Phoretic motion in active matter

A new continuum perspective for phoretic motion is developed that is applicable to particles of any shape in 'microstructured' fluids such as a suspension of solute or bath particles. Using the reciprocal theorem for Stokes flow it is shown that the local osmotic pressure of the solute adjacent to the phoretic particle generates a thrust force (via a 'slip' velocity) which is balanced by the hydrodynamic drag such that there is no net force on the body. For a suspension of passive Brownian bath particles this perspective recovers the classical result for the phoretic velocity owing to an imposed concentration gradient. In a bath of active particles that self-propel with characteristic speed U-0 for a time tau(R) and then change direction randomly, taking a step of size l = U-0 tau(R), at high activity the phoretic velocity is U similar to -U(0)l del phi(b), where phi(b) is a measure of the 'volume' fraction of the active bath particles. The phoretic velocity is independent of the size of the phoretic particle and of the viscosity of the suspending fluid. Because active systems are inherently out of equilibrium, phoretic motion can occur even without an imposed concentration gradient. It is shown that at high activity when the run length varies spatially, net phoretic motion results in U similar to -phi U-b(0)del l. These two behaviours are special cases of the more general result that phoretic motion arises from a gradient in the swim pressure of active matter. Finally, it is shown that a field that orients (but does not propel) the active particles results in a phoretic velocity U similar to -phi(b)U(0)l del psi, where psi is the (non-dimensional) potential associated with the field.

Automated summary

A new continuous perspective for phoretic motion applicable to particles of any shape in 'microstructured' fluids has been developed, explaining how the local osmotic pressure of solute adjacent to the phoretic particle generates a thrust force. The study covers passive Brownian bath particles in suspension and active particles with characteristic speed and run length variations, showing that phoretic motion arises from a gradient in swim pressure of active matter.