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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]

Ï• 1 s a t

1.00

 

\(\tilde {\rho }_{2}\)

2.21 ·103

(kg/m3)

[20]

Ï• 3 t h r

0.00

 

\(\tilde {\rho }_{3}\)

1.84 ·103

(kg/m3)

[20]

Ï• 2 r e s

1.00

 

\(\mathcal {M}_{1}\)

0.172164

(kg/mol)

[20]

Ï• 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

Ï• 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