Understanding ion transport in conjugated polymers is essential for developing mathematical models of applications of these materials. Previous experimental studies have suggested that cation transport in a conjugated polymer could be either diffusion or drift controlled, with debate over which dominates. In this paper we present a new model of cation transport that explains most of the features seen in a set of recent experiments. This model gives good agreement with measured concentration profiles, except when the profile has penetrated the polymer by more than 60%. The model shows that both diffusion and drift processes can be present. An application of a micro-actuator based on a conjugated polymer is presented to demonstrate that this technology could be used to develop a micro-pump.