Water Activity- Sucrose And Water
Páginas: 10 (2267 palabras)
Publicado: 13 de mayo de 2012
Water activity in aqueous solutions of sucrose: an improved temperature dependence
Maciej STARZAK
School of Chemical Engineering University of KwaZulu-Natal Durban, South Africa
Mohamed MATHLOUTHI
Laboratoire de Chimie Physique Industrielle Université de Reims, Champagne-Ardenne Reims, France
Outline
1. 2. 3. 4. 5. Introduction Previous studies Experimental database Selection of thewater activity model Relationships between experimental variables and activity coefficients 6. Data regression 7. Results 8. Recommended equation for water activity coefficient
Water activity formulae popular amongst food technologists
Norrish, 1966 Chen, 1989
ln γ A = α x γA
2 B
1000 + M A m = n 1000 + M A m ( A + Bm ) ln γ A = α x + β x
2 B 3 B
Miyawaki, 1997
Models used topredict water activity coefficient
n Redlich-Kister expansion - empirical (includes Margules equation) n UNIQUAC - phenomenological (two-fluid theory) n group contribution methods (UNIFAC, ASOG)
Starzak & Peacock, 1997
Q 2 2 ln γ A = xB (1 + bxB + cxB ) RT
Based on 1197 experimental points (56 data sets), mainly VLE data (BPE, vapour pressure, ERH, isopiestic solutions)
Catté et al.,1994
1.4 1.3 1.2 1.4 1.3
Starzak & Peacock, 1997
UNIQUAC
Water activity coefficient
1.2 1.1 1 0.9 0.8 0.7 0.6 0.5 0.4 0
Margules eq.
Water activity coefficient
1.1 1 0.9 0.8 0.7 0.6 0.5 0.4
0
20
40
60
80
100
20
40
60
80
100
% mas. sucrose
% mas. sucrose
Water activity coefficient (boiling curve)
1.8
Water activity coefficient onthe boiling curve
1.6
1193 points
Starzak & Peacock, 1997
1.4
1.2
1
0.8
0.6
0.4
0
10
20
30
40
50
60
70
80
90
100
% mass sucrose
Theoretical models of activity for highly concentrated sucrose solutions
§ §
Van Hook, 1987: - sucrose hydration - sucrose association (clustering) Starzak & Mathlouthi, 2002: - water association -sucrose hydration - sucrose association (clustering)
Previous studies (small exptl. databases)
Ø Ø Ø Ø Ø Le Maguer, 1992 (UNIQUAC) Caté et al., 1994 (UNIQUAC) Peres & Macedo, 1996 (UNIQUAC) Peres & Macedo, 1997 (UNIFAC) Spiliotis & Tassios, 2000 (UNIFAC)
Objective of this study:
q an empirical activity equation q wide range of temp. & concentrations q large database
Thermodynamic datatypically used to determine the activity coefficient
q VLE data (BPE, VPL, ERH,
osmotic coeff. by isopiestic method) q q SLE data (FPD, sucrose solubility) Termochemical data (heat of dilution, excess heat capacity)
EXPERIMENTAL DATABASE
Data type VLE FPD Solubility Heat of dilution Heat capacity Total
Experimental points Literature sources
1507 213 265 283 70 2338
64 13 34 10 4 125 Distribution of experimental data
Distribution of experimental data
Selection of water activity model
n-suffix Margules equation
ln γ A =
Advantages: Drawbacks:
∑α
k =2
n
k
x
k B
linear with respect to its coefficients lack of sound theoretical foundation
General temperature dependence
αk 0 α k (θ ) = + α k1 + αk 2 ln θ + α k 3θ + α k 4θ 2 + α k 5θ 3 θwhere θ = T T0
Disadvantage: large number of parameters
Simplified temperature dependence
ln γ A = a(θ ) ∑ bk − 2 x
k =2
n
k B
a0 2 3 a(θ ) = + a1 + a2 ln θ + a3θ + a4θ + a5θ θ
Advantage: reduced number of parameters
Disadvantage: temperature effect pattern independent of composition
Sucrose activity coefficient
ln γ B =
∑β
k =2
n
k
x
k A
Gibbs-Duhemequation
d ln γ A d ln γ B xA = xB d xA d xB
Expansion coefficients of sucrose activity
l β k = (−1) ∑ Al , l³ k k
n k
k³ 2
where
l +1 Al = αl − αl +1 , l = 2,3,..., n − 1 l An = α n
Expansion coefficients of sucrose activity, n = 7
β2 = β3 = β4 = β5 = β6 = β7 = 3 5 7 α 2 + α3 + 2α 4 + α5 + 2α6 + α7 2 2 2 8 35 − α3 − α 4 − 5α 5 − 8α6 − α7 3 3 15 35 α 4 + α5 +...
Maciej STARZAK
School of Chemical Engineering University of KwaZulu-Natal Durban, South Africa
Mohamed MATHLOUTHI
Laboratoire de Chimie Physique Industrielle Université de Reims, Champagne-Ardenne Reims, France
Outline
1. 2. 3. 4. 5. Introduction Previous studies Experimental database Selection of thewater activity model Relationships between experimental variables and activity coefficients 6. Data regression 7. Results 8. Recommended equation for water activity coefficient
Water activity formulae popular amongst food technologists
Norrish, 1966 Chen, 1989
ln γ A = α x γA
2 B
1000 + M A m = n 1000 + M A m ( A + Bm ) ln γ A = α x + β x
2 B 3 B
Miyawaki, 1997
Models used topredict water activity coefficient
n Redlich-Kister expansion - empirical (includes Margules equation) n UNIQUAC - phenomenological (two-fluid theory) n group contribution methods (UNIFAC, ASOG)
Starzak & Peacock, 1997
Q 2 2 ln γ A = xB (1 + bxB + cxB ) RT
Based on 1197 experimental points (56 data sets), mainly VLE data (BPE, vapour pressure, ERH, isopiestic solutions)
Catté et al.,1994
1.4 1.3 1.2 1.4 1.3
Starzak & Peacock, 1997
UNIQUAC
Water activity coefficient
1.2 1.1 1 0.9 0.8 0.7 0.6 0.5 0.4 0
Margules eq.
Water activity coefficient
1.1 1 0.9 0.8 0.7 0.6 0.5 0.4
0
20
40
60
80
100
20
40
60
80
100
% mas. sucrose
% mas. sucrose
Water activity coefficient (boiling curve)
1.8
Water activity coefficient onthe boiling curve
1.6
1193 points
Starzak & Peacock, 1997
1.4
1.2
1
0.8
0.6
0.4
0
10
20
30
40
50
60
70
80
90
100
% mass sucrose
Theoretical models of activity for highly concentrated sucrose solutions
§ §
Van Hook, 1987: - sucrose hydration - sucrose association (clustering) Starzak & Mathlouthi, 2002: - water association -sucrose hydration - sucrose association (clustering)
Previous studies (small exptl. databases)
Ø Ø Ø Ø Ø Le Maguer, 1992 (UNIQUAC) Caté et al., 1994 (UNIQUAC) Peres & Macedo, 1996 (UNIQUAC) Peres & Macedo, 1997 (UNIFAC) Spiliotis & Tassios, 2000 (UNIFAC)
Objective of this study:
q an empirical activity equation q wide range of temp. & concentrations q large database
Thermodynamic datatypically used to determine the activity coefficient
q VLE data (BPE, VPL, ERH,
osmotic coeff. by isopiestic method) q q SLE data (FPD, sucrose solubility) Termochemical data (heat of dilution, excess heat capacity)
EXPERIMENTAL DATABASE
Data type VLE FPD Solubility Heat of dilution Heat capacity Total
Experimental points Literature sources
1507 213 265 283 70 2338
64 13 34 10 4 125 Distribution of experimental data
Distribution of experimental data
Selection of water activity model
n-suffix Margules equation
ln γ A =
Advantages: Drawbacks:
∑α
k =2
n
k
x
k B
linear with respect to its coefficients lack of sound theoretical foundation
General temperature dependence
αk 0 α k (θ ) = + α k1 + αk 2 ln θ + α k 3θ + α k 4θ 2 + α k 5θ 3 θwhere θ = T T0
Disadvantage: large number of parameters
Simplified temperature dependence
ln γ A = a(θ ) ∑ bk − 2 x
k =2
n
k B
a0 2 3 a(θ ) = + a1 + a2 ln θ + a3θ + a4θ + a5θ θ
Advantage: reduced number of parameters
Disadvantage: temperature effect pattern independent of composition
Sucrose activity coefficient
ln γ B =
∑β
k =2
n
k
x
k A
Gibbs-Duhemequation
d ln γ A d ln γ B xA = xB d xA d xB
Expansion coefficients of sucrose activity
l β k = (−1) ∑ Al , l³ k k
n k
k³ 2
where
l +1 Al = αl − αl +1 , l = 2,3,..., n − 1 l An = α n
Expansion coefficients of sucrose activity, n = 7
β2 = β3 = β4 = β5 = β6 = β7 = 3 5 7 α 2 + α3 + 2α 4 + α5 + 2α6 + α7 2 2 2 8 35 − α3 − α 4 − 5α 5 − 8α6 − α7 3 3 15 35 α 4 + α5 +...
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