We model the transport of electrically charged solute molecules by a laminar flow within a nanoslit microfluidic channel with electrostatic surface potential. We derive the governing convection–diffusion equation, solve it numerically, and compare it with a Taylor–Aris-like approximation, which gives excellent results for small Péclet numbers. We discuss our results in light of designing an assay that can measure simultaneously the hydrodynamic size and electric charge of single molecules by tracking their motion in such nanoslit channels with electrostatic surface potential.