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Table 1 Table with numerical values of material constants, normalization constants, dimensionless parameters, and numerical parameters

From: A mixture theory-based concrete corrosion model coupling chemical reactions, diffusion and mechanics

  Material constants   Dimensionless parameters
  Value (MKS unit) Reference   Value Definition
E 1 1.60 ·109 (kg/m s2) [32] E 1 0.038 E1/E
E 2 4.20 ·1010 (kg/m s2) [41] E 2 1.00 E2/E
χ 1 2.67 ·1010 (kg/m3s) χ 1 1.00 χ1/χ
χ 2 2.67 ·1010 (kg/m3s) χ 2 1.00 χ2/χ
\(\mathcal {J}_{2}\) 0.326 ·10−5 (m/s) * \(\mathcal {J}_{2}\) 0.40 \(\mathcal {J}_{2}/J\)
\(\mathcal {J}_{3}\) 1.632 ·10−5 (m/s) * \(\mathcal {J}_{3}\) 2.00 \(\mathcal {J}_{3}/J\)
γ 1 3.604 ·1010 (kg/ms) * γ 1 0.50 γ1/γ
γ 2 3.604 ·1010 (kg/ms) * γ 2 0.50 γ2/γ
A 1 0.821 ·10−3 (1/m) * A 1 0.50 A1/A
A 2 0.821 ·10−3 (1/m) * A 2 0.50 A2/A
\(\tilde {\rho }_{1}\) 2.32 ·103 (kg/m3) [20] ϕ 1 s a t 1.00  
\(\tilde {\rho }_{2}\) 2.21 ·103 (kg/m3) [20] ϕ 3 t h r 0.00  
\(\tilde {\rho }_{3}\) 1.84 ·103 (kg/m3) [20] ϕ 2 r e s 1.00  
\(\mathcal {M}_{1}\) 0.172164 (kg/mol) [20] ϕ 3 r e s 1.00  
\(\mathcal {M}_{2}\) 0.074093 (kg/mol) [20] κ 1 23.00 Eq. 51
\(\mathcal {M}_{3}\) 0.098079 (kg/mol) [20] κ 3 13.50 Eq. 51
δ 5.10 (kg/m s) * δ 1 1.00 δ1/KH2
δ 1 2.20 ·10−3 (m2/s) δ 2 1.05 δ2/KH2
δ 2 2.31 ·10−3 (m2/s) δ 3 1.26 δ3/KH2
δ 3 2.77 ·10−3 (m2/s)    
k 1.00 ·10−6 (m3/mol s) [3]    
  Normalization Constants   Numerical Parameters
  Value (MKS unit) Definition   Value Definition
H 1.643 ·100 (m) h(0) Δ t 0.001  
K 0.816 ·10−3 (1/s) Eq. 44 t f 0.5 Tf/T
S K -1 (-) Eq. 44 1/Δz 300  
χ 2.67 ·1010 (kg/m3s) χ 1 ϕ min 10−5  
E 4.20 ·1010 (kg/m s2) E 2 V max 106  
T 1.716 (s) χH2/E    
U 2.300 ·10−3 (m) χH3K/E    
V 1.341 ·10−3 (m/s) HK    
J 0.816 ·10−3 (m/s) HK    
γ 7.208 ·1010 (kg/m s) χ H 2    
ε 0.0014 (-) χH2K/E    
  1. * An experimental value of this parameter is unknown to us; we have chosen their values such that their dimensionless values are of order one of magnitude. Specifically, the values of J2 and J3 are so large that they guarantee growth of the layer; see also remark just below Eq. 55
  2. We estimated the values of χα from the Darcy law with χα=μ/k0 with μ the dynamic viscosity of sulfuric acid (value of 26.7·10−3 kg/ms, see ([15], p. 304-305) and k0 the average pore size or permeability (about 1 μm2 = 10−12 m2); see [11, 24]
  3. We used \(\delta _{\alpha } = \delta /\tilde {\rho }_{\alpha }\) for α=1,2,3