Explaining drying of free water by
percolation theory
Jarl-Gunnar Salin
SP Technical Research Institute of Sweden SP Wood Technology
Stockholm, Sweden
Fibres filled with water (cross section)
Evaporation
First fibre emptied
Evaporation
Second fibre emptied
EvaporationAgain the fibre with the widest opening is emptied – not the one with the highest evaporation.
Drying from two sides of a 100 x 180
square network
The water phase is gradually fragmentized. No clear receding front – as in a typical diffusion process – is seen.
Evaporation from the upper and lower
surfaces of a 30 x 30 x 98 fibre network.
Process continued.
Adaptation to softwood
1. Comstock fibre model (hexagonal and rectangular cross sections). 2. Only 20 % of the tangential walls
assumed to have openings. 3. Radial ray cells (5 %) introduced. 4. Different diffusion coefficients in
the principal directions of the “dry” region are taken into account. 5. Periodic 3-dimensional network. 6. Opening (bordered pit) size and
lumen volume are stochastic variables
Moisture profiles in the radial direction in a
initially saturated 60 x 60 x 98 fibre network
0 20 40 60 80 100 120 140 160 180 0 20 40 60 80 100 Radial distance M o is tu re c o nt e n t, %
Drying takes place from both vertical sides in the diagram. In the beginning “gradient-free” drying is seen, which stops at a rather well defined point and receding fronts are formed.
Moisture profiles in the tangential direction in
a initially saturated 60 x 60 x 98 fibre network
0 20 40 60 80 100 120 140 160 180 0 20 40 60 80 100 Tangential distance M o is tu re c o n te n t, %
Density profiles obtained by CT-scanning
of a piece of wood during drying
Important result
• “Gradient free” profiles are quickly developed
in the beginning.
• At a certain threshold point a receding front
process starts instead.
• This point corresponds to the breakdown of the
continuous water cluster and corresponds to
“irreducible saturation” introduced by Spolek
and Plumb.
“The ant and the tiled terrace”- problem
A man wants to cover his big terrace with white and black tiles. He asked for offers from several workers and the cheapest one was chosen. The worker was however blind and the tiles
were put in a stochastic order without any structure. An ant wants to cross the terrace from one side to the opposite side. It is a clever ant and it walks only on black tiles as it would be clearly seen by the birds on a white background and picked for food. What should the ratio of
black tiles be in order to provide a path for the ant?
For large networks there is a certain ratio, “percolation threshold” above which a path is established. In the same manner, if the ratio of water filled fibres in wood exceeds a certain
59,68 % black tiles (critical value = 59,2746 %)
Location of evaporation front.
Kiln brown stain
0 10 20 30 40 50 R e la ti v e e v a p or a tion 1 3 5 7 9 11 13 15 17 19 Fibre layer
Location of evaporation front,
damaged wood surface
0 5 10 15 20 25 30 35 40 R e la ti ve e vap o rat io n 1 5 9 13 17 21 25 29 33 37 41 45 49 Fibre layer
Influence of damaged wood surface.
Kiln brown stain
0 20 40 60 80 100 120 140 160 180 0 40 80 120 160 Radial distance M o is tu re c o n te n t, %
Drying rates for radial drying
0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1 0 20 40 60 80 100 120 140 160 Moisture content, % R e la ti ve d ryi n g r a te Undamaged Damaged
Drying rates for tangential drying
0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1 0 20 40 60 80 100 120 140 160 Moisture content, % R e la ti ve d ryi n g r a te Undamaged Damaged
Relative permeability in the tangential direction
0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1 0 0,2 0,4 0,6 0,8 1 Water saturation R e la ti ve p e rm ea b il ity Gas LiquidRelative permeability in the radial direction
0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1 0 0,2 0,4 0,6 0,8 1 Water saturation R e la ti v e p e rm e a b ilit y Gas Liquid
Relative permeability – sample size effect
0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1 0 0,2 0,4 0,6 0,8 1 Water saturation Re la ti v e pe rm e a b il it y 30x30x10 30x30x38 30x30x98
Film flow phenomenon
Film flow phenomenon
Film flow incorporated
0 20 40 60 80 100 120 140 160 180 0 5 10 15 20 25 30 35 40 Radial distance M o is tu re co n ten t, %
