= Lubrication resistance integrals for a nearly occluding sphere
{title2=$I_n=\int h^{-n}\,dz$}
A <sphere> almost filling a tube has local <parabolic lubrication gap> $h\simeq a[\epsilon+(z/a)^2]/2$. The resistance integrals are $I_1=2\pi\epsilon^{-1/2}$, $I_2=(2\pi/a)\epsilon^{-3/2}$ and $I_3=(3\pi/a^2)\epsilon^{-5/2}$, obtained with $z=a\sqrt\epsilon\,\xi$ and $\int(1+\xi^2)^{-n}d\xi$. <Moving-boundary lubrication flux> weights shear-driven and pressure-driven transport by different powers of the gap, explaining the three distinct divergence rates.
Back to article page
