Confined-polymer entry and recoil times (${\tau }_{\mathrm{in}}={\zeta }_{\ell }L/(qE),{\tau }_{\mathrm{out}}={\zeta }_{\ell }{L}^2/(2f)$)

With friction $\gamma (x)={\zeta }_{\ell }x$, inward force $qEx$ gives constant entry speed after capture. With the field off, constant outward entropic force gives $x\dot{x}=-f/{\zeta }_{\ell }$ and a quadratic recoil time. Exterior drag, adsorption and the short final end region are omitted. These ideal transport times alone do not establish steady size separation through a whole uniform channel.