Open nanofluidic systems, where liquids flow along the
outer surface
of nanoscale structures, provide otherwise unfeasible capabilities
for extremely miniaturized liquid handling applications. A critical
step toward fully functional applications is to obtain quantitative
mass flow control. We demonstrate the application of nanomechanical
sensing for this purpose by integrating voltage-driven liquid flow
along nanowire open channels with mass detection based on flexural
resonators. This approach is validated by assembling the nanowires
with microcantilever resonators, enabling high-precision control of
larger flows, and by using the nanowires as resonators themselves,
allowing extremely small liquid volume handling. Both implementations
are demonstrated by characterizing voltage-driven flow of ionic liquids
along the surface of the nanowires. We find a voltage range where
mass flow rate follows a nonlinear monotonic increase, establishing
a steady flow regime for which we show mass flow control at rates
from below 1 ag/s to above 100 fg/s and precise liquid handling down
to the zeptoliter scale. The observed behavior of mass flow rate is
consistent with a voltage-induced transition from static wetting to
dynamic spreading as the mechanism underlying liquid transport along
the nanowires.