Biological cell membranes have very special properties, one of which is the ability to pump ions against a concentration gradient. Valve properties are a key to this.
Living cells have the ability to move materials across their membranes as needed to maintain their internal conditions. Nutrients are moved in, waste is moved out, and ion concentrations are established. Nerve cells, for example, transmit impulses by establishing a concentration gradient of ions across their membranes. The key to this "action potential" is the relative concentrations of sodium and potassium ions.
Nerve cells fibers, or nerve axons, expel sodium ions and concentrate potassium ions inside. This is the "charged" condition. Upon receiving a stimulus, potassium rushes out, and sodium rushes in, discharging the potential. This is the mechanism by which nerve impulses are transmitted down the length of an axon. After the impulse passes, there is a brief recharge period, in which energy is expended (ATP hydrolysis) to force the ions back to their original concentrations. Ion concentration gradients are also used to drive many of the other cellular transport processes. This was an area I found quite intriguing, for I was interested in a biomedical career, and one area that particularly had my interest was to come up with alternatives to dialysis, the blood-cleaning process that substituted for the function of failed kidneys.
Cell membranes tend to be bi-layers. Two membranes sandwich a lipid layer to form the functioning whole. A close look at each individual membrane shows further structure, and the whole system is a mosaic of patches of membranes with certain very specific properties.
Studying cell physiology, we learned that the electronic activity sparked by ATP hydrolysis evidently caused reversals in the charge on the lipids sandwiched between the membrane layers. This caused the lipids to alternatively attract and repel ions of a particular charge. This made great sense to my mechanical mind: the analogy to the piston of a reciprocating pump was quite clear to me.
However, a piston, by itself, does not a pump make. Reciprocating pumps need a pair of valves, one to allow fluid in only from one side of the pump, the other to allow fluid out only to the other side. So, I surmised, the two membranes of the bilayer must have valve properties. Indeed, subsequent research by cell physiologist seemed to bear this out.
I was the chemistry department evening librarian, a job that allowed time to browse the incoming journals. One night I discovered a paper which documented a mathematical model of the valve properties of certain man-made membranes. The math paper gave little hint as to what membrane systems actually had these properties, but referenced a paper in, I think, Industrial Chemistry, by C.E. Rogers, et. al., circa 1958 (sorry for the sloppy citation, but this was a long time ago, and my files from that period are a bit, um, disorganized).
I dashed for the back of the library and found the article. Rogers and company had put membranes of Nylon 6 and Ethocel 610 in series, and had verified that the system was more permeable to water vapor in one direction than in the other. A bit of reading of the two papers uncovered the simple reason: one membrane was purely "Fickian", the other was not.
Fick's Law is essentially something like Ohm's Law for membranes. It says that the rate of diffusion thru a membrane should be proportional to the concentration gradient across the membrane, just as current thru a resistor is proportional to voltage drop across the resistor. This is a very nice principle when it is true (Ohm's law is not always true, either). One characteristic that can make a membrane non-Fickian is if the absolute concentration of something in the system affects the permeability. In the case of Nylon 6, it is notoriously prone to swelling in the presence of moisture, and high concentrations of water vapor reduced its permeability to water vapor.
So, if you put Nylon 6 on the high-concentration side of a pair of membranes, its permeability was lower than if on the low-concentration side. Diffusion across the system would be lower if Nylon 6 were on the high-concentration side.
I surmised that the same principle should apply in ionic solutions. Late in my senior year, I did manage to obtain some samples of various ion exchange membranes with which to try to make a valve membrane system. Alas, I ran out of time before I could demonstrate the effect, partly because the ion exchange membranes were incredibly permeable, so much so that I had trouble devising a suitable test for the effect. However, certain of the systems were supposedly non-Fickian, and I have no doubt the effect could have been measured with a suitable lab setup.
At best, however, such a valve would be quite "leaky." Biological valve membranes probably work on very different mechanisms, using specific molecular-scale features to effect the valve.
I have never had the opportunity to pursue this area of research. However, if someone out there does have the means and motivation, I hope this gives you a little inspiration.
