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