Two different containers full up with pure water and salt water in osmosis. What happens?
In your described scenario, there will be osmotic flow in an attempt to equalize the chemical potential of the solvent (water in this case, assuming the membrane is only permeable to water). The effect of the osmotic flow will be that pure water from container 1 will flow into container 2. Since this is a closed system, one will observe the liquid level rise in container 2 and fall in container 1, and the amount of displacement will be a function of how different the chemical potential of the water is between container 1 and container 2. There is no classical force that will push or pull the liquid from one container to another, osmotic flow is an instance of diffusion which is governed by the concentration gradient that is present.