A small spheroid settling in a quiescent fluid experiences an inertial torque that aligns it so that it settles with its broad side first. Here we show that an active particle experiences such a torque too, as it settles in a fluid at rest. For a spherical squirmer, the torque is $\boldsymbol{ T}^\prime = -{ \tfrac{ 9}{ 8}} m_f (\boldsymbol{ v}_s^{ (0)} \wedge \boldsymbol{ v}_g^{ (0)})$ where $\boldsymbol{ v}_s^{ (0)}$ is the swimming velocity, $\boldsymbol{ v}_g^{ (0)}$ is the settling velocity in the Stokes approximation, and $m_f$ is the equivalent fluid mass. This torque aligns the swimming direction against gravity: swimming up is stable, swimming down is unstable.
Categories: physics.flu-dyn