Cationic lipophilic dyes can accumulate in mitochondria, and especially in mitochondria of tumor cells. We investigated the chemical properties and the processes allowing selective uptake into tumor cells using the Fick-Nernst-Planck equation. The model simulates uptake into cytoplasm and mitochondria and is valid for neutral molecules and ions, and thus also for weak electrolytes. The differential equation system was analytically solved for the steady-state and the dynamic case. The parameterization was for a generic human cell, with a 60 mV more negative potential at the inner mitochondrial membrane of generic tumor cells. The chemical input data were the lipophilicity (log K(OW)), the acid/base dissociation constant (pK(a)) and the electric charge (z). Accumulation in mitochondria occurred for polar acids with pK(a) between 5 and 9 owing to the ion trap, and for lipophilic bases with pK(a)>11 or permanent cations owing to electrical attraction. Selective accumulation in tumor cells was found for monovalent cations or strong bases with log K(OW) of the cation between -2 and 2, with the optimum near 0. The results are in agreement with experimental results for rhodamine 123, a series of cationic triarylmethane dyes, F16 and MKT-077, an anticancer drug targeting tumor mitochondria.