nelson research, inc. 2142 – n. 88 th st. seattle, wa. 98103 usa 206-498-9447 craigmail @ aol.com...
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Nelson Research, Inc. 2142 – N. 88th St. Seattle, WA. 98103 USA 206-498-9447 Craigmail @ aol.com
The Effect of Pin Holes of Varying Size and Number
in
Porous Reacting Membranes
A Finite Element Analysis (FEA) Numerical Model
Craig E. Nelson
Nelson Research, Inc. 2142 – N. 88th St. Seattle, WA. 98103 USA 206-498-9447 Craigmail @ aol.com
1. They are formed by localized process variation (dust particle “point masking”) and thus their own statistical distribution.
2. They may be assumed to typically be 5 to 20 times larger than “normal” membrane pores.
3. They are assumed to be “rare”, with only a few pin holes per cm^2 of membrane area..
The Nature of “Pin Hole” Defects
Nelson Research, Inc. 2142 – N. 88th St. Seattle, WA. 98103 USA 206-498-9447 Craigmail @ aol.com
1. They demonstrate imperfect control of the fabrication process environment in an exasperating manner.
2. They “rob” surrounding nearby porous reacting regions of reactant flow.
How do Pin Holes Harm Performance ?
Nelson Research, Inc. 2142 – N. 88th St. Seattle, WA. 98103 USA 206-498-9447 Craigmail @ aol.com
Calculated Flow Volume Results For Membranes with One Pore Size
Flow through a pore goes up as the fourth power of pore diameter !!!!
Therefore: if Q = 10 ml/min for a membrane with 10micron diameter poreswe get the following data plot for flow with other pore diameters
The Deleterious Effect of Large Pin Holes is Truly Amazing
Relative Flow vs. Pore Diameter
1.00E-06
1.00E-04
1.00E-02
1.00E+00
1.00E+02
1.00E+04
1.00E+06
1.00E+08
1 10 100
Diameter (microns)
Rel
ativ
e F
low
Rat
e
ml/min
uL / min
Liters / min
Nelson Research, Inc. 2142 – N. 88th St. Seattle, WA. 98103 USA 206-498-9447 Craigmail @ aol.com
Diameter Flow Flow Flow(microns) (ul/min) (ml/min) (liters/min)
1 1 0.001 0.000 2 16 0.016 0.000 5 625 0.625 0.001
10 10,000 10.000 0.010 20 160,000 160.000 0.160 50 6,250,000 6,250.000 6.250
100 100,000,000 100,000.000 100.000
The Deleterious Effect of Large Pin Holes is Truly Amazing
Flow through a pore goes up as the fourth power of pore diameter !!!!
Therefore: if Q = 10 ml/min for a membrane with a 10micron diameter poreswe get the following data plot for flow with other pore diameters
Calculated Flow Volume Results For Membranes with One Pore Size
Nelson Research, Inc. 2142 – N. 88th St. Seattle, WA. 98103 USA 206-498-9447 Craigmail @ aol.com
Now We Look at Flow Resulting
from Combinations of both
Standard Size and Large Hole Diameters
Nelson Research, Inc. 2142 – N. 88th St. Seattle, WA. 98103 USA 206-498-9447 Craigmail @ aol.com
Total Flow – The Combination of Two Pore Diameter Distributions
(A Simplified But Quite Useful Analysis Approach)
Mean = 4 u Mean = 40 u
Millions of Pores
A few Pores
Mean = 4 u Mean = 40 u
Millions of Pores
A few Pores
Actual Pore Size Statistical Distribution Idealized Pore Size Statistical Distribution
Normal Pores Pin Holes Normal Pores Pin Holes
Number of Pores
Number of Pores
Pore Diameter
Pore Diameter
Nelson Research, Inc. 2142 – N. 88th St. Seattle, WA. 98103 USA 206-498-9447 Craigmail @ aol.com
Using The Following Ratios Simplifies the Analysis
1. The ratio of pin hole diameter to regular pore diameter : Diameter Ratio
Diameter Ratio = Pin Hole Diameter / Normal Pore Diameter
2. The number of pin holes divided by the total number of pores : Nbig Ratio
Nbig Ratio = Npin holes / (Nnormal pores + Npinholes)
Nelson Research, Inc. 2142 – N. 88th St. Seattle, WA. 98103 USA 206-498-9447 Craigmail @ aol.com
The Effect of a Mixture of Normal Pores and Pin Holes in a Membrane
Apparently one or two 20 x normal pin holes per cm^2 “steal” about 15% of the total flow
1.00
E+
00
1.00
E-0
1
1.00
E-0
2
1.00
E-0
3
1.00
E-0
4
1.00
E-0
5
1.00
E-0
6
2
100
0.2
0.4
0.6
0.8
1
Fraction of Total Flow "Stolen" by Pin Holes
Relative Number of Pin Holes
Relative Diameter of Pin Holes
Pin Hole Flow vs. Number of Pin Holes and Relative Diameter
2
5
10
20
Nelson Research, Inc. 2142 – N. 88th St. Seattle, WA. 98103 USA 206-498-9447 Craigmail @ aol.com
The Effect of a Mixture of Normal Pores and Pin Holes
Apparently one or two 20 x normal pin holes per cm^2 “steal” about 15% of the total flow
FluidRelative number Relative dia. Pinholes Conductivity ratio of
of big pores of big pores per big pores to the to small pores to small pore dia. cm^2 total of all pores
1.00E+00 10 - 1.0001.00E-01 10 - 0.9991.00E-02 10 - 0.9901.00E-03 10 - 0.9091.00E-04 10 150 0.5001.00E-05 10 15 0.0911.00E-06 10 1.5 0.010
FluidRelative number Relative dia. Pinholes Conductivity ratio of
of big pores of big pores per big pores to the to small pores to small pore dia. cm^2 total of all pores
1.00E+00 20 - 1.0001.00E-01 20 - 1.0001.00E-02 20 - 0.9991.00E-03 20 - 0.9941.00E-04 20 - 0.9411.00E-05 20 15 0.6151.00E-06 20 1.5 0.138
Nelson Research, Inc. 2142 – N. 88th St. Seattle, WA. 98103 USA 206-498-9447 Craigmail @ aol.com
Variation in Reactant Concentration in a Complex Domain with “Inside Out” Single Phase Fluid Flow
Fluid Flow Vector Reactant 1 Concentration
Reacting Porous Region 1 Reacting Porous Region 1
Reacting Porous Region 2 Reacting Porous Region 2
Reactant 1 In
Reactant 2 In
Reactant 1 In
Reactant 2 In
Large Pin Hole Location Could Matter When Concentration Gradients are Present
Barrier Barrier
Crossover
Bad Location for a Pin Hole
Not so Bad Location for a Pin Hole
Blocked Blocked
Nelson Research, Inc. 2142 – N. 88th St. Seattle, WA. 98103 USA 206-498-9447 Craigmail @ aol.com
Conclusions
1. Large (50x) pin holes are a disaster and can not be present in viable membranes
2. A few 5x-10x pin holes per cm^2 is probably OK
3. Location of pin holes should be tracked. Pin holes on the inlet end of membranes may be expected to have a larger effect on performance than same sized pin holes on the outlet end of reacting membranes