A fluid mixing method using a micromixing apparatus which includes a mixing microchannel having a channel length and a continuously variable channel width defined by a first sidewall surface and an opposing second sidewall surface. The channel width varies from a minimum channel width h to a maximum channel width H in a ratio of H:h≧1.1:1.0. A first inlet injects a first fluid and a second inlet a second fluid into the mixing microchannel which both flow in a flow direction in the mixing microchannel along the channel length. The first sidewall surface includes first curved surface portions and the second sidewall surface includes second curved surface portions. The first and second curved surface portions are non-overlapping to provide the variable channel width. The flow velocity profile is passively varied and exclusively controlled by the continuously variable channel width.