Biologically motivated magnetic microfluidic rheostats for precise and scalable flow control.

Precise regulation of hydraulic resistance is essential for controlling flow distribution, particle transport, and chemical synthesis in microfluidics. Despite frequent comparisons between microfluidic networks and electronic circuits, components analogous to electronic rheostats for high-precision continuous resistance tuning remain absent, with flow regulation typically relying on microvalves with discrete open/closed states and external flow-control hardware. Inspired by geometry-modulated flow resistance in heart valves, we introduce magnetic microfluidic rheostats composed of soft magnetic cantilever arrays, whose field-controlled bending modulates the hydraulic diameter to achieve stable and continuous resistance tuning with a minimum measured increment of ~1.7%. Using external permanent magnets instead of complex actuation systems, the rheostat enables low-cost, energy-efficient operation while maintaining high precision. Incorporating the rheostat into a Wheatstone fluidic bridge allows sub-10 µm/s flow balancing and precise microparticle manipulation. Moreover, rheostats with tailored magnetic responses enable one-to-many control under a single magnetic field, allowing multiple channels to be regulated synchronously or asynchronously. This approach simplifies system architecture compared with conventional one-to-one actuation, while maintaining 1-2% composition accuracy across multi-component streams. These results establish microfluidic rheostats as dedicated resistance regulators that expand the functional toolkit of microfluidics for scalable, high-precision manipulation and synthesis.