Electrophoretic transit time in a conical pore ($t=\int dz/[\mu E(z)]$)

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 $b/a+a/b\ge 2$ 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.