= Electrophoretic transit time in a conical pore
{title2=$t=\int dz/[\mu E(z)]$}
For a point-like object with constant <electrophoretic mobility>, deterministic traversal is the integral of inverse local drift speed. In a conical frustum of <length> $L$ at pore voltage $V$, the one-dimensional field is $E(z)=Vab/[Lr(z)^2]$. Integrating gives $t=L^2(b/a+1+a/b)/(3\mu V)$ for positive $\mu V$. For two symmetric frusta of total <length> $2l$ and the same total pore voltage, replace $L$ by $2l$. The inequality $b/a+a/b\geq2$ shows that this nonuniform field cannot produce a shorter deterministic point-particle transit than a uniform field at fixed total <length> and voltage. Reservoir <forces>, <diffusion>, adsorption and finite-object conformation are additional physics.
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