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The vapour–liquid interface and stresses in dried bodies

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Abstract

The paper presents a contribution to modelling the problem of vapour–liquid interface receding into dried body and stresses induced by drying of capillary-porous bodies. A complex algorithm comprising the specific mechanisms of drying in the first and second periods of drying is constructed. It enables calculation and drawing of the body temperature and drying curves for the whole drying process and identification of the vapour–liquid interface receding into the body. The drying induced stresses caused by the receding vapour–liquid interface and the non-uniform distribution of moisture content and/or temperature are analyzed. Numerical calculations of the temperature and drying curves and the drying induced stresses are carried out for the example of a finite dimensional kaolin cylinder dried convectively.

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Abbreviations

a :

Reciprocal of relaxation time [1/s]

A :

Elastic bulk modulus [MPa]

c v :

Specific heat [J/kg · K]

c T :

Coefficient of thermodiffusion [m2/s2· K]

c X :

Coefficient of diffusion [m2/s2]

D T :

Thermal diffusivity [m2/s]

e ij :

Strain deviator [1]

f(X l):

Moisture transport parameter [kg · s2/m4]

g i :

Gravity acceleration [m/s2]

H :

Cylinder height [m]

l :

Latent heat of evaporation [J/kg]

K :

Elastic volumetric modulus [MPa]

M :

Elastic shear modulus [MPa]

p :

Pressure [Pa]

q :

Heat flux [W/m2]

r, R :

Cylinder radius [m]

\(\Re\) :

Specific gas constant [J/kg · K]

s, s α :

Entropy, entropy of α-constituent [J/kg · K]

s ij :

Stress deviator [Pa]

t :

Time [s]

T :

Temperature [K]

u(u r , u z ):

Displacement vector [m]

W α :

Mass flux of α-constituent [kg/m2· s]

x a , x n :

Mole fractions of vapour in air [1]

x, y, z :

Spatial Cartesian co-ordinates [m]

X α :

Dry basis content of α-constituent [1]

Greek symbols :

 

α m :

Coefficient of convective vapour exchange [kg · s/m4]

α T :

Coefficient of convective heat exchange [W/m2· K]

κ:

Ratio of vapour chemical potential to that of liquid [1]

κ v :

Viscous bulk modulus [Pa · s]

κ(T) :

Coefficient of thermal expansion [1/K]

κ(X) :

Coefficient of humid expansion [1]

\(\varepsilon_{ij}\) :

Strain tensor [1]

\(\varepsilon\) :

Volumetric strain [1]

σ ij :

Stress tensor [Pa]

σ:

Spherical stress [Pa], surface tension [N/m]

ρ, ρα :

Mass density, mass concentration of α-constituent [kg/m3]

\(\hat{\rho}^{\alpha}\) :

Rate of α-constituent mass change by phase transitions [kg/m3· s]

μα :

Chemical potential of α-constituent [J/kg]

η:

Viscosity [Pa · s]

\(\omega\) :

Phase transition coefficient [kg · s/m5]

\(\vartheta =T-T_{0}\) :

Relative temperature [°C]

\(\theta = X^{l}-X_0^l\) :

Relative moisture content [1]

Λα :

Mass transport coefficient of α-constituent [kg · s/m3]

Λ T :

Coefficient of thermal conductivity[W/m · K]

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Authors and Affiliations

  1. Institute of Technology and Chemical Engineering, Poznań University of Technology, pl. Marii Skłodowskiej-Curie 2, 60-965, Poznań, Poland

    Stefan Jan Kowalski & Andrzej Rybicki

Authors
  1. Stefan Jan Kowalski
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  2. Andrzej Rybicki
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Correspondence to Stefan Jan Kowalski.

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Kowalski, S.J., Rybicki, A. The vapour–liquid interface and stresses in dried bodies. Transp Porous Med 66, 43–58 (2007). https://doi.org/10.1007/s11242-006-9021-3

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  • DOI: https://doi.org/10.1007/s11242-006-9021-3

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