Inertial torque on a squirmer

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 $T^prime = -(9/8) m_f (v_s⁽⁰⁾ x v_g⁽⁰⁾) where v_s⁽⁰⁾ is the swimming velocity, 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. This talk is based on the preprint F. Candelier, J. Qiu, L. Zhao, G. Voth & B. Mehlig, Inertial torque on a squirmer, arXiv:2209.03129.