The invention is a microfluidic device particularly well suited to mix chemical or particulate matter, even living cells. The device uses a unique geometry of microchannels that allows passive, nonenergy-intensive mixing of fluids. The geometry also allows a smooth flow of materials, which facilitates more biochemical reactions and avoids problems over multiple cycles. The system works equally well for both mixing thick and watery fluids. Making the device is a simple, single-layered process.