A microfluidic device for microbial single-cell cultivation of bacteria was modeled and simulated using COMSOL Multiphysics. The liquid velocity field and the mass transfer within the supply channels and cultivation chambers were calculated to gain insight in the distribution of supplied nutrients and metabolic products secreted by the cultivated bacteria. The goal was to identify potential substrate limitations or product accumulations within the cultivation device. The metabolic uptake and production rates, colony size, and growth medium composition were varied covering a wide range of operating conditions. Simulations with glucose as substrate did not show limitations within the typically used concentration range, but for alternative substrates limitations could not be ruled out. This lays the foundation for further studies and the optimization of existing picoliter bioreactor systems.