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 = -9/8  m_f (v_s⁽⁰⁾  x v_g⁽⁰⁾), where v_s⁽⁰⁾  is the swimming velocity, v_g⁽⁰⁾ the settling velocity in the Stokes approximation, and m_f 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 Candelier, F., Qiu, J., Zhao, L., Voth, G., & Mehlig, B. (2022). Inertial torque on a squirmer. Journal of Fluid Mechanics, 953, R1.