A Mathematical Approach for Modeling the Effects of Moisture Transfer and Sustained Delivery of Antimicrobial Compounds in Composite Food

Transcription

1 3rd International Workshop on Water in Food 9-30 March 004, Lausanne, Switzerland V. Guillard, E. Roca, V. Issoupov, S. Guilbert, N. Gontard A Mathematical Approach for Modeling the Effects of Moisture Transfer and Sustained Delivery of Antimicrobial Compounds in Composite Food Joint Research Unit Agropolymers Engineering and Emerging Technologies INRA, ENSA.M, UM II, CIRAD Montpellier, place Viala, Montpellier, France

2 Water influence on the food safety, stability, quality, physical properties and shelf-life Composite food is an association of food products with contrasting properties (texture, apparent density, porosity, moisture content) «wet» part, a w1 «dry» part, a w The influence of water is from: interactions between water molecules and other constituents of food chemical composition of the medium the state of water in food Water has an influence on the rheological, thermal, diffusion, acoustic and microbiological properties of food The state of water in food is expressed as water activity: a w = p p 0 P, T

3 Outline and scientific goals Experimental characterization of water transfer in food Modeling water transfer in multi-compartment food moisture sorption isotherms moisture content distribution profiles Studying the moisture diffusivity in materials Simulation of moisture distribution profiles in two-compartment food (ice cream in a cereal cone or cake with fresh cream filling) Simulation and control of moisture transfer for preservation the texture properties using edible films in three-compartment food (the edible film is placed at the interface between the «wet» and «dry» compartments) Application of the developed model to describe the sustained delivery of antimicrobial agents for preservation of the food shelf-life

4 Characterization of moisture transfers: experiment and modeling Evaluation of moisture distribution profiles during storage in composite food. Prevention of moisture transfer in food

5 Mathematical statement of the one-dimensional moisture transfer problem in composite food «Wet» compartment Film «Dry» compartment X 1, ρ ms1 Non rate-limiting X, D, ρ ms X 3 3 ( X3), ms3, D ρ 0 e 1 e 1+ e e 1+ e + e 3 x X ρ 1 X D = ρ 1 ms1 D ms X and 1 c = B1 X A c X ρ X3 D ms = D3 ρms3 X 3 and 1 c = B3 X A c 3 X D 3 3 = 0 ρ dx dt = ρ D X L X t = D X X t = D X ( X ) unknown parameters: sorption isotherms and diffusivity

6 DVS kinetic data and calculated curves for water adsorption of sponge-cake at 0 C The diffusivity D eff is determined from Fick s second law Moisture content (g/g dry basis) D eff (X) a X = ln a w Time (hours) 1 b a w is from 0.8 to 1 The Ferro Fontan equation is used to describe the sorption behavior c Relative humidity (%)

7 Effective moisture diffusivity of sponge-cake as a function of moisture content at 5, 0 and 5 C 8.0E E-10 Environmental Scanning Electron Microscopy Diffusivity (m²/s) 6.0E E E E-10.0E-10 Initial moisture content of the sponge-cake Formation of a swollen matrix DX ( X) = D X Deff 0 1.0E E Equilibrium moisture content of the monolayer Moisture content (g/g dry basis) Vapor-phase diffusion Liquid diffusion

8 Moisture distribution profiles in two-compartment food: validation of the model Model food: agar gel/sponge-cake Different water activities in agar gel: 0.99, 0.95 and 0.90 Different temperatures: 5, 0 and 35 C Real food: agar gel/dry biscuit Nature: processed cheese/sponge-cake Moisture content (g/100g h.b.) Processed cheese initial a w = days days days 1 day Distance (cm) Sponge-cake initial a w = C

9 Moisture distribution profiles in three-compartment food: validation of the model Model food: agar gel/edible film/sponge-cake Different water activities in agar gel: 0.99, 0.95 and 0.90 Different temperatures: 5, 0 and 35 C Films with different composition (acetylated monoglycerides (ACETEM), dark chocolate, wheat gluten) Moisture content (g/100g h.b.) Agar gel Time (days) without film 0 C Sponge-cake ACETEM film of 93±30 µm

10 Sorption isotherms and moisture diffusion mechanism relative to sponge-cakes of different density 1.8E-09 Apparent diffusivity (m /s) 1.6E E-09 1.E E E E E-10 porosity diffusivity Density (kg/m 3 ) types of sponge-cake y = x y = x y = x E E Moisture content (g/g dry basis)

11 Experimental and predicted water sorption isotherms: influence of the sponge-cakes density Moisture content (g/g dry basis) experimental data is underestimated at high a w Ferro Fontan equation a 1 X = ln a w b c Water activity Density, Porosity The density affects the diffusion kinetics Change from liquid to vapor-phase diffusion Diffusivity The sorption equilibrium is not affected by the materials structure

12 Stability of food with an active coating: application of developed models Modeling the growth inhibition of biological microorganisms in food with an antimicrobial coating (sustained active agent delivery)

13 Active coating with antimicrobial agents used to improve the microbiological stability of food Antimicrobial agent added to food Storage C 1 antimicrobial coating F and to an active coating Storage C model food Agar-agar gel: e = 8 mm, D = m /s Sorbic Acid migration from a superficial wheat gluten or beeswax film into a model food Wheat gluten film: e = 10 µm, D = m /s Beeswax layer: e = 30 µm, D = m /s

14 Release of Sorbic Acid from wheat gluten and beeswax films placed on a model food antimicrobial coating e 1 +e sorbic acid agar-agar gel D 1, D, X 1, X x Mathematical model y Release kinetics (mg) Saturation point Beeswax coating Model food Wheat gluten coating Fick s nd law: X1 X1 = D1, t X X = D t for t > 0, e 1 < x < +e Initial and boundary conditions: D 1 = D 1 X ( x ) ( 0, t) X X,0 = X, 0 X = Storage time (days) A two-compartment system Crank-Nicolson finite-difference method is used to solve the system of equations numerically

15 Concentration profiles of Sorbic Acid in wheat gluten (a) and beeswax films (b) Concentration (mg) (a) Film Film Film t = 0 8 min. 60 min. Food Food Food Distance (µm) Distance (µm) Distance (µm) Concentration (mg) (b) Film t = 0 Film 7 days Film 15 days Food Food Food Distance (µm) Distance (µm) Distance (µm)

16 Modeling the overall initial concentration of Sorbic Acid to maintain the surface concentration at 0. g/ml Overall initial SA concentration (g/ml) beeswax film myvacet film wheat gluten film 0.% 0.01% Storage time (days)

17 Evolution of the surface concentration of Sorbic Acid and its potential antimicrobial activity in food 0.0 [ I] = f C t, 0, The concentration [I] appears in models of predictive microbiology 1 D Growth rate constant [I] = [SA] at the surface (%) saturation is reached within 1 day the mass release is delayed significantly beeswax wheat gluten µ µ = max K i [ I] + Ki Storage time (days) Reference: Han & Floros, J. Food Sci. 63 (1), 1 (1998)

18 «Transferomatic» software for modeling multiple mass transfer and assisted food engineering - experimental database on diffusion properties of foodstuffs, film barrier properties and fresh fruits respiratory activity - mathematical models developed at University of Montpellier II - mathematical tool Matlab 6.5 for numerical solution - models validation and adjustment on experimental data Wet compartment: jam cheese agar gels Dry compartment: biscuit sponge-cake Edible film: ACETEM TSED dark chocolate wheat gluten Vegetables: endives tomatoes mushrooms Packaging film: polyethylene wheat gluten PEBD film prediction of moisture content profiles and food shelf-life

19 Selection of food products for the compartments and definition of the food parameters

20 Definition of the parameters of numerical simulation (discretization of the model, storage conditions) Discretization parameters Calculation parameters Profiles to be visualized on the graph Storage time and storage temperature Output file name Discretization of the food compartments Temperature regime

21 water activity a w (x) superposition with experimental data overall moisture content

22 Conclusion: The idea of the assisted food engineering Nature of the compartments Limiting factors Desirable shelf-life D eff database water transfer microorganisms «Transferomatic» simulation tool Theoretical shelf-life Michaëlis-Menten equation parameters MAP assisted by gas absorbers Film thickness Visit our web-site at