Mathematical Modeling of a Solid-Liquid Mixture with Mass Exchange Between Constituents

2006 ◽  
Vol 11 (6) ◽  
pp. 575-595 ◽  
Author(s):  
L. Fusi ◽  
A. Farina ◽  
D. Ambrosi
Keyword(s):  
Mathematical Modeling ◽  
Mass Exchange ◽  
Liquid Mixture ◽  
Solid Liquid

Mathematical Modeling of a Solid–Liquid Mixture with Mass Exchange Between Constituents

2006 ◽  
Vol 11 (6) ◽  
pp. 575-595 ◽  
Author(s):  
L. Fusi ◽  
A. Farina ◽  
D. Ambrosi
Keyword(s):  
Mathematical Modeling ◽  
Liquid Mixture ◽  
Solid Phase ◽  
Deformation Gradient ◽  
Elastic Solid ◽  
Solid Deformation ◽  
Solid Stress ◽  
Phase Deformation ◽  
Mass Conversion ◽  
Solid Liquid

The mechanical behavior of a mixture composed by an elastic solid and a fluid that exchange mass is investigated. Both the liquid flow and the solid deformation depend on how the solid phase has increased (diminished) its mass, i.e. on the mass conversion between constituents. The model is developed introducing a decomposition of the solid phase deformation gradient. In particular, exploiting the criterion of maximization of the rate of entropy production, we determine an explicit evolution equation for the so-called growth tensor which involves directly the solid stress tensor. An example of a possible choice of the constitutive functions is also presented.

Mathematical Modeling of Betanin Extraction from Red Beet (Beta vulgaris L.) by Solid–Liquid Method

2015 ◽  
Vol 11 (1) ◽  
pp. 17-22 ◽  
Author(s):  
Honggao Xu ◽  
Qiang Peng ◽  
Fang Yuan ◽  
Yanxiang Gao
Keyword(s):  
Mathematical Modeling ◽  
Effective Diffusion ◽  
Spherical Model ◽  
Extraction Process ◽  
Extraction Temperature ◽  
Optimal Parameters ◽  
Practical Application ◽  
Sulfurous Acid ◽  
Red Beet ◽  
Solid Liquid

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.

scholarly journals MATHEMATICAL MODELING OF THERMOGRAVITATIONAL AND THERMOCA-PILLARY CONVECTION IN GAS-LIQUID PROCESSES

2021 ◽  
Vol 2021 (1) ◽  
pp. 58-66
Author(s):  
Evgeniy Podoplelov ◽  
Aleksey Bal'chugov ◽  
Anatoliy Dement'ev ◽  
Anatoliy Glotov
Keyword(s):  
Mathematical Modeling ◽  
Mass Transfer ◽  
Phase Boundary ◽  
Mass Exchange ◽  
Exchange Process ◽  
Transfer Coefficients ◽  
Mass Exchange Process ◽  
Convective Flows ◽  
Liquid Phases ◽  
Turbulent Pulsations

. The interaction of gas and liquid phases in some cases is accompanied by the spontaneous occur-rence of convective flows and turbulent pulsations at the phase boundary and in adjacent areas. Hy-drodynamic instability allows to accelerate the interfacial transfer of matter and leads to an increase in mass transfer coefficients. Research in this field is not only theoretical, but also practical, since sur-face convection can be artificially created in apparatus for intensifying the mass exchange process.

Measuring Solid-Liquid Mixture in Closed Conduits

1968 ◽  
Vol 94 (4) ◽  
pp. 453-464
Author(s):  
Richard N. Weisman ◽  
Walter H. Graf
Keyword(s):  
Liquid Mixture ◽  
Solid Liquid
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