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University of Ljubljana, Biotechnical Faculty, Department of Wood Science and Technology, Ljubljana, Slovenia; [email protected]
A. Straže, Ž. Gorišek
COST FP0802 Workshop “Experimental and Computational Micro-Characterization Techniques in Wood Mechanics“, Vila Real, 27 – 28 April 2011
Analysis of external and internal mass transfer
resistance at steady state diffusion experiments
on small clear wood specimens
Agenda
COST FP0802, Vila Real, 27-28.04.2011 2
Background
Diffusion cup method – Fick’s first law
Basic principles
Preferences and drawbacks
Real wood structure and surface properties
Experimental
Material & Methods
Diffusion experiments - climatic conditions, determination of water
mass flow and moisture content
Structural and surface properties
Results and discussion
Concluding remarks
Background
COST FP0802, Vila Real, 27-28.04.2011 3
Measuring of diffusion coefficients by steady state principle, i.e.
“Diffusion cup method”
Various potentials:
moisture content, relative humidity, partial vapour pressure, chemical
or water potential, free energy, spreading pressure
SOLUTION
RH2 → MC2
RH1 → MC1
ΔL L
cD
A
m
Fick’s first law:
100
MCGc w
Substitution of concentration gradient (Δc)
with moisture content gradient:
Background
COST FP0802, Vila Real, 27-28.04.2011 4
Drawbacks of diffusion cup method:
SOLUTION
RH2 → MC2
RH1 → MC1
ΔL
surface equilibrium moisture
content has to be available
Solution: 2 specimens
the water vapour flux causes a
differential of relative humidity
Solution: correction of potential
SOLUTION
RH2 → MC2
RH1 → MC1
ΔL
RHs
Δ(RH)
Background
COST FP0802, Vila Real, 27-28.04.2011 5
Drawbacks of diffusion cup method:
the effect of convective surface
resistance is neglected
Solution: correction factors?
Salin, J.G. 1996. Mass transfer from wooden surfaces. Drying Tech., 14(10):2213-2224
Aim and research objectives
COST FP0802, Vila Real, 27-28.04.2011 6
to test the hypothesis of addition of internal and external mass
transfer resistance during steady state diffusion experiments.
L
cADm a
ΔL
Rs
RD
Rs
ASRs
1
AD
LRD
ASRs
1
Rt sD
a
t RRAD
LR 2
…Da…apparent diffusion coefficient
Resistances:
Rs - convective surface
RD – internal diffusion
Rt – total
Fick’s first law:
Flux in the material:
L
cADm 1
2cASm
Flux at the surfaces:
Aim and research objectives
COST FP0802, Vila Real, 27-28.04.2011 7
Adding of resistances:
L1 L2 L3
Rt×A
L
S
12intercept
Dslope
1
D
L
SARRAR Dst
122
Material and methods: Sampling
COST FP0802, Vila Real, 27-28.04.2011 8
Material: European spruce (Picea abies Karst.)
Initial MC: 8%, industrial dried
Sampling: radial (R), tangential (T) and longitudinal (L)
Diameter: 45 mm
Thickness:
2 mm, 4 mm, 6 mm (R, T)
4 mm, 10 mm, 18 mm (L)
R
T
L
Material and methods: Conditioning
COST FP0802, Vila Real, 27-28.04.2011 9
Equipment: Diffusion cups and thermostatic climatic chambers with
saturated salt solutions.
Temperature: 20 ± 0.1 °C
lid
cup
specimen
washer
Material and methods: Diffusion experimentation
COST FP0802, Vila Real, 27-28.04.2011 10
Procedure:
pre-drying of specimens at state 0
successive exposing of specimens to different RHs (1st to 4th run) at
constant temperature (20 ± 0.1 °C)
State Medium Relative
humidity [%]
0 T = 40 °C 10
1 LiCl 18
2 K2CO3 44
3 NaNO2 65
4 ZnSO4 87
5 Distilled water 97
6 T = 103 ± 2 °C 0
1st run
2nd run
3rd run
4th run
Material and methods: Surface properties
COST FP0802, Vila Real, 27-28.04.2011 11
Procedure:
Light emission microscopy
Visual assessment
Surface roughness
Tactile needle method
Results: Radial direction
COST FP0802, Vila Real, 27-28.04.2011 12
Rt = 7,762,740.49L + 17,391,446.33R² = 0.99
Rt = 77953L + 389818R² = 0.90
1.0E+05
1.0E+06
1.0E+07
1.0E+08
0 1 2 3 4 5 6 7
(Rt)
R[s
/m]
L [mm]
y = 0.794x-0.583
R² = 0.9842
y = 0.909e-0.12x
R² = 0.883
0.0
0.2
0.4
0.6
0.8
1.0
0 1 2 3 4 5 6 7
(2R
s/
Rt)
R[
]
L [mm]
1st run; MCavg = 8.4%
4th run; MCavg = 22.8%
Total resistance increases with
decrease of MC.
External mass transfer resistance
has strong influence (> 25%)
Results: Radial direction
COST FP0802, Vila Real, 27-28.04.2011 13
Decreasing of diffusion coefficient and surface emission coefficient with
reduction of average moisture content.
1.0E-11
1.0E-10
1.0E-09
1.0E-08
1.0E-07
1.0E-06
0 5 10 15 20 25 30
DR
[m2/s
]
MC [%]1.0E-08
1.0E-07
1.0E-06
1.0E-05
0 5 10 15 20 25 30
S R[m
/s]
MC [%]
Results: Tangential direction
COST FP0802, Vila Real, 27-28.04.2011 14
Rt = 9,400,198.29L + 21,061,065.36R² = 1.00
Rt = 70538L + 510978R² = 0.97
1.0E+05
1.0E+06
1.0E+07
1.0E+08
0 1 2 3 4 5 6 7
(Rt)
T[s
/m]
L [mm]
y = 0.8132x-0.608
R² = 0.9999
y = 0.9263e-0.088x
R² = 0.9816
0.0
0.2
0.4
0.6
0.8
1.0
0 1 2 3 4 5 6 7
(2R
s/
Rt)
T[
]
L [mm]
1st run; MCavg = 8.2%
4th run; MCavg = 23.0%
Total resistance increases with
decrease of MC.
External mass transfer resistance
has strong influence (> 20%)
Results: Tangential direction
COST FP0802, Vila Real, 27-28.04.2011 15
Decreasing of diffusion coefficient and surface emission coefficient with
reduction of average moisture content.
1.0E-11
1.0E-10
1.0E-09
1.0E-08
1.0E-07
1.0E-06
0 5 10 15 20 25 30
DT
[m2/s
]
MC [%]1.0E-08
1.0E-07
1.0E-06
1.0E-05
0 5 10 15 20 25 30
S T[m
/s]
MC [%]
Results: Longitudinal direction
COST FP0802, Vila Real, 27-28.04.2011 16
Rt = 178,139.70L + 2,047,519.96R² = 1.00
Rt = 7532.1L + 360901R² = 0.991.0E+05
1.0E+06
1.0E+07
1.0E+08
0 5 10 15 20
(Rt)
L[s
/m]
L [mm]
y = 0.8747e-0.046x
R² = 0.98
y = 0.9854e-0.017x
R² = 0.99
0.0
0.2
0.4
0.6
0.8
1.0
0 5 10 15 20
(2R
s/
Rt)
L[
]
L [mm]
1st run; MCavg = 8.4%
4th run; MCavg = 23.9%
Total resistance increases with
decrease of MC.
External mass transfer resistance
has strong influence (≥40%)
Results: Longitudinal direction
COST FP0802, Vila Real, 27-28.04.2011 17
Increasing of diffusion coefficient and surface emission coefficient at
average MC bellow 20%
Significantly higher values at average MC above 20% - possibility of
capillary condensation.
1.0E-11
1.0E-10
1.0E-09
1.0E-08
1.0E-07
1.0E-06
0 5 10 15 20 25 30
DL
[m2/s
]
MC [%]1.0E-08
1.0E-07
1.0E-06
1.0E-05
0 5 10 15 20 25 30
S L[m
/s]
MC [%]
Results: Surface characteristics – cross section (RT plane)
COST FP0802, Vila Real, 27-28.04.2011 18
Raised wood tissue with low connection to the
underlying material have influence on:
convective surface resistance,
rate of equilibration,
equilibrium moisture content (?)
Results: Surface characteristics – longitudinal direction
COST FP0802, Vila Real, 27-28.04.2011 19
Roughness depending on processing
characteristics and on wood structure influencing:
air movement at surface layer. x
Results: Surface characteristics – RL plane
COST FP0802, Vila Real, 27-28.04.2011 20
Raised wood tissue with low connection to the
underlying material have influence on:
convective surface resistance,
rate of equilibration,
equilibrium moisture content (?)
Results: Surface characteristics – RL plane
COST FP0802, Vila Real, 27-28.04.2011 21
Roughness depending on processing
characteristics and on wood structure influencing:
air movement at surface layer. x
Concluding remarks
COST FP0802, Vila Real, 27-28.04.2011 22
There is a need to precise experimentation using diffusion cup
method – problems with thin specimens, having low internal
resistance.
Internal and external mass transfer resistance at steady state
experimentation can be analysed by varying the material thickness.
Material homogeneity is needed (successive, parallel samples) to
achieve reliable results – problem at wood material!
University of Ljubljana, Biotechnical Faculty, Department of Wood Science and Technology, Ljubljana, Slovenia; [email protected]
A. Straže, Ž. Gorišek
COST FP0802 Workshop “Experimental and Computational Micro-Characterization Techniques in Wood Mechanics“, Vila Real, 27 – 28 April 2011
Analysis of external and internal mass transfer
resistance at steady state diffusion experiments
on small clear wood specimens
Thank you for the attention!
