Chemical potential vs hydro-static pressure during osmosis

[Urmi Roy]

So when osmosis between two solutions (separated by a semipermeable membrane),takes place, the solvent travels from the side where its chemical potential is higher to the side where its chemical potential is lower.
However, this results in a difference of levels of fluids across the membrane.

Doesn't this contradict the laws of hydro-statics? Is chemical potential enough of a driving force to overcome hydro-static forces?

Thanks a lot!

 

[Useful nucleus]

Can you describe the setup of the system you are interested in? Typically one is interested in systems where the exchange takes place only through the membranes.

 

[Urmi Roy]

Yeah, I'm just considering a system in which a structure that looks like a u-tube manometer, but with a semipermeable membrane at the bottom of the 'U' shape, which separates 2 solutions and supposed the one on the left is more concentrated. The exchange does take place only via the membrane.

 

[DrDu]

Yes, the forces are quite large. The chemical potential of the solvent depends on both the concentration of the solute and the pressure. In equilibrium, the chemical potential of the solvent has to be equal on both sides, hence for different concentrations of the solute, pressure has to be different, too.

 

[Urmi Roy]

Yes, the forces are quite large. The chemical potential of the solvent depends on both the concentration of the solute and the pressure. In equilibrium, the chemical potential of the solvent has to be equal on both sides, hence for different concentrations of the solute, pressure has to be different, too.

The hydro-static forces are basically due to the weight of fluid column, so when chemical equilibrium is established, is it like the gravitational potential energy is just balanced by the chemical potential energy?