Particle pushing by a freezing front
= Particle pushing by a freezing front
{title2=$V=A/(36\pi\mu a d)$}
A planar freezing front can push a spherical particle steadily when repulsive <sphere-plane dispersion force> balances <lubrication resistance>. The thin parabolic gap gives hydraulic drag $6\pi\mu Va^2/d$, and balancing it against $Aa/(6d^2)$ gives the displayed speed. This balance assumes a nonretarded interaction, small gap and negligible inertial and other particle forces.