= Lubrication prevents finite-time collision of smooth spheres
{title2=$F_n\sim\mu a^2(-\dot\delta)/\delta$}
For smooth no-slip <spheres> of radius scale $a$ with minimum gap $\delta\ll a$, the lateral gap scale is $(a\delta)^{1/2}$. Squeeze-film <lubrication theory> gives <pressure> $p\sim\mu a(-\dot\delta)/\delta^2$ and the displayed normal resistance. Bounded forcing therefore gives $-\dot\delta=O(\delta)$, so the gap cannot vanish in finite time. The conclusion uses smooth surfaces, no slip and continuum creeping flow; it is not a contact model for rough particles.
Back to article page
