alf_gam[1/s]_tau[Pa]F t-modl[Pa]Fh[mPas]_0a!ђB?DDD ~  ? 30.0C ? ׁ? A@q6A+@W@I:`L@ sup>>? _6a_@Ŷ@Af'@ך@Kk^)R@_   ? z6>? A@q6A+@9eP@ |down_ _7a~ _*@V-JX@X9@AKR@7R@_0I\{?DDD ~  ? 40.0C V}b? x? A@q6A+f@; !B@ sup_ _8a_@@(-)@纕)@BTHR@_  W2ġ? b=y? A@q6A+@tD@ |down_ _9a_@v@0L FU5@Q#_a5@}VR@_0߸Ș?DDD ~  ? 50.0C &†? hs? A@q6A+@B)48@ sup_ _10a_@A@0*LC@{OC@e!gR@_  !u? '? A@q6A+@:@ |down_ _11a_12.5F1Y@@Vx"$P@)uR@_0c`=?DDD ~  X@ 60.0C X5;N? ı.n? A@q6A+ܤ@R k0@ supDhln&}}}}}..x2 Q/% T0 !" #16$ % &'()82*+ ,-./0123w45678w9 :G;<=>T0? UUUUUU? _12a _22.1F~ q6A Pn]@  >']@ ,)!R@ _  9v? oT? A@q6A+@ (92@ |down!P-}? !_12a!_21.0F~ !q6A!v\@! >']@!,)!R@!_0!/Y?D!D!D! ~ ! X@! 70.0C! +?! !I.!?! A@q6A+P@!G Մ̔)@ !sup"_ "_11a"_12.5F"1Y@@"Vx"$P@")uR@"_ " ":pΈ?" # q?" A@q6A+6@"`h +@ "|down#_ #_10a#_@A@#sAB@#{OC@#e!gR@#_0#d؊F?!D#D#D# ~ #  X@# 80.0C# $@Lj?# %гY?# A@q6A+.@#gr#@ #sup$_ $_9a$_C@v@$"~*5@$Q#_a5@$}VR@$_ $ &ŏ1w-!?$ '߾3?$ A@q6A+ؘ@$m$@ $|down%_ %_8a%_l@@%Pk(@%纕)@%BTHR@%_0%%m?#D%D%D% ~ % W@% 90.0C% (ׁsF?% )s?% A@q6A+p@%Ȝ@ %up&_ &_7a~ &_)@&V-JX@~ &…@&AKR@&7R@&_7777777777'xwwwww? '_6a'_@Ŷ@'Af'@'ך@'Kk^)R@'_7777777777(_(} from90 to (t25oC (_(/XWR@(_7777777777)88? )_6a)_"@Ŷ@)Zd;O @)yr@);ıW,U@)_7777777777*_ *_7a~ *_-@*V-JX@*I +' @*[:sw; @*}30f"SU@*_7777777777+_ +_8a+_@@+ c-@+Yx.@+@ bU@+_7777777777,_ ,_9a,_F@v@@,Bo! ?9@,ڦU@,_7777777777-_ -_10a-_@A@-d]FF@-XF@--U@-_7777777777._ ._11a._15.0F~ .1Y@.Zd;O T@.R:S@. >8a>Л@@>N#E#@>׏#@>‰ҍbL@>? ?9a?H@v@?b=0@?y><˝0@?Ytq#L@?Dl8&%syzpoouw2>V]}o@T0ABC16D EFGHI82JK LMNOPQRSwTUVWXwY ZG[\]^T0_@ @10a@@A@@HPs=@@~!>@@Q}L@@A A11aA@1Y@A I@A`&I@AjZL@ABqP}? B12aB17.4F~ Bq6AB&SBW@B?4ɨV@BKL@BC` ` ? C12aC17.2F~ Cq6AC.1V@C?4ɨV@CKL@CD D11aD@V@1Y@DMbXH@D`&I@DjZL@DE E10aEȴ@A@Ee=@E~!>@EQ}L@EF F9aF=@v@FX9vn0@Fy><˝0@FYtq#L@FG G8aG@@G^K=#@G׏#@G‰ҍbL@GHߦ5}? H7a~ H$@HV-JX@~ Hh@HZoG@HZXm?L@HII from90 to I30oC III:`L@IJll? 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Michel Crepeau, 17042 La Rochelle, France e-mail: vsobolik@univ-lr.fr, kallaf @univ-lr.fr 2 Institute of Chemical Process Fundamentals, Academy of Sciences of the Czech Republic, Rozvojov 135, 16502 Prague 6, e-mail: tovcigrecko@icpf.cas.cz 3 Institute of Process Engineering, Czech Technical University, Technick 4, 16000 Prague 6, e-mail: zitny@fsid.cvut.cz Abstract Viscosity of concentrated solutions (w = 0.5-0.8) of soluble coffee was measured in the temperature range 25 - 95C. After homogenisation, the rheological behaviour was found to be Newtonian. The viscosity was correlated by a five parameter function of concentration and absolute temperature. Specific electrical conductivity of coffee solutions in water (w = 0 - 0.8) was measured in the temperature range 25  72C. A seven parameter model based on the assumption that the solution is composed of a partially dissociated species and water describes very well the measured data. Modified Casteel-Amis model equation has been identified for comparison. The conductivity dependence on concentration exhibits maxima which are the more shifted towards higher concentrations the higher is the temperature. Introduction Coffee is composed of more than 700 components. Purine alkaloids (caffeine etc.), minerals, bases, chlorogenic acids, lipids, aliphatic acids and carbohydrates (arabinose, sucrose etc.) and amino acids (tryptophan) are some of them [1]. The data on physical properties of the aqueous solutions of soluble coffee are scarce although the world production is very important and the coffee extracts enjoy extensive consumer market. The manufacturers guard probably the confidentiality of processing. We have found only one paper [2] which deals with the viscosity of aqueous coffee solutions. In this paper, the viscosity, surface tension, thermal conductivity, index of refraction and the freezing curves were measured in the solutions with coffee mass fraction 00.5. Different mixtures were examined of several coffee sorts prepared either by freeze drying (Vox Mocca, Vox Robusta) or by spray drying (Nescaf Gold, Maxwell Exquisit). As the paper [2] is written in Czech, the most important results are summarised in the following paragraphs. The dependence of the refractivity index on the coffee mass fraction w was expressed by the relation: At w=0.5, the refractivity indexes of the coffee and sucrose are about 1.44 and 1.42, respectively. It is difficult to measure the refractivity index of more concentrated coffee solutions because the dark brown colour hinders in scale observation. The density was calculated from the density of water rW and the true density of the solid coffee rC: where rW = 1000 - 0.036T - 0.004T 2 and rC= 1654 - 1.79T - 0.0063 T 2. The difference in the densities of the coffee and sucrose is about 1% at w=0.5. The flow curves were measured by a rotational viscometer Haake. The rheological behaviour was characterised as slightly pseudoplastic and thixotropic. The values of the limiting viscosity h( are also given, i.e. the values which did not change with increasing shear rate. The viscosity increased non recoverably when the solution was stored for a longer time. This fact was explained by swelling of high molecular substances which are present in the coffee. Weisser did not found any important difference in viscosity of different sort of coffee prepared either by spray drying or by freeze drying. Due to presence of surface active substances, the surface tension of coffee solutions was found to be smaller than that one of water. For w > 0.1, the surface tension was equal to 0.042 N.m-1 at 20C and 0.037 N.m-1 at 40C. The thermal conductivity of coffee solutions was found to be the same as the conductivity of sucrose solutions. It was described by the relation: Intensification of soluble coffee production requires the treatment of more concentrated solutions. The present paper focuses on the properties, which are important for ohmic heating and treatment of highly concentrated coffee solutions, i.e. viscosity and electric conductivity. The coffee studied was a freeze dried mixture of 65% coffee arabica (Colombia) and 35 % coffee robusta (Brazil), sold under the mark  Caf filtr by Carrefour (France). 1 Viscosity The dependencies of shear stress on shear rate [3] were measured in a controlled rate viscometer Rheotest II, (VEB Prfgerte, Medingen, Germany). Two different geometry were used consisting of one external cup with a diameter of 40 mm and two internal cylinders, S1 and S2 with diameters 39.2 and 37.6 mm and a length of 72 mm. The temperature of the external cup and hence of the sample was controlled by a water circulator. Solutions with coffee mass fraction w=0.5  0.8 in tap water were examined in a temperature range of 2595C. The samples with the lower concentrations, w<0.75, were prepared in a glass beaker whereas the more concentrated samples were mixed directly in the viscometer cup. The preparation was similar in both cases. The dry coffee was poured into water with a temperature of 25C. The sample was then agitated with a glass bar and heated to 70C. The stainless steel viscometer cup was preheated to 60C before it was filled with a prepared sample. The cup was then pressed onto the measuring cylinder. A thin plastic disc covered the sample surface with the aim to diminish water evaporation. By means of the external cup, the sample was then cooled to the low temperature at which the viscosity measurements started. The torque was measured at shear rates going from the minimum to the maximum one and reverse. The temperature was then increased to the next one and measurements were done at increasing and then decreasing shear rate. After reaching the maximum temperature of 95C, the measurements were repeated at decreasing temperature steps. The measurements of one sample took about 4 hours. The flow curves measured immediately after the sample preparation, i.e. in the series with increasing temperature, exhibited slightly pseudoplastic behaviour with the flow index of about 0.9 and a higher apparent viscosity than the curves measured some time later after passing the maximum temperature of 95C. The latter curves exhibited Newtonian behaviour. An example of primary data is shown in Fig.1. This difference in flow behaviour can be explained by the presence either of larger molecules or of solid particles during the first phase. The concentrated solution of coffee extract needs a higher temperature (90-95C) or a longer exposition to shear rate to become homogeneous or to destroy the large molecules. The data presented in this paper correspond to the viscosity measured in the second phase after passing 95C. The measurements were done until the maximum shear rates shown in Fig.2. The range of the shear rate applied in the measurements lies below the corresponding lines. For example the dotted area represents the range for w = 0.8. The shear rate was limited either by the maximum rotational rate or by the maximum torque, which can be achieved in the viscometer. For w = 0.5, this limit was the maximum shear rate generated by the largest cylinder S1 (smallest gap). The value of the shear rate in this case is equal to 1574 s-1. For the solutions with higher viscosity, w>0.5, the limiting factor was the maximum torque and the smaller cylinder S2 (larger gap) has to be used. For this geometry, the maximum shear rate is equal to 455 s-1 . The viscosity dependence on the absolute temperature and concentration is shown in Fig.3. For w((0.5-0.8), the viscosity was fitted by the relation  The maximum error of viscosity evaluation using this relation was estimated to be less then 15 %. The viscosity measured by Weisser [2] for w = 0.5 is shown by the open diamond symbols. It does not exhibit great deviations from our measurements. For 60C, we determined 0.019 Pa.s whereas Weisser has found 0.024 Pa.s. This quite good agreement confirms the conclusion of paper [2] that the viscosity is almost independent of the coffee sort and its treatment. With the aim to extend the range of viscosity dependence also for low concentrations, w ((0-0.5), the results of paper [2] are shown in Fig. 4. The best fit of these data is by the relation 2 Specific electrical conductivity 2.1 Model design Specific electric conductivity of electrolytes ( [S.m-1] depends upon concentration, mutual interactions and mobility of ions. It is known that increasing viscosity decreases conductivity, nevertheless our attempt to correlate viscosity and conductivity of the coffee solutions failed totally. Some theoretical results originated from Debye-Hckel theory can be applied for weak electrolytes [4], but for concentrated electrolytes empirical models, e.g. normal distribution of ((() or models of the form ((()=a(() exp[b(()], are usually preferred[5]. A new empirical model describing the temperature and concentration dependency of specific electrical conductivity is based on the idea, that the coffee solution is composed of water having conductivity (w [S.m-1], dissociated coffee species with conductivity (c and non dissociated species which is an insulator. It is assumed than the amount of dissociated species is proportional to the mass fraction of coffee, (, and also to the mass fraction of water, 1-(,  EMBED Equation.2  EMBED Equation.2 . (6) Experiments indicate that the conductivity of concentrated coffee depends strongly on temperature and therefore we shall assume linear relationship for approximation of (c(T), while temperature dependency of tap water will be neglected in view of the fact, that (w is very small. Combining specific electrical conductivity of three components (non dissociated species  insulator, water, and dissociated species) according to a simple model of parallel resistors, we obtain  EMBED Equation.2  (7) This model is not able to describe the experimental data properly with a constant exponent m which must be considered as a function of temperature and concentration, m(T,(). The following quite empirical Eq.(8) will be used for processing data, exhibiting a slight change of trends at concentration (c  EMBED Equation.2  . (8) The resulting model is rather complicated 7-parametric relation  EMBED Equation.2   EMBED Equation.2  (9) The proposed model (9) will be compared with the Casteel-Amis equation for ((c, T) modified by Diego [5] by inclusion of temperature. The Diego's model is based on fitting of maximum conductivity (max at the corresponding concentration cmax . The following Eq.(10) differs from the original Diego's model only by replacing concentration c with the mass fraction (:  EMBED Equation.2 . (10) The modified Casteel-Amis equation has 6 parameters, (max0, (max1, (max0, (max1, x, y and only two of them, (max0, (max1, are linear. In view of the fact, that the predicted conductivity equals zero for (=0, the model (10) cannot describe the conductivity of pure water. 2.2 Experimental results and model identification The specific electrical conductivity was measured by the conductivity probe LF 340 TetraCon 325/S, (Wissenschaftlich-Technische Werkstatten GmbH, Weilheim, Germany) suitable for highly viscous materials and pastes. The probe is composed of four graphite electrodes and a thermometer embedded in an epoxy casing. The electrodes are flush mounted in an axial groove. Dimensions of the probe and the amount of coffee sample follow from Fig.5. The samples were prepared by mixing the coffee extract with a cold tap water in a beaker which was then immersed in water heated to 80C. The homogenous sample was then filled into a small cylindrical glass cup and the probe was immersed into the sample. The temperature of the cup was controlled by a water circulator. The measurements started at the low temperature (25C) and continued until 72C. The range of temperature and concentration is shown in Fig.6. Approximately 50 values of the conductivity were recorded for each concentration at different temperatures. The simplest approach of modelling is based upon the quadratic approximation of temperature dependence evaluated separately for each measured concentration (i (i (T) = p0i + p1iT + p2iT2 (11) Identification of the coefficients p0i, p1i, p2i by linear regression was done with a relative standard deviation smaller than 1.5%. The results are summarised in Tab.1. Parameters of model (9), (c0, (c1, (w, a, b, c, (c, were identified by nonlinear regression (in house program XREGA), minimising sum of squares of deviations from 542 observation points (Ti, ( i , (i), see Tab.2. Interpretation and reliability of more or less empirical model with such a high number of parameters is always questionable, however, confidence intervals of all parameters calculated from covariance matrix are sufficiently narrow (see Tab.2) and some predicted values can be verified directly: For example (w=0.05 S.m-1 corresponds rather well to the electric conductivity of tap water (~0.043 S.m-1 at 500C) and ( c=0.454 visually fits the mass fraction characterising sudden change of trends at higher temperatures, see Fig.7. All parameters have correct sign, and for example the negative sign of the parameter c ensures not only a progressive increase of conductivity with temperature at a constant (, but also an observed mild shift of maxima ((() towards higher concentration with increasing temperature. It seems that physical relevance of parameters would allow a slight extrapolation of conductivity to higher temperatures, may be up to 900C. Exactly the same procedure and primary data were used for identification of modified Casteel-Amis model (10), and results are presented also in the Tab 2. This model approximates experimental data rather well, describes all trends, confidence intervals of parameters are acceptable, nevertheless basic statistics of errors are significantly worse in comparison with the suggested model (9). Adding the term (w(1-() to the model (10) had no significant influence upon the standard deviation (in fact unbiased estimate was slightly higher, (=0.099 S.m-1, because the number of parameters had been increased from six to seven). 3 Conclusions Immediately after preparation of the coffee solution, its rheological behaviour was slightly pseudoplastic with a flow index about0.9. After some time of the shear application in the viscometer and passing a temperature of 95C, the coffee solutions became Newtonian in the range of measured shear rates (10( g ( 1574 s-1). The viscosity dependence on temperature and concentration was described by a five parameter relation. The estimated error of viscosity measurements was about 15%. It is not bad result with respect to the inherent experimental difficulties with handling concentrated coffee solutions (swelling, caramelisation, evaporation etc.). Quite good agreement with the viscosity data measured by Weisser [2] confirmed that the coffee viscosity does not depend much on the coffee sort and the way of the coffee drying and treatment. The specific electrical conductivity was described by a seven parameter model based on the idea that the amount of dissociated coffee molecules is proportional to the coffee mass fraction and water mass fraction. This model describes the conductivity with a standard deviation of 0.062 [S.m-1] which is much lower than the standard deviation of the modified Casteel-Amis model ((=0.098 S.m-1). The specific electrical conductivity exhibits maxima at concentrations about w=0.35. The higher temperature the greater is the shift of the maximum towards higher concentration. The maximum electric conductivity of coffee solution is about 40 times higher then the conductivity of tap water at the same temperature. The viscosity and specific electrical conductivity data obtained in this article render possible the design of apparatuses for the treatment of highly concentrated coffee extracts. Acknowledgements: This research has been subsidized by the Research project of Ministry of Education of the Czech Republic J04/98:21220008. References: Caffeine, coffee, and health. (Ed. Silvio Garattini),: Raven Press, New York, 1993. Weisser H.: Measurements of physical properties of solutions of coffee extract (in Czech), PotravinYsk a chladc technika 3, 136-138 (1972). Bird R.B., Armstrong R.C., Hassager O.: Dynamics of polymeric liquids, Volume 1 Fluid mechanics, John Wiley & Sons, 1987. Koryta J. et al: Theory of electrolytes (in Czech), CSAV, No.7, Academia Praha, 1976. De Diego A., Madariaga J.M., Chapela E.: Empirical model of general application to fit ((, c, T) experimental data from concentrated aqueous electrolyte solutions, Electrochemica Acta, Vol.42, No.9, pp.1449-1456, (1997) Notation a, b, c parameters in Eqs.(8 and 9) k number of model parameters nD20 refraction index (yellow Na light at 20oC) N number of data pji parameters in Eq.(11) R correlation coefficient, T temperature [C] x, y parameters of modified Casteel-Amis model, Eq.(10), [-] g shear rate [s-1] k specific electrical conductivity [S.m-1] mean value specific electrical conductivity [S.m-1] kij parameters in Eqs.(9) l thermal conductivity [W.m-1.C-1] m viscosity [Pa.s] r density [kg.m-3] w coffee mass fraction [kg dry coffee/ kg solution] s standard deviation [S.m-1] , t shear stress [Pa] Figure captions Fig.1 Flow curves of coffee solutions, w=0.7, at 40C measurements immediately after sample preparation measurements after 2 hours after passing 95C Fig.2 Range of measured shear rates Fig.3 Dependence of viscosity on temperature and concentration for concentrated coffee solutions w : - 0.5, - 0.6, - 0.66, - 0.7, - 0.74, - 0.8,  - data [2] for w =0.5 Fig.4 Dependence of viscosity on temperature and concentration for coffee solutions with low concentration [2] w : - 0, - 0.1, - 0.2, - 0.3, - 0.4, - 0.5 Fig.5 Experimental set-up for conductivity measurements a) front view, b) cut of side view 1  conductivity probe, 2  electrodes, 3  cup, 4  cap, 5 - sample. Dimensions are in millimetres. Fig.6 Range of measured specific electrical conductivity Fig.7 Specific electrical conductivity as function of mass fraction and temperature T: - 30, - 40, - 50, - 60, - 70C Small open rectangles stand for temperatures which differ by 1 and 2C from the rated temperatures. Full lines represent Eq.(9). Tab.1 Coefficients of quadratic approximation (11) of specific electrical conductivity ki[S.m1], measured within the temperature range 25 to 72 C. i( p0i [S.m-1]p1i [S.m-1.C-1]p2i [S. m-1.C-2]101.48E-57.20E-71.70E-1020.021.33E-15.25E-36.00E-6 30.053.07E-11.28E-21.40E-540.104.22E-11.90E-21.90E-550.205.88E-12.87E-24.70E-560.305.47E-13.13E-27.80E-570.404.81E-12.96E-21.21E-480.502.73E-11.92E-21.49E-490.609.02E-29.71E-31.47E-4100.701.79E-21.20E-39.20E-5110.80-4.10E-59.39E-71.18E-8  Tab.2 Identifications of the model (9) and the modified Castel-Amis model (10) for the specific electrical conductivity of coffee (minimisation of standard deviation for N=542 observation points, within the range T((25C, 72C) and ( ((0, 0.8)) Parameters of model (9)Values and confident. intervalsParameters of model (10)Values and confident. intervals(c0 [S.m-1]5.833 (0.5(max0 [S.m-1]0.3606 (0.140(c1 [S.m-1.C-1]0.2439 (0.01(max1 [S.m-1.C-1]0.04198 (0.0028a1.731 (0.11(max00.2667 (0.020b2.648 (0.16(max1 [C-1]0.000678 (0.00034c [C-1]-0.0111 (0.0012x0.4055 (0.111(w [S.m-1]0.0503 (0.0005y-9.941 (1.06(c0.454 (0.01s [S.m-1]0.0621s [S.m-1]0.0982R0.9975R0.9936  Fig.1 Sobolik et al.  Fig.2 Sobolik et al.  Fig.3 Sobolik et al.  Fig.4 Sobolik et al.  Fig.5 Sobolik et al.  Fig. 6 Sobolik et al.  Fig.7 Sobolik et al. 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Normal_C50T30@ Normal_C50T40A Normal_C50T50B Normal_C50T60C Normal_C50T70D Normal_C50T80E Normal_C50T90F Normal_c75%GNormal_c75%_upHNormal_c75%-downINormal_cafe_04_00&J!Normal_cafe_06_00.xls Graphique 1(K#Normal_cafe_06_00.xls Graphique 1-1&L!Normal_cafe_06_00.xls Graphique 2&M!Normal_cafe_06_00.xls Graphique 3&N!Normal_cafe_06_00.xls Graphique 4&O!Normal_cafe_06_00.xls Graphique 5&P!Normal_cafe_06_00.xls Graphique 6&Q!Normal_cafe_06_00.xls Graphique 7&R!Normal_cafe_06_00.xls Graphique 8S Normal_F85_75T`3Graph2Q visc (4) e1Fig3rR 0-50% (3) 0Fig4!!*WProjetscafecafe_04_00.xlsPreparing samplessolution average visc visc (2) visc (3) visc (4)Fig3table table (2) table (3)T=25oCT=30oCT=40oCT=50oCT=60oCT=70oCT=80oCT=90oCT=95oCc=75%C=80%c=85%c=50%water0-50% 0-50% (2)YYYYZU 9@>@D@I@N@Q@T@V@W@ZU YR@̌L@fffff&B@3333338@1@)@#@333333@@ZU v;@G9Д^|@Dp n@uʂa@U@ L@{2ǴC@č(=@ɺh9@ZU mkQp@>e+'@~ҮYz@u~.Xa@{n@ k7q@UBZ@& UP@pK@ZU %sp@,9L@mwӵ@Br&M7@3@mHS@L0@%:Sm@Une@`@ZC O@OAVB@mHY4D@Dջ@O%@@v@K:/u@Z:  ~[v4%@=J@7۝_&@kT@+/0dş@$;@YYYYYY Y Y Y Y YYYYYYYYYY!Z Z &:?Z b]?Z $@Z /N[?Z U ߻^?Z 4@Z Fe?Z ?Z >@Z 'ɯ?Z gn^?Z D@Z |ws?Z ^_?Z I@Z  IR?Z  ?Z N@Z    =?Z   m?Z Q@Z  rpk{?Z  : gQ;?Z T@Z  Yv?Z  㖡f?Z V@Z  uD '?Z  R<L?Z Y@Z (kO?Z  Z?YYV$ solver_adj;!3 solver_adj); ; " solver_cvgh㈵>" solver_cvg-C6? solver_drv solver_drv solver_est solver_est solver_itr' solver_itr' solver_lin solver_lin solver_neg solver_neg solver_num solver_num solver_nwt solver_nwt  solver_opt:+   solver_opt: " solver_preư>" solver_preư> solver_scl solver_scl solver_sho solver_sho solver_timd solver_timd" solver_tolh㈵>" solver_tolh㈵> solver_typ solver_typ solver_val solver_valrj0 3  @@  %upT= 25..90..95.. ..90..30=downT25oC30oC40oC50oC60oC70oC80oC90oC95oCh[mPas] C%\T h[Pas] . .RTitre_de_la_feuillestw`T0D8{<nDLDwXw,Paw`T0Dn4;nL?Vwn`T0D4;x{w8{<n`T0D4;w<w< G7  xع!Н04;6;pT00e00(zm00r E000rrt߿0rptW:\Projets\casolver_val_00.xlsee_ visitb;wT{@0ixnc;hwi4;w<w<nc;6;;7>74;6;w<6;G7 b;lwh4;6;c;6;Iwi4;w<c;p@֜z0d{0cT0}0RT0ppPz0pr"%0r` 0rn  "05oDmPas<~?<~? 3` >YL` >YM还>3d23 M NM4 3QQ ;&(Q ;&(Q3_ M NM   x4E4  3QQ ; Q ; Q3_  NM ]  <4E4  3QQ ; Q ; Q3_  NM ] !!d4E4  3QQ ; Q ; Q3_  NM ] ""d4E4  3QQ ; Q ; Q3_  NM ] ##d4E4  3QQ ; Q ; Q3_  NM ] $$d4E4  3QQ ;!! 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@   `" @     ,!@  ,! @  ,!@  ,! @  ,!@       D  ,!@   `!@  @  (  A "0  ,  d  d  d  d 3a ( A#8 "X  "X A"X  A"X Milliers [0]_cafe_04_00.)Milliers [0]_cafe_04_00_A.xls Graphique 1.)Milliers [0]_cafe_04_00_A.xls Graphique 2Milliers [0]_cafe-30-12-99Milliers_cafe_04_00*%Milliers_cafe_04_00_A.xls Graphique 1*%Milliers_cafe_04_00_A.xls Graphique 2Milliers_cafe-30-12-99Montaire [0]_cafe_04_00/*Montaire [0]_cafe_04_00_A.xls Graphique 1/*Montaire [0]_cafe_04_00_A.xls Graphique 2 Montaire [0]_cafe-30-12-99 Montaire_cafe_04_00+!&Montaire_cafe_04_00_A.xls Graphique 1+"&Montaire_cafe_04_00_A.xls Graphique 2#Montaire_cafe-30-12-99$ Normal_C=80%% Normal_c=85%& Normal_C50T25' Normal_C50T30( Normal_C50T40) Normal_C50T50* Normal_C50T60+ Normal_C50T70, Normal_C50T80- Normal_C50T90. Normal_c75%/Normal_c75%_up0Normal_c75%-down1Normal_cafe_04_00(2#Normal_cafe_04_00_A.xls Graphique 1(3#Normal_cafe_04_00_A.xls Graphique 24Normal_cafe-30-12-995 Normal_F85_756dGraph3 v|c=50% &v60% 965% q70% c=75% C=80% gmaxVT=70oC ZFig1 Fig2!! 2$ solver_adj;    solver_adj:" solver_cvgMbP? solver_drv  solver_drv solver_est  solver_est solver_itrd  solver_itrd solver_lin  solver_lin solver_neg solver_num  solver_num solver_nwt  solver_nwt  solver_opt:    solver_opt:" solver_preư>" solver_preư> solver_scl  solver_scl solver_sho  solver_sho solver_timd  solver_timd" solver_tol?" solver_tol? solver_typ  solver_typ solver_val  solver_vald       /$rB]"I<9k_izaB]"I<9k_( 3  @@ IDate21.09.99Smpl.:CAFEFILTRESpec.:VODATemp.:upTAveragedownT Viscometer:Rheotest1688/S1C%Knspdalfgam[1/s]tau[Pa]h[mPas]9a10a11a12afrom 958aDate:1688/S211b12b6a7a12.3F19.0F12.0F18.2F11.4F11.0F17.8F14.3F14.6F5a17.3F27F42.6F26.5F17.2F12.2F19.9F35.3F34.4F20.1F20.2F35.8F3a4a11.3F19.4F30.4F49.5F70.9F49.3F30.0F68.0F41.3F23.0F24.2F43.0F70.6Ftime62.6F41.0F24.6F15.3F2a1a16.0F25.3F64.2F98.0F55.9F34.2F11.9F19.5F35.0F57.4F101.0F t= K *g ^ n  70oC  to 95oC R2h[mPas] t-modl[Pa]to 70oC  gmaxgminTC25.0Cupto 90Cdown30.0C40.0C50.0C60.0C70.0C80.0C90.0C12.5F22.1F21.0F from90 to25oC15.0F26.0F14.5F17.4F30oC11.6F20.0F11.5F11.2F40oC12.8FR2.h[mPas]/from90oC12gmin4gmax4ToCR282.0F52.2F30.7F19.2F11.1F81.1F88.0F57.3F21.2F13.0F13.7F37.2F60.1F89.5F71.0F44.8F29.0F17.0F11.8F18.0F30.3F45.7F70.1F84.0F53.7F30.6F19.7F20.4F32.8F54.0F64.5F23.9F25.0F41.2F56.8F59.0F36.0F20.8F12.9F 16:0000000713.3F20.5F34.0F54.2F95.3F95.0C72.6F40.6F25.4F15.9F26.4F42.4F72.2Fto 90oC  last three pointstmaxh[mPas]10.0F17.5F28.6F50.1F80.0F78.4F48.4F27.6F16.8F9.8F97.0F33.5F61.0F100.3F72.8F43.2F27.0F15.4F16.2F28.0F74.0F76.0F14.9F26.8F43.8F77.4F92.2F54.6F90.4F60.6F37.0F13.2F38.0F62.0F48.8F10.5F21.3F33.6F55.2F57.1F32.2F19.8F32.6F56.9F90.1C27.2F18.4F29.8F18.3F18.5F95.1C23.2F23.8Fto 50oC  to 60oC  to 80oC  delta^2 t-modl[Pa]20.3F13.9F24.4F24.3F14.0F40oC  h[mPas]|to 40oC  t50oC  tau-model14.2F60oC  80oC   90oC   95oC  Last three points16.5F26.1F43.6F67.0F43.3F25.8F17.7F31.5F52.8F95.0F53.3F32.0F10.8F22.7F59.3F59.6F22.2F24.0F72.0F43.5F13.5F10.6F18.7F21.4F12.1Fh[mPas]27.8F71.3F15.5F21.8F36.3F30oC  9;5413.6F23.7F38.3F99.2F99.0F64.0F23.3Fto 30oC  33.0F59.1F97.1F96.3F58.3F12.7F34.7F54.3F88.2F53.5F34.3F28.5F47.0F83.0F46.6F28.3F20.6F53.4F53.0F32.1F14.7F24.5FdoluJT ZTP TiT_U lQUGeUlUVqEV;VuV SWI W W#XmXcXX?Y5YuYDZFZ<ХZZ4%[e[[[`[&\\ \d]Z h] %-] 0^& x^n x^  _ xL_B _ Н046lT00e00wwzm00r E000rrt߿0rlte0p solver_valrcentagee_ visޝ0Űp0X{ 0T0\ZFƁT0LZFt46h6--H`EHrza dpd{0cT0t $pd{0cT0zaz0p|pB]"d{0cT0}0RT0ppPz0p%0` 0 ~ ~I*0 T IDate21.09.99Smpl.:CAFEFILTRESpec.:VODATemp.:upTAveragedownT Viscometer:Rheotest1688/S1C%Knspdalfgam[1/s]tau[Pa]h[mPas]9a10a11a12afrom 958  "`teDotes<~?<~?3` wHbTd<( 3f3f3 d  d 3 B#CDE6F"A@6\#W#@`5%x f ] `hrr d 0$S  @>L]$SL! <w = 0.5<$xx d 6S  @]S! < 0.6<xx d 6S  @ z j ]SL" < 0.8<xx d 6dT  @^0]dTX# < 0.65< xx d 6T  @O} sm ]T# < 0.7<xx d 6@U  @$z  ]@U@ < 0.75< 还33d  3Q:'  0.5Q ;(0Q ;(0Q3_  NM   <4E4  3Q:'  0.6Q ;(0Q ;(0Q3_  NM  !!<4E4  3Q:'  0.65Qi ;(0Q ;(0Q3_  NM  ""<4E4  3Q:'  0.7Qi ;(0Q ;(0Q3_  NM  ##<4E4  3Q:'  0.75Qi ;(0Q ;(0Q3_  NM  $$d4E4  3Q:'  0.8Qi ;(0Q ;(0Q3_  NM  %%<4E4D$% M 3O&Q4$% M 3O&Q4FA\M 3O: 3*4@4@4@ #M&43*??.N#M&4%  gTM 3Ov0"&PQ T, C'4% IIrM 3OI[,%&PQ g, s-1'4523   43d" 3_ M NM  MM<4444 e9@9@9@9@9@9@>@>@>@>@>@>@D@D@D@D@D@D@I@I@I@I@I@I@N@N@N@N@N@N@33333SQ@33333SQ@33333SQ@33333SQ@33333SQ@33333SQ@T@T@T@T@T@T@V@V@V@V@V@V@W@W@W@W@W@W@e@Gzn|@@Gzn|@Qo@@Gzn|@Gzn|@Zd;U@@Gzn|@Gzn|@?1zj@Zd;U@$@@Gzn|@Gzn|@Gzn|@{Okyg@an|M:@@Gzn|@Gzn|@Gzn|@Gzn|@L8aS@@Gzn|@Gzn|@Gzn|@Gzn|@Qo@@Gzn|@Gzn|@Gzn|@Gzn|@Gzn|@@Gzn|@Gzn|@Gzn|@Gzn|@Gzn|@e> Gz   dMbP?_*+%&A Page &PMSecretariatw 3dXgO$dPage personnalise 1XCCPage personnalise 2XCCPage personnalise 3XCC" dX??U } $ 7T0 ;16      82  "         " w ;w  g T0 _Date:~ ``@77___a bDate c21.09.99 7777_Smpl.: _CAFE_FILTRE~ d?_Spec.: _VODA~ e?a777777"7777777a777777 fTC gK gnhR2.ih[mPas] j7 kTC  lK  mn nR2 oh[mPas]/  77p25.0Cqb('?q*s?qx#?r/XWR@ suptto 90Cu25.0C vx&1? wM(D!? wr)? xG\@  ?uptto 90Cyz0|?z <.9?zu?zHP?9eP@ |down7D7^^~7740.0CqE?qoŏ1?qgj+?; !B@ sup740.0C vا? wz{U? w9? x`J@  77 y z£#֢? zgCV? z`$@M-? V ? ? rB)48@ sup 7 50.0C v?W[? wc? Zڊ? &ZpfrA@ 7 y ,)W? l/Z? ׆q? :@ |down 777 60.0C s? NbX9? ׆q? R k0@ sup 7 60.0C v&? ǵb? w? x4۽7@ 77 y b? v? 8EGr? (92@ |down 77770.0CiUMu?+5{?j?G Մ̔)@ sup770.0C v#? wY? w*? xloF1@  77y^T?K?N`?`h +@ |down777780.0C~Tˆ?{Nz?J_{f?gr#@ sup780.0C vJ8? wo%;6? w6? .h*@ 77777 7ym?D$]3?5?m$@ |down7D7^^~77777790.0C8d`?s?L2r?Ȝ@ up90.0C vK8|? wN? wy@e? x º'%@ 77777*777777b77777*7777777777__Date:~ `@77___  last three points 77777__Smpl.: _CAFE_FILTRE~ d?_Spec.: _VODA~ e? K  n  TC  K  n gmin4gmax4*tmaxh[mPas]__Temp.:t25.0C}to 90C____0H6bȲ?%DDD ~  ? 25.0C 7A`в? &S? A@q6A+@/XWR@ sup__ Viscometer:_Rheotest_1688/S1____  Oe? z6>W? A@q6A+`a@{N?۩U@ |down time _spd _alf_gam[1/s]_tau[Pa]F t-modl[Pa]Fh[mPas]_0a!ђB?DDD ~  ? 30.0C ? ׁ? A@q6A+@W@I:`L@ sup>>? _6a_@Ŷ@Af'@ך@Kk^)R@_   ? z6>? A@q6A+@9eP@ |down_ _7a~ _*@V-JX@X9@AKR@7R@_0I\{?DDD ~  ? 40.0C V}b? x? A@q6A+f@; !B@ sup_ _8a_@@(-)@纕)@BTHR@_  W2ġ? b=y? A@q6A+@tD@ |down_ _9a_@v@0L FU5@Q#_a5@}VR@_0߸Ș?DDD ~  ? 50.0C &†? hs? A@q6A+@B)48@ sup_ _10a_@A@0*LC@{OC@e!gR@_  !u? '? A@q6A+@:@ |down_ _11a_12.5F1Y@@Vx"$P@)uR@_0c`=?DDD ~  X@ 60.0C X5;N? ı.n? A@q6A+ܤ@R k0@ supDhln&}}}}}..x2 Q/% T0 !" #16$ % &'()82*+ ,-./0123w45678w9 :G;<=>T0? UUUUUU? _12a _22.1F~ q6A Pn]@  >']@ ,)!R@ _  9v? oT? A@q6A+@ (92@ |down!P-}? !_12a!_21.0F~ !q6A!v\@! >']@!,)!R@!_0!/Y?D!D!D! ~ ! X@! 70.0C! +?! !I.!?! A@q6A+P@!G Մ̔)@ !sup"_ "_11a"_12.5F"1Y@@"Vx"$P@")uR@"_ " ":pΈ?" # q?" A@q6A+6@"`h +@ "|down#_ #_10a#_@A@#sAB@#{OC@#e!gR@#_0#d؊F?!D#D#D# ~ #  X@# 80.0C# $@Lj?# %гY?# A@q6A+.@#gr#@ #sup$_ $_9a$_C@v@$"~*5@$Q#_a5@$}VR@$_ $ &ŏ1w-!?$ '߾3?$ A@q6A+ؘ@$m$@ $|down%_ %_8a%_l@@%Pk(@%纕)@%BTHR@%_0%%m?#D%D%D% ~ % W@% 90.0C% (ׁsF?% )s?% A@q6A+p@%Ȝ@ %up&_ &_7a~ &_)@&V-JX@~ &…@&AKR@&7R@&_7777777777'xwwwww? '_6a'_@Ŷ@'Af'@'ך@'Kk^)R@'_7777777777(_(} from90 to (t25oC (_(/XWR@(_7777777777)88? )_6a)_"@Ŷ@)Zd;O @)yr@);ıW,U@)_7777777777*_ *_7a~ *_-@*V-JX@*I +' @*[:sw; @*}30f"SU@*_7777777777+_ +_8a+_@@+ c-@+Yx.@+@ bU@+_7777777777,_ ,_9a,_F@v@@,Bo! ?9@,ڦU@,_7777777777-_ -_10a-_@A@-d]FF@-XF@--U@-_7777777777._ ._11a._15.0F~ .1Y@.Zd;O T@.R:S@. >8a>Л@@>N#E#@>׏#@>‰ҍbL@>? ?9a?H@v@?b=0@?y><˝0@?Ytq#L@?Dl8&%syzpoouw2>V]}o@T0ABC16D EFGHI82JK LMNOPQRSwTUVWXwY ZG[\]^T0_@ @10a@@A@@HPs=@@~!>@@Q}L@@A A11aA@1Y@A I@A`&I@AjZL@ABqP}? B12aB17.4F~ Bq6AB&SBW@B?4ɨV@BKL@BC` ` ? C12aC17.2F~ Cq6AC.1V@C?4ɨV@CKL@CD D11aD@V@1Y@DMbXH@D`&I@DjZL@DE E10aEȴ@A@Ee=@E~!>@EQ}L@EF F9aF=@v@FX9vn0@Fy><˝0@FYtq#L@FG G8aG@@G^K=#@G׏#@G‰ҍbL@GHߦ5}? H7a~ H$@HV-JX@~ Hh@HZoG@HZXm?L@HII from90 to I30oC III:`L@IJll? J6aJ@Ŷ@Jx&1@Jʱio@JPP@JK K7a~ K @KV-JX@K*D@KVT@KK:pqP@KL L8aL@@@L@a+'@Lk^6'@LD[V]`T0abc16d efghi82jk lmnopqrswtuvwxwz {G|}~T0` `8a`@@`2w-!@`%@`'A@`a a9aa2@v@aCl$@aښg%@aQB@ab b10abh@A@b߾2@b}ΐ 3@b1AS1B@bc c11ac@1Y@c' ?@c&?@@cٝ44NB@cd~? d12ad11.2F~ dq6AdM@d36AM@d;8@Kj%I3@с8@BXooppppoo]ooppzzdpooy2>V]T016 82 ww GT0 9a@v@&S@۽t@ cRh8@ 10a6@A@@c)@S/̪X28@ 11at@1Y@r4@ȣ44@Xz8@~ ? 12a@q6ATt$B@PXV]wppxT016 82 ww GT0 11a:@1Y@L7A`-@0}-@3,0@ 10a0@A@m!@2/!@5N'y1@ 9a"@v@Zd;O @L@bp51@ 11b@!Y@@Na@ .Ht1@#"""""? 12b7@6@-*@ְ͠*@4R-0@} from90 to60.0C R k0@? 9a@v@†W@9^D@q3@ 10a@A@Oec%@wBK$@y\A3@ 11a?@1Y@S㥋1@_1@0"Dh3@88? 12a@q6A>@ ꦜ2?@r X3@hE#߼? 12a@q6A>@ ꦜ2?@r X3@ 11a?@1Y@S㥋1@_1@0"Dh3@ 10a@A@Oec%@wBK$@y\A3@xKs‚? 9a@v@D@9^D@q3@(92@Date:~ `@77Smpl.: CAFEFILTRE~ ?Spec.: VODA~ ?Temp.:70.0C}to 90C Viscometer:Rheotest1688/S1 time spd alfgam[1/s]tau[Pa]F t-modl[Pa]Fh[mPas]ll? 9a@v@?ܵ @Ւ @}hx )*@ 10a @A@x#| @"t@,&)@ 11b$@!Y@h@yC@7)@ 11a@1Y@K=%@@,&@WK \)@ 12b@6@#@zom$@WEmo)@7Bp? 12aD@q6A!up3@4[Ț3@(@-؂-? 12aD@q6A!up3@4[Ț3@(@ 12b@6@#@zom$@WEmo)@ 11a@1Y@K=%@@,&@WK \)@ 11b$@!Y@h@yC@7)@ 10a@A@N@a@"t@,&)@BXppopx_wppxxppw2>V]wpdppxxppdT016 82 ww GT0`!8e|? 9a@@v@:M@Ւ @}hx )*@} from90 to70.0C G Մ̔)@` ` ? 9a @v@m@ݸʙ@ J.@ 10ah@A@g~5@ۏ@[-@ 11a6@1Y@5^I (@Yպ(@x+,@? 12aC@q6AMb6@sՠ5@t{Ͱ+@֮1_7? 12aC@q6AMb6@sՠ5@t{Ͱ+@ 11a@1Y@2w-!(@Yպ(@x+,@ 10ah@A@g~5@ۏ@[-@~ ? 9a @v@m@ݸʙ@ J.@`h +@Date:~ `@77Smpl.: CAFEFILTRE~ ?Spec.: VODA~ ?Temp.:80.0C}to 90C Viscometer:Rheotest1688/S1 time spd alfgam[1/s]tau[Pa]F t-modl[Pa]Fh[mPas]7~ ? 10a@A@ h"l@c>G@oeS#@ 11b`@!Y@pΈ`@ɴ@~+t#@ 11a@1Y@%#gaO !@ԼSJ @%"@ 12b@6@(-@@} #@D9"? 12a@q6AHPs-@"*?-@K"@o^M<+? 12a@q6AHPs-@"*?-@K"@ 12bȔ@6@e@@} #@ 11a@1Y@%#gaO !@ԼSJ @%"@ 11b@!Y@Af'@ɴ@~+t#@u< ? 10a`@A@S!u@c>G@oeS#@} from90 to80.0C gr#@? 10a@A@†W@hf@S)Y%@ 11b@@!Y@eX@'%U@k8{%@ 11ax@1Y@*:("@]B#"@vj$@ 12b@6@{/L @l @2E $@BXw_wppxxpps2>V]tpppxxpppx_xppT016 82 wrq? 12a<@q6A9v/@ I[/@GL$@!8e|? 12a<@q6A9v/@ I[/@GL$@ 12b-@6@I +' @l @2E $@ 11ax@1Y@*:("@]B#"@vj$@ 11b@!Y@( ~@'%U@k8{%@k׍? 10a@@A@$bJ$+@hf@S)Y%@m$@Date:~ `@77Smpl.: CAFEFILTRE~ ?Spec.: VODA~ ?Temp.:90.0C}to 90C Viscometer:Rheotest1688/S1 spd alfgam[1/s]tau[Pa]F t-modl[Pa]Fh[mPas] 10a @A@x#|@@@s@ 11b`@!Y@ - @u/4{ @nʔ~@ 11a(@1Y@#~j@3@_?@ 12b@6@2w-!@i̱F`@NK@ 12a@q6A=,Ԛ'@eq'@-R-@ 12a|@q6Aea'@eq'@-R-@ 12b@6@(-@i̱F`@NK@ 11a(@1Y@#~j@3@_?@ 11b@!Y@lV}. @u/4{ @nʔ~@ 10a @A@x#|@@@s@Ȝ@2N xxpppx2>V]ppppppppppP8(  p  6NMM? !,<]`  "<~?<~?3` >Y5` >Y6Љ3d23 M NM4 3QQ ;#Q ;#Q3_4E4 &&3QQQQ3_ O NM  MM<4JK4D$% M 3O&5Q4$% M 3O&6Q4FAq t 3O 3*#M43*#M! 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