Precise control of media delivery to cells in microfluidic systems in a simple and efficient manner is a challenge for a number of cell-based applications. Conventional syringe pumps can deliver culture media into microfluidic devices at precisely controlled flow rates, but they are bulky and require a power source. On the other hand, passive microflow-generating systems cannot maintain continuous, controllable and long-term delivery of media. We have developed an on-chip microflow control technology that combines flow rate control and passive, long-term delivery of media to microwell tissue culture chambers. Here, a passive flow is initiated using the siphon effect and a yarn flow resistor is used to regulate the flow rate in the microchannel. Using the yarn flow resistor, the medium flow rate into the microfluidic cell culture system is made adjustable to a few hundred microliters per hour. To evaluate the effects of controlled flow on microfluidic cell culture properties (feasibility test), we measured the cell alignment and cytoskeletal arrangement of endothelial cells cultured in a microwell array inside the microfluidic channel.