Eccentricity increases narrow-gap bypass mobility ($U(e)/U(0)=(2\pi {)}^{-1}{\int }_0^{2\pi }(1+(e/d)\cos \varphi {)}^{5/2}d\varphi$)

For an off-axis nearly occluding sphere with radial offset $e<d$, the local minimum gap is $d(\varphi )=d+e\cos \varphi$ to leading order. Each circumferential strip has pressure-driven conductance proportional to $d(\varphi {)}^{5/2}$, and the strips act in parallel. Thus its speed at fixed load is multiplied relative to the concentric value byConvexity and the zero average of cosine make this greater than one for nonzero $ϵ$. It increases strictly with $ϵ$: pair the positive and negative cosine contributions to the derivative, obtaining factors $c[(1+ϵc{)}^{3/2}-(1-ϵc{)}^{3/2}]>0$ for $c>0$. Consequently an off-axis sphere falls faster in this narrow-gap, no-through-flow regime.