Van't Hoff's law for active suspensions: the role of the solvent chemical potential

TL;DR

This paper generalizes Van't Hoff's law to active suspensions, showing that active particles alter solvent chemical potential and osmotic pressure, leading to measurable solvent flows and height differences in microswimmer experiments.

Contribution

It introduces a modified Van't Hoff's law accounting for active particles' influence on solvent chemical potential and osmotic pressure, highlighting the role of membrane interactions.

Findings

Active particles exert reaction forces on solvent.

Osmotic pressure increases due to altered solvent chemical potential.

Solvent flow and suspension height are affected by activity and membrane potential.

Abstract

We extend Van't Hoff's law for the osmotic pressure to a suspension of active Brownian particles. The propelled particles exert a net reaction force on the solvent, and thereby either drive a measurable solvent flow from the connecting solvent reservoir through the semipermeable membrane, or increase the osmotic pressure and cause the suspension to rise to heights as large as micrometers for experimentally realized microswimmers described in the literature. The increase in osmotic pressure is caused by the background solvent being, in contrast to passive suspensions, no longer at the chemical potential of the solvent reservoir. The difference in solvent chemical potentials depends on the colloid-membrane interaction potential, which implies that the osmotic pressure is a state function of a state that itself is influenced by the membrane potential.