Analysis of hydraulic permeability calculated from centrifuge experiments

The current method of testing water permeability through SepCons is to place a volume of water inside a SepCon and spin it inside a centrifuge.  After a set period of time, the volume passed is collected.  The “approximate” permeability can be calculated as: volume passed/(pressure*area*time of experiment) in units of uL/PSI/cm^2/min.

The reason this is an approximation is because as the SepCon passes water, the fluid height decreases and thus reduces the effective driving pressure (P = ρ*g*h, where ρ is the density of water, g is the amount of g force exerted by the centrifuge, and h is the water height).  With some help from Jim and Tom, we derived the following equation that takes into account this continuous decrease and can write the true permeability as:

Where V_collected is the volume passed, V₀ is the starting fluid volume, t_final is the spin duration, A_chip is the area of the SepCon, and A_membrane is the active area of the membrane.

For our current geometry, a 5-slit square SepCon:

The density of water is:

The initial volume was:

At 2000 RPM in the swinging bucket centrifuge, the g-force is:

Here is a graph showing the approximate permeability and the adjusted permeability over a range of volumes passed.

It appears that when less than 240 uL passes, the approximate solution over-estimates the permeability.  Volumes greater than 240 uL are grossly underestimated.

Due to the added complexity that is introduced by using the centrifuge configuration, I will be working on creating a simple pressure cell that will be able to apply a constant driving force.