Field-amplified sample stacking (FASS) uses conductivity gradients and resulting non-uniform electromigration fluxes to effect concentration increases of analyte ions. For cases where the initial sample concentration is much smaller than the background electrolyte (BGE) concentration, the ideal maximum concentration enhancement is equal to $\gamma $, the ratio of conductivity of the sample solution to that of the BGE. However, in practice both molecular diffusion and convective dispersion limit concentration enhancement. We present a theoretical and experimental study of concentration enhancement using FASS. We model the FASS process as electromigration, diffusion, and advection of two background electrolyte ions and multiple sample species across a known initial concentration gradient. Regular perturbation methods and a generalized Taylor dispersion analysis are used to derive area-averaged species conservation and electric field equations. The model predicts the spatial and temporal development of background electrolyte concentration field, electric field, and sample-ion distribution of the FASS process. We have validated this model using on-chip FASS experiments. We use an acidified poly(ethylene oxide) (PEO) coating to minimize dispersion due to electro-osmotic flow (EOF), and thereby evaluate the low- (but finite) dispersion regime of most interest. We have used CCD-based quantitative epifliuorescence imaging to quantify unsteady concentration fields and validate the model. This experimentally validated model is useful in developing optimal designs of sample stacking assay devices.