Diffusion aof oxygen through ceramic systems related to wine ageing

1. Oxygen Covalent Radius 73 pm
Hydrogen Covalent Radius 37 pm
Water Molecule Angle 104.45°
Oxygen-Oxygen Distance in O2 121 pm
Oxygen-Hydrogen Distance in Water 95.84 pm
Hydrogen-Hydrogen Distance in Water152.50 pm
169
146
267
226
H20
H20
O2
O2
H20
H20
O2
O2
WoodCeramic
It is reported that oxygen can diffuse into wood not only trough porosity but mainly trough its
molecular structure (Micro-oxygenation of Wine in Barrels, Mark Kelly and David Wollan,
The Australian & New Zealand Grapegrower & Winemaker, 2003 Annual Technical Issue)

2. R
H
y
V=225 l
Let us use the Darcy formula to calculate the flow rate of a fluid trough a porous cylinder
simulating a barrique
Q( y)=
kA
μ
Δ P( y)
L
k=permeability (m2
) (*)
 liquid viscosity and P hydraulic
pressure
L
dQ (y)=
k2π Rdy
μ
ρgy
L
Q( y)=
2πRk ρg
μ L
∫0
H
ydy if K =
k ρ g
μ
Q=
K π RH
2
L
(side)+
K πR
2
H
L
(bottom)
Kmax(cemento)=7.7∘10
−13
m/sec
Kmax(claybrick)=3.8∘10
−9
m/ sec
If R= 0.267m H=1 m L=2.7 cm
(values typical of a barrique)
Qconcrete=10
−4
l /h
Qclay brick=0.54l /h
(*) For packed particles porous systems it is found that k=Cd2 where d is the
particle radius and C a geometrical constant. In these systems d is proportional
to pore dimensions.
(**) K takes into account the characteristics of both the porous media and the
fluid flowing through.
(***) The University of Edinburgh, Division of Engineering, Session 2001-2002,
Materials Science and Engineering
K=Hydraulic Conductivity (m/sec) (**)
(***)
For the Barrique side
In a clayware system the fluid loss can be
very high

3. Let us try to calculate oxygen flow through a porous clayware barrique using Fick
diffusion equation
ΦO2=Deff
ΔCO2
Δ X
Deff =DH20
O2 εδ
τ
2
1lO2
=1.43g
 = Pores constrictivity ~ 0.7
= Pores tortuosity ~ 1.4
 = Porosity ~ 0.2
They are typical values for a clayware brick (*)
DO2
H20
= 2*10-9
m2
/sec
Deff
~ 7*10-11
m2
/sec
CO2
= 0 Inside wine
CO2
= 7.2 mg/l On the external saturated surface
Barrique thickness = 2.7 cm Barrique surface ~ 2 m2
Barrique volume = 225 l
O2
~0.6 mlO2
/litre/month
The usual value for a oak wood barrel is 2.2 mlO2
/litre/month (**)
Therefore is possible that a porous system let a small oxygen go in but a lot of fluid go out!!
(*) M.Raimondo, M.Dondi, D.Gardini, G.Guarini, F.Mazzanti, Predicting the initial rate of water
absorption in
clay bricks, Construction and Building Materials, 23 (2009) 2623-2630.
(**) Micro-oxygenation of Wine in Barrels, Mark Kelly and David Wollan, The Australian & New
Zealand Grapegrower & Winemaker, 2003 Annual Technical Issue
δ=
√DMAX DMIN
DAVERAGE
=
̄DGeometric
̄DAritmetic
ε=
Vol.Holes
Vol.Total
τ=
Covered ( A−B)distance
(A−B)Gap A B
DMAX
DMIN

4. To calculate k and K we correlate Darcy and Poiseuille relations (open
porosity systems)
A
L'
2r
Q=∑ Qi
Qi=
π r
4
8μ
Δ P
L
y
Qi=
π r
4
8μ
ρ gy
L
If  is the porosity, it comes out that the number of pores in a section A is
n(pori)
=A/r2
Q( y)=
ε Ar
2
ρ gy
4μ L
For a cylindrical container A=2Rdy
Q=
εr
2
ρg π R
2μ L
∫0
H
ydy But L=L' and is the tortuosity
Q=
ρg επr
2
RH
2
4μ τ L'
(side)+
ρgεπ r
2
R
2
H
4μ τ L'
(bottom)
But according to Darcy
Because L'=L we finally have k=
εr
2
4 τ
with r average pore radius
Q=
K π RH
2
L
(side)+
K πR
2
H
L
(bottom)
After mercury porosimeter measurements we obtain for our Clayver

5. Dati tecnici caratteristici di Clayver
Water absorption 2.1% Dry weight of 250 l Clayver 95 Kg
Open porosity 5% Volume 250 l
Bulk Density 2.34 g/cm3
Average pore diameter 0.04 m
Constrictivity 0.76
Permeability 4.60▪10-18
m2
Hydraulic conductivity 2.50▪10-11
m/sec
O2 flow rate 0.2 mlO2
/litre/month
(Barrique ratio) ~0.1
Hydraulic loss 0.0035 l/h
(initial stage)