The physics of osmotic pressure

TL;DR

This paper explains osmotic pressure using the virial theorem, providing a clear, unified physical understanding that connects different theoretical approaches and emphasizes the role of differential solvent pressures.

Contribution

It offers a novel, exact formulation of osmotic pressure based on the virial theorem, unifying various treatments and clarifying the physical mechanisms involved.

Findings

Osmosis is driven by differential solvent pressures.

The virial theorem provides a complete explanation of osmotic pressure.

The approach unifies different theoretical treatments of osmosis.

Abstract

The proper application of the virial theorem to the origin of osmotic pressure provides a simple, vivid and complete explanation of the physical processes involved; osmosis is driven by differential solvent pressures. This simple and intuitive notion is widely disregarded, but the virial theorem allows an exact formulation and unifies a number of different treatments. It is closely related to a kinetic treatment devised by Ehrenfest over 100 years ago.