In thin-layer cells the electrochemical current flow can give rise to electrohydrodynamic (EHD) convection of the electrolyte. If combined with a system exhibiting electrochemiluminescence, these convective patterns become directly visible. Following previous experimental work, in this paper a theoretical model is presented and analyzed. It comprises numerical simulation of diffusion and migration of electroactive species (rubrene molecules and ions) and of electroinactive ions of supporting electrolyte across the 100 mu m wide gap between the electrodes. The driving force for convection across the thin layer results from the product of the local uncompensated charge (carried by the liquid) and the local electric field. Characteristic concentration profiles of the species involved are presented, and the role of varying mobilities of the ions of the supporting electrolyte, as well as the additional complexity of the local electric field distribution, resulting from recombination of the rubrene ions is analyzed. Finally, comparison with experimental data is sketched.