Impact of membrane thickness on EO
One of the surprising results of Jiracai’s studies with thick and thin membranes was that the thicker membranes had a lower capacity to support back pressure than the thinner membranes he used (see table in this post). This is counter to our original expectation; Since we know that much thicker EO membranes can support 50 atm of pressure and more, we guessed that 30 nm membranes would support slightly higher back pressures than 15 nm.
The two membranes had similar porosity, but thicker membranes also naturally have thicker pores. See …
Fang, D.Z., Striemer, C.C., Gaborski, T.R., McGrath, J.L. and Fauchet, P.M. (2010) Methods for
controlling the pore properties of ultra-thin nanocrystalline silicon membranes J. Phys. Condens.
Matter 22:454134-41
Assuming monodisperse pores, Jess calculated the permeability for the two membranes:
So the lower back pressure is plausibly explained by the higher permeability. Thinking of the net flow rate as Positive EO – negative hydraulic, and assuming EO is the same for the two, zero net flow will occur at a lower back pressure for the more permeable membrane first.
Jess investigated the impact of pore diameter on EO flow rate using her theory and confirmed that the same EO flow is predicted for the two membranes. I’ll make this the subject of another post. The interesting suggestion is that small pore membranes (holding porosity constant) should be much better at supporting back pressure for a given EO flow rate. The dependence on thickness appears to be weaker than the dependence on pore size.