Inertial migration of slender prolate and thin oblate spheroids in plane Poiseuille flow

A neutrally buoyant rigid spheroid suspended in a wall-bounded plane Poiseuille flow undergoes cross-stream migration, driven by inertia. We examine theoretically the migration of a spheroid of aspect ratio kappa κ $\kappa$ in the limit of small but finite particle Reynolds number ( italic Re Subscript p Re p ${\textit{Re}}_{\!p}$ ), and for small confinement ratios ( lamda λ $\lambda$ ), with the channel Reynolds number, italic Re Subscript c Baseline equals italic Re Subscript p Baseline divided by lamda squared Re c = Re p / λ 2 ${\textit{Re}}_c = {\textit{Re}}_{\!p}/\lambda ^2$ , assumed arbitrary; here, lamda equals upper L divided by upper H λ = L / H $\lambda =L/H$ with upper L L $L$ being the semimajor axis of the spheroid and upper H H $H$ denoting the separation between channel walls. For small