Two phases (liquid–liquid extraction) stratified flows in a rectangular geometry are investigated in a double-Y shape glass chip. The influence of physical properties, in particular the viscosity of the two liquids, on the velocity profiles is determined numerically. Viscosity affects the shapes of the velocity profiles of each phase. The extraction conditions (acid concentrations, contact times) in batch and in the microfluidic device were considered for a neutral extractant, N,N′-dimethyl N,N′-dibutyl tetradecylmalonamide (DMDBTDMA) and a liquid anion exchanger (Aliquat® 336), for the extraction of Eu(III) from HNO3 and U(VI) from HCl, respectively. The effects of viscosity and operating conditions on extraction performances were investigated, and the apparent rate constants were evaluated for the extraction of uranium by Aliquat® 336 k app = (0.55 ± 0.03) s−1 and for the extraction of europium by DMDBTDMA: k app = (2.9 ± 0.2) × 10−3 s−1.