Explaining drying of free water by percolation theory Jarl-Gunnar - - PDF document

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

The fibre with the widest opening is emptied.

Second fibre emptied

Evaporation

Again 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

Continues.

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

20 40 60 80 100 120 140 160 180 20 40 60 80 100

Radial distance Moisture content, %

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

20 40 60 80 100 120 140 160 180 20 40 60 80 100

Tangential distance Moisture content, %

Density profiles obtained by CT-scanning

• f a piece of wood during drying

The gradient-free drying behaviour is clearly seen in this experiment.

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

• ne 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

value, a continuous water phase is established – otherwise not.

59,68 % black tiles (critical value = 59,2746 %)

Location of evaporation front.

Kiln brown stain

10 20 30 40 50

Relative evaporation

1 3 5 7 9 11 13 15 17 19

Fibre layer

Location of evaporation front, damaged wood surface

5 10 15 20 25 30 35 40 Relative evaporation 1 5 9 13 17 21 25 29 33 37 41 45 49 Fibre layer

Influence of damaged wood surface.

Kiln brown stain

20 40 60 80 100 120 140 160 180 40 80 120 160 Radial distance Moisture content, %

Drying rates for radial drying

0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1 20 40 60 80 100 120 140 160

Moisture content, % Relative drying rate

Undamaged Damaged

Drying rates for tangential drying

0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1 20 40 60 80 100 120 140 160

Moisture content, % Relative drying rate

Undamaged Damaged

Relative permeability in the tangential direction

0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1 0,2 0,4 0,6 0,8 1

Water saturation Relative permeability

Gas Liquid

Relative permeability in the radial direction

0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1 0,2 0,4 0,6 0,8 1 Water saturation Relative permeability

Gas Liquid

Relative permeability – sample size effect

0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1 0,2 0,4 0,6 0,8 1

Water saturation Relative permeability 30x30x10 30x30x38 30x30x98

Film flow phenomenon

Film flow phenomenon

Film flow incorporated

20 40 60 80 100 120 140 160 180 5 10 15 20 25 30 35 40

Radial distance Moisture content, %

Conclusions

• The invasion percolation approach can be used

to describe drying of free water in the fibre structure of solid wood.

• It explains or increases the understanding of at

least these items:

– Gradient free drying – Percolation threshold – Dry shell development – Apparent reduced external mass transfer – Kiln brown stain – Relative permeability – Shrinkage above FSP

More information: jarlgunnar.salin@sp.se