Generalising Stokes laws for an active particle
ABSTRACT :
The physics of soft and biological matter seeks to understand the mechanics of living materials and some remarkable non-living imitations, both of which fall under the umbrella term of active matter. Their building blocks, active particles, are intermediate in size between atoms and grains, at length scales of about a thousandth of a thousandth of a metre, i.e., a micron. Examples include microorganisms and autophoretic particles. These mesoscopic self-propelled units can metabolise energy into systematic movement on an individual level and are affected by physics that is negligible at human scales. The mechanics of a suspension of active particles is determined by the traction (force per unit area) on their surfaces, arising from long-ranged hydrodynamic interactions at low Reynold’s number. Here, we present an exact solution for the traction on a minimal self-consistent model of an active particle based on the direct boundary integral formulation of Stokes flow. The obtained relations generalise Stokes laws for the force and torque on a freely translating and rotating spherical body.