5.2 Osmotic Pressure in an Ideal Gas
The selective permeability of a membrane gives rise to some striking effects. The flow of water that occurs because solutes are present that cannot get through the membrane is called osmosis. This phenomenon seems strange when it is first encountered, and explanations are often fraught with misconceptions (Kramer and Myers 2012).
What are these misconceptions that explanations are often fraught with? The reference is to the paper “Five Popular Misconceptions About Osmosis” (American Journal of Physics, Volume 80, Pages 694-699, 2012). The paper raises five questions.
Later in the paper, the authors answer these questions.
So, how did Russ and I do?
Kramer and Myers have an illuminating discussion about the force causing the solvent to cross the membrane (I’ve removed all their references; you can find them in the original paper).
Consider an idealized semipermeable membrane as a force field that repels solute but has no effect on the solvent. The Brownian motion of the solute molecules bring them into occasional contact with this field, at which time they receive some momentum directed away from the membrane. Viscous interactions between solute and solvent then rapidly distribute this momentum to the solvent molecules in the neighborhood of the membrane. In this way, the membrane exerts a repulsive force on the solution as a whole. Since additional pure solvent can freely cross our idealized membrane, it flows into the solution compartment, gradually increasing the hydrostatic pressure in the solution. Thus, a pressure gradient builds up across the thickness of the membrane. This pressure gradient exerts a second force on the solution, capable of counteracting the membrane force. Quantitative treatments show that the pressure difference required to stop solvent flow into a dilute solution is exactly Π = kBTcB. Nelson has aptly called the mechanism by which the membrane drives fluid flow the rectification of Brownian motion.
Overall I would say Russ and I do okay. We don’t propagate any of the five misconceptions. We answer three of their questions correctly and are silent on two others. Most of the discussion about osmosis goes back to the 3rd or earlier editions of IPMB, so Russ is the one who got it right. At least I didn’t screw it up.