Inertial torque on a squirmer

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