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Treatment of building porous materials with protective agents. Jan Kubik Opole University of Technology kubik@po.opole.pl. 1. Introduction - PowerPoint PPT Presentation
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Jan Kubik
Opole University of Technology
kubik@po.opole.pl
Treatment of building porous materials with protective agents
1. IntroductionProtective agent spread on the porous surface of damaged building materials (for example wooden elements, monumental brickwork) leads first to wetting of this surface, next to spreading of liquid on it and finally to saturation of pores. Wetting of this surface is the first one of conditions which have to be satisfied in order to saturate material under the influence of capillary forces.
2. Process of surface-saturation
r2
th
th
v
x
11vc
22vc
1
2
r2v 2v
0v1
2,1,0
Rdivt
v
v
v
u
uj
,c
Figure 1. Model of the process
The starting point of the considerations will be an analysis of viscous liquid flow in a capillary tube of radius r described by Poiseuille`s equation
Figure 2. Force in capillary.
14 )8( htprV (1)
th
h
pr
V
1212
2)8( )8( hpr
t
hhpr
tr
V
(2)
Liquid flux which flow within time and surface unit is given by the formula
So velocity of penetration range can be expressed as
12 )8( hprtd
hd
In this dependence differential pressure p should be specified between both ends of capillary tube. Assuming that capillary forces (capillary pressure) are the only reason of differential pressure, that is
rp /cos2
(3)
(4)
(5)
we will obtain the saturation range equation
Integral of this equation
makes possible a determination of depth of liquid penetration which is dependent on time t, radius of capillary tube r and
velocity of penetration
(6)
0)0( ,)8(cos2 1 hhrtd
hd
1212
)2(cos,)2(cos
trhr
t
r
h
1)2(cosor vr
h
2/cosv
h
t
v1
v3
v2
h0
t0
h
r
v1
v3
v2
v1 > v2 > v3
h0
r
h (t)
2r
Figure 3. Saturation range in material.
3. Liquid fixation in a net of capillary tubesIn the simplest case, the following relations describe the process
(7)10 , 1
)( 0
t
0
1
0,0 t
0, t
r
h
v
1
t
1
321
321
0
Figure 4. Dependence between shear stress and velocity of liquid flow .
where the dimensionless parameter satisfies an evolution equation as follows
(8)1)(0,0)0(,),...,,,( tprTftd
d
Substituting in the equation (5) the variable value of viscosity coefficient determined by the relation (7), we would obtain that
0)0()),(1()4(cos 10
hthrtd
hd
t
ktdtv
r
h
0
10
1))(()2(cos
This formula in a dimensionless version will have a form
(9)
(10)
Figure 5. The wooden church in Olszowa (The Opole Region)
Figure 6. Remainder of the gothic Upper Castle in Opole
Figure 7. The Upper Castle in Opole
Figure 8. The upper castle in Opole
Figure 9. The Upper Castle in Opole
THANK YOUFOR ATTENTION
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