Combining Pores Affects the PoreImageProcessor, but Not Enough to Throw Permeability Off 2x
In Tuesday’s NRG, we wondered if the fact that some of Josh’s pores overlap could throw the PoreImageProcessor off enough to explain a 2x discrepancy between our theoretical hydraulic permeability and our experimental permeability (the experimental was lower).
From this picture:
I took the following close up:
If we assumer that each of the sub-pores has a radius of 10nm, and that the PoreImageProcessor is counting them as one pore with a radius of 20nm, we can use Dagan’s equation to get the following flow rates:
For pores of a radius of 10nm and a thickness of 50nm Q = 1.68E-21 m^3/s (per pore) = 6.72E-21 m^3/s (for 4 pores)
For pores of a radius of 20nm and a thickness of 50nm Q = 13.3E-21 m^3/s (per pore)
In this extreme case (four pores close enough to overlap) we do get a two-fold difference in predicted flow through the membrane. However, this is unusual in the original image, and the more likely case of two overlapping pores is not quite so dramatic:
For pores of a radius of 10nm and a thickness of 50nm Q = 1.68E-21 m^3/s (per pore) = 3.36E-21 m^3/s (for 2 pores)
For pores of a radius of 14.14nm (10nm *sqrt(2)) and a thickness of 50nm Q = 4.74E-21 m^3/s (per pore)
So we should expect the PoreImageProcessor to overestimate flow by ~50% if every pore overlapped just one identical pore. I think it is far more likely that my experimental setup is the reason for the disparity – at 4.7PSI the Sepcon almost immediately emptied (in 15s or so), and if we redo the permiability using 1PSI we should get more accurate numbers.
With higher flow rates, make sure there are not other restrictions in the system that could lower the effective pressure across the membrane. Not sure if the output of the sepcon cup would cause any pressure reduction…