(c) viscosity of water
Equilibrium between liquid and vapor phase of water under arbitrary temperatures
Pl 2
r
(T ) 2.66104 T 2 3.17 103 T 9.46101
RT
60.00
Measured value Proposed equation (273<T[K]<373)
280 300 320 340 360
Temperature [K]
(a) density of water
55.00
380
260
280 300 320 340 360 380
Temperature [K]
Porosity distribution dV/d ln r
0.20 0.15
Mature mortar 0.25 = 60 % 0.45 = 85 % 0.65 = 95 %
V : Porosity function
0.10 0.05
Measured porosity distributions of 7 day cured mortars
φ is the interlayer porosity lr
S is the degree of saturation of capillary pores cp
S is the degree of saturation of gel pores gl
S is the the degree of saturation of interlayer pores lr
Degree of saturation
1.0
20C
0.8
60C
0.6 W/C50%
Drying path
0.4
0.2
Wetting path
0
0.2
0.4
0.6
0.8
1.0
Relative humidity
Moisture mass loss [g/cm3]
0.20
Experiment (60ºC)
ln
pvap p
Vl Pl
（273<T<373）
Pl
lRT
Mw
ln
pvap p
d ln p Hvap dT RT 2
Pl
lRT
Mw
ln
pvap p
pvap p exp( plMw ) p0 exp{( Hvap )( 1 1 )}exp( plMw )
lRT
R T T0
lRT
Modeling of moisture flux
3 Micro-pore structure formation and moisture transport
Luo Mian 2011.9.30
Contents
4
3.1 Basic modeling of micropore structure development
Goal: predict the micro-pore structure with time
vPlຫໍສະໝຸດ Kl )Pl(Dv
v
T
KT )T
(DpPl DT T )
Calculation of the degree of saturation in a porous system
Multi-scale modeling of moisture existing in capillary, gel and interlayer pores.
inner products outer products
Total surface area (/m3) capillary pores gel (CSH internal)
Hydration Degree of Matrix
Volumetric Balance
Bulk porosity of capillaries gel and interlayer
W/C : 0.46
W/C : 0.25
0.00
-4
-9
-8
-7
-6
-5
-4
Log (r [m])
Outline of the pore structure development computation
Cluster Expansion Model
The particle growth Volume and weight of
J (Dppl DTT )
Moisture for bothe vapor and liquid water Dp is moisture conductivity with respect to the pore presure gradient Dt is moisture conductivity with respect to the temperature gradient
Density of liquid water [g/cm3]
1.02
Surface tension 103 [N/m]
80.00
1.00 0.98 0.96 0.94
260
75.00
70.00
65.00
Measured value Proposed equation (273<T[K]<373)
These rsults idicate that the most important issue for future consideration is an oppropriate expression of moisture equilibrium based on a microscopic viewpoint.
T 2
ql
l 2 50
rc
(
0
rdV )2 Pl
KlPl
(2)
i
exp(
Ge RT
)
i 3.38108 T 4 4.63105 T 3 2.37 102 T 2 5.45 T 4.70 102
J (Dvv KlPl KTT )
Dv
( v
Pl
Pl
v
T
T
)
KlPl
KT T
(Dv
ch 0.28
1: Unhydrated core
l (twsl gvs ) / 2
2: Inner products
3: CSH grains
4: Capillary pores 5: Gel pores
6
v 6: Interlayer porosity
g
s ch
l
4
CSH size scale
(r) l g 1 exp Bgr c 1 expBcr
Porosity distribution dV/d ln r
0.25
0.20
Young mortar all = 15 %
0.15 0.10 0.05
W/C Ratio
0.25 0.45 0.65
0.00 -9
-8
-7
-6
-5
Log (r [m])
the total degree of saturation Stotal is calculated as follow
Stotal
cp Scp gl Sgl lr cp gl lr
Slr
φ is the capillary porosity cp
φ is the gel porosity gl
the law of mass conservation governing the balance in a system
w div( J ( w,T , w, T )) Q 0
t
the potential term for moisture in a porous material
w (l S )
qv
D0 (T )
rc
1
dV N
k
v
Dvv
Nk
lm 2(r ta )
J (Dppl DTT )
D0 (T1) ( T1 )3/2 ( D,T 2 )
D0 (T2 ) T2
D ,T 1
(1)
ΩD is
the collision integeral at temperature T or 1
B parameters
Matrix micro pore structure
(r) i 1 expBir
The authors subdivide the overall cementitious micro-pore structures into three basic components：
(b) surface tension
Viscosity of liquid water 10-3 [Pa.s]
2.00
Measured value
1.50
Proposed equation
(273<T[K]<373)
1.00
0.50
0.00 260
280
300
320
340
360
380
Temperature [K]
interlayer
l
Micro-pore structures
Gel pore
g(r) g
Capillary pore
(r) The total porosity distribution
c (r)