Mathematical Modeling of Betanin Extraction from Red Beet (Beta vulgaris L.) by Solid–Liquid Method
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Honggao Xu
Abstract
Effective diffusion coefficient (D-value) is an important parameter for the extraction process. In this study, a cylindrical model to estimate the D-value of betanin extraction from red beet roots was developed. The influence of extraction temperature, pH, cylindrical thickness and type of acids on the D-value was also investigated. The optimal parameters of betanin extraction were 30°C, pH 4.0 adjusted with sulfurous acid or acetic acid. D-values under the above conditions were 18.95×10−11 m2/s and 17.87×10−11 m2/s, respectively. The result showed that D-value elevated with the increase of cylindrical thickness, which was consistent with earlier conclusion from spherical model. The modeling may be useful for the investigation into extraction process and practical application.
Nomenclature
- A
Corrected absorbance
- a and b
Absorbance values at 540 and 600 nm, respectively
- Bi
Biot number
- c
Concentration in sample (kg/m3)
- ca
Average concentration in sample (kg/m3)
- ci
Concentration in sample at initial (kg/m3)
- c∞
Concentration in sample at equilibrium (kg/m3)
- Clbk
Concentration in bulk liquid (kg/m3)
- Clbk∞
Concentration in bulk liquid at equilibrium (kg/m3)
- D
Effective diffusion coefficient (m2/s)
- J0
Bessel function of the first kind of zero order
- J1
Bessel function of the first kind of first order
- k
Mass transfer coefficient (m/s)
- L
Half-thickness of the slab (m)
- R
Radius of the cylinder (m)
- r
Distance from circular center (m)
- t
Time (s)
- Greeks
- Δ
Half thickness for an infinite slab or radius for an infinite cylinder (m)
- δ
Distance from the center of an infinite slab or radius of an infinite cylinder (m)
- λ
Root of the characteristic equations
- μ
Root of the characteristic equations
- Ψ
Dimensionless concentration
- Ψa
Average dimensionless concentration
- Ψc
Dimensionless concentration in infinite cylinder
- Ψs
Dimensionless concentration in infinite slab
References
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©2015 by De Gruyter
Articles in the same Issue
- Frontmatter
- Research Articles
- Investigation of UF and MF Membrane Residual Fouling in Full-Scale Dairy Production Using FT-IR to Quantify Protein and Fat
- Mathematical Modeling of Betanin Extraction from Red Beet (Beta vulgaris L.) by Solid–Liquid Method
- Rapid Discrimination of Apple Varieties via Near-Infrared Reflectance Spectroscopy and Fast Allied Fuzzy C-Means Clustering
- Formulation Development of Multilayered Fish Oil Emulsion by using Electrostatic Deposition of Charged Biopolymers
- Reduction of Turbidity of Beet Sugar Solutions by Mechanical and Chemical Treatment
- Purification of a Bacteriocin from Lactobacillus plantarum ZJ217 Active Against Methicillin-Resistant Staphylococcus aureus
- Influence of Different Wall Materials on the Microencapsulation of Virgin Coconut Oil by Spray Drying
- A CFD Study of the Effects of Feed Diameter on the Pressure Drop in Acyclone Separator
- Electrolyzed Water Generated Using a Circulating Reactor
- Determination of Volatile Compounds of Chinese Traditional Aromatic Sunflower Seeds (Helianthus annulus L.)
- Static Rheological Study of Ocimum basilicum Seed Gum
- Finite Element Model to Predict the Bioconversion Rate of Glucose to Fructose using Escherichia coli K12 for Sugar Production from Date
- Influence of Hot Bed Spray Dryer Parameters on Physical Properties of Peppermint (Mentha piperita L.) Tea Powder
- Foam-Mat Drying of Muskmelon
- Simulating Continuous Time Production Flows in Food Industry by Means of Discrete Event Simulation
- Shorter Communication
- Effect of Vacuum Soaking on the Properties of Soybean (Glycine max (L.) Merr.)
Articles in the same Issue
- Frontmatter
- Research Articles
- Investigation of UF and MF Membrane Residual Fouling in Full-Scale Dairy Production Using FT-IR to Quantify Protein and Fat
- Mathematical Modeling of Betanin Extraction from Red Beet (Beta vulgaris L.) by Solid–Liquid Method
- Rapid Discrimination of Apple Varieties via Near-Infrared Reflectance Spectroscopy and Fast Allied Fuzzy C-Means Clustering
- Formulation Development of Multilayered Fish Oil Emulsion by using Electrostatic Deposition of Charged Biopolymers
- Reduction of Turbidity of Beet Sugar Solutions by Mechanical and Chemical Treatment
- Purification of a Bacteriocin from Lactobacillus plantarum ZJ217 Active Against Methicillin-Resistant Staphylococcus aureus
- Influence of Different Wall Materials on the Microencapsulation of Virgin Coconut Oil by Spray Drying
- A CFD Study of the Effects of Feed Diameter on the Pressure Drop in Acyclone Separator
- Electrolyzed Water Generated Using a Circulating Reactor
- Determination of Volatile Compounds of Chinese Traditional Aromatic Sunflower Seeds (Helianthus annulus L.)
- Static Rheological Study of Ocimum basilicum Seed Gum
- Finite Element Model to Predict the Bioconversion Rate of Glucose to Fructose using Escherichia coli K12 for Sugar Production from Date
- Influence of Hot Bed Spray Dryer Parameters on Physical Properties of Peppermint (Mentha piperita L.) Tea Powder
- Foam-Mat Drying of Muskmelon
- Simulating Continuous Time Production Flows in Food Industry by Means of Discrete Event Simulation
- Shorter Communication
- Effect of Vacuum Soaking on the Properties of Soybean (Glycine max (L.) Merr.)
