The existence of a non-axisymmetric magnetic field in the transition regions between the central cell and end-plugs of a tandem mirror device can lead to significant radial transport of central-cell ions. Self-consistent calculation of the consequences of this non-ambipolar process requires the solution of a highly non-linear charge balance equation for the ambipolar potential. In this paper, radial transport in tandem mirrors is studied, with particular emphasis on the charge balance equation and its consequences. A time-dependent radial transport code is presented. Simulations of the Tandem Mirror Experiment (TMX) are performed. Generally, good agreement between code and experiment is obtained. The phenomenon of quenching of radial transport is analysed and demonstrated numerically.