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Treatment of building porous materials with protective agents. Jan Kubik Opole University of Technology kubik@po.opole.pl. 1. Introduction
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Treatment of building porous materials with protective agents Jan Kubik Opole University of Technology kubik@po.opole.pl
1. Introduction Protective 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 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. (1)
Liquid flux which flow within time and surface unit is given by the formula (2) So velocity of penetration range can be expressed as (3) In this dependence differential pressure Dp should be specified between both ends of capillary tube. Assuming that capillary forces (capillary pressure) are the only reason of differential pressure, that is (4)
we will obtain the saturation range equation (5) Integral of this equation (6) makes possible a determination of depth of liquid penetration which is dependent on time t, radius of capillary tube r and velocity of penetration
v1 > v2 > v3 h v1 h0 2r v2 v3 r r h (t) h v1 h0 v2 v3 t0 t Figure 3. Saturation range in material.
t h0 1 3. Liquid fixation in a net of capillary tubes In the simplest case, the following relations describe the process (7) Figure 4. Dependence between shear stress and velocity of liquid flow .
where the dimensionless parameter w satisfies an evolution equation as follows (8) Substituting in the equation (5) the variable value of viscosity coefficient h determined by the relation (7), we would obtain that (9) This formula in a dimensionless version will have a form (10)
