Variable hydration of small carbohydrates for prediction of equilibrium properties in diluted and concentrated solutions

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Roger Archibald Ellis
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1 Variable hydration of small carbohydrates for prediction of equilibrium properties in diluted and concentrated solutions J.-B. Gros LGCB, Université B. Pascal, Clermont-Ferrand, France

2 Which thermodynamic properties in food processing, formulation and control? Water activity Osmotic pressure Activity of dissolved species Solubility of gases Solubility of solids in water Partition factors ph

3 Food products = nonideal complex mixtures Excess free energy f,p Osmotic properties g E Solid-liquid equilibrium properties T f, T m Solubility S K i LL Liquid-liquid equilibrium properties γ i Dissociation properties ph Vapor-liquid equilibrium properties K i LV,a w T b Solubility G

4 Our selected γ i model: main characteristics Group-contribution method glucose-water solution Hydration of ions NaCl solution CH 2 4 CH 5 OH CH-O Structural decomposition Hydration number

5 Our selected γ i model U L P D H S Unifac Larsen Pitzer Debye Hückel Solvation - the predictive group-contribution UNIFAC (975) model modified by Larsen (987) for short range physical interactions - for long range interactions : a Pitzer term (Debye-Hückel) - hydration of ions by water molecules No salt dependent coefficients Only ions or group dependent coefficients

6 Example: mean ionic activity coefficients for some salts in aqueous solutions gamma KCl, gamma NaCl Modèle ULPDHS Modèle ULPDHS g molal 0,7 0,6 gmolal 0,7 0,5 0, m KCl (mol/kg) m NaCl (mol/kg),4,2 NaOH ULPDHS 4 3,5 3 gamma HCl Modèle ULPDHS gmolal g molal 2,5 2,5 0, m NaOH (mol/kg) 0, m HCl (mol/kg)

7 Example: water activity in sugar aqueous solutions aw aw 0,7 0,6 Modèle ULPDHS 0,5 Modèle ULPDHS 0,7 0 0, 0,2 0,3 0,4 0,5 0,6 0,7 Glucose weight fraction 0,4 0 0,2 0,4 0,6 Sucrose weight fraction aw aw 5 0,7 0,6 Modèle ULPDHS 0 0,2 0,4 0,6 Fructose weight fraction Modèle ULPDHS 0 0, 0,2 0,3 0,4 0,5 Maltose weight fraction

8 Scope Improve the estimation for aqueous system containing sugars Constraint: predict properties of aqueous solutions of single and multiple solutes including electrolytes: group-contribution method

9 What is to be done? Add new groups in the physical model: pyranose ring, furanose ring, osidic bond... Have a better description of the strong forces between molecules

10 Hydration of species Electrolytes Sugars Water molecules are bound to ions,forming stochiometric complexes Hydroxyl groups play a major role

11 Hydration number nh Glucose Fructose Sucrose Mannose Xylose nh 3,0 3,0 6,4 (literature) 3,26 3,26 3,7 8,4 c 8,8 c 8, c 6,8 c 5 Hydration varies with concentration hydration number ,2 0,4 0,6 solute weight fraction

12 Chemical part of the model S + nh H O 2 K ( ) S, nh H O 2 S Free form: X SL Hydrated form : X SH Ideal mixture of the 3 species The equilibrium constant K is given by K = exp 0 G R T = X SL X SH nh W X X SH ; X SL : molar fractions nh : hydration number

13 Chemical part of the model: true composition?? Apparent composition True composition Mass balance X XS app = + SH + X n X SL SH X W app X = W and + n X K SH 3 equations and 3 unknowns X SH, X SL et X W

14 Physical part of the model - interaction between the true species At high concentrations, interactions exist between species X SH, X SL et X W : physical model size of the true molecules London dispersion forces, etc. K becomes: K = exp 0 G R T = X SH X SL γ γ SL SH a nh W

15 Example: water activity in sugar aqueous solutions: glucose, mannose, fructose K=,4 K=4 5 aw aw Modèle ULPDHS (nh=0) Modèle ULPDHS (nh=0) Modèle ULPDHS (solv variable) Modèle ULPDHS (solv variable) 0,7 0 0, 0,2 0,3 0,4 0,5 0,6 0,7 Glucose weight fraction 5 0 0, 0,2 0,3 0,4 0,5 0,6 Mannose weight fraction K=,9 aw 0,7 0,6 Modèle ULPDHS (nh=0) Modèle ULPDHS (solv variable) 0 0,2 0,4 0,6 Fructose weight fraction

16 Xylose, sucrose, maltose K=0,32 K=6,9 aw 5 aw 0,6 Modèle ULPDHS (nh=0) 0,4 Modèle ULPDHS (nh=0) Modèle ULPDHS (solv variable) 0 0, 0,2 0,3 0,4 Xylose weight fraction 0,2 Modèle ULPDHS (solv variable) 0 0,2 0,4 0,6 Sucrose weight fraction K=6,9 aw 5 Modèle ULPDHS (nh=0) Modèle ULPDHS (solv variable) 0 0, 0,2 0,3 0,4 0,5 Maltose weight fraction

17 Results: nh and K Glucose Fructose Sucrose Mannose Xylose nh (literature) 3,0 3,0 6,4 3,26 3,26 3,7 8,4 c 8,8 c 8, c 6,8 c nh (OH) = ,2 2 2 K,4,9 6,9 4 0,32 nh,766 (0,35) 2,5 (0,5) 2,95 (0,35),34 (0,268) 06 () K,7,78 6,42,769,4

18 Water activity and molar activity coefficient of water 5 5 Sucrose: a w, g w, g s and average Brix, % w/w sucrose 3 2,5 2,5 Molal activity coefficient of sucrose hydration number nh (sucrose) = 3.2 The apparent or average hydratation number varies with concentration average hydration number 3 2,5 2,5 0,5 0 n eq = n x sh xsh + x sp γsl n Ka w γ sh = n γ sl + Ka γ 0 0,2 0,4 0,6 sh Sucrose weight fraction n w

19 Solubility of sucrose and glucose Sucrose weight fraction 0,6 0,4 0,2 0 Experiments Model Temperature ( C) Glucose weight fraction 0,6 0,4 0,2 0 Experiments Model Temperature ( C) ln H C C ( ) f,s p m,s p γ = + + SXSapp ln R T Tm,S R T R Tm,S T T

20 Glucose: a w,g w and g s,4 Water activity and molar activity coefficient of water 5 5,35,3,25,2,5,,05 Molal activity coefficient of glucose Brix, w/w glucose

21 Concentrated apple juice Water activity Fontan and Chirife 0,7 Model Total sugar concentration (% w/w)

22 Honey: model honey and Geek honeys Water activity 0,7 0,6 0,5 0,4 Rüegg and Blanc Model Total sugar concentration (% w/w) Botanic/Geographical origin Water activity 20 C after melting at 50 C Calculated water activity Honey-dew (pine)/thasos Floral/Livadia Floral(orange blossom)/argos Lazaridou et al., J. Food Eng. (2004)

23 Conclusion We need reliable data for hydration of species, by experiments and/or by molecular modelling A second-approximation form of chemical solution theory (a chemical part and a physical part) gives better estimates at high concentration of solutes than classical physical models Sandler

24 Acknowledgements Former students: C. Achard, M. Catté PhD student: L. Ben Gaïda Prof. C.G. Dussap

Estimation of water equilibrium properties in food processing. J.-B. Gros LGCB, Université Blaise Pascal

Estimation of water equilibrium properties in food processing J.-B. Gros LGCB, Université Blaise Pascal Equilibrium properties: for what? Analysis and design of processes material balances operating conditions-