Microfluidic multipoles (MFMs) have been realized experimentally and hold
promise for "open-space" biological and chemical surface processing. Whereas
convective flow can readily be predicted using hydraulic-electrical analogies,
the design of advanced MFMs is constrained by the lack of simple, accurate
models to predict mass transport within them. In this work, we introduce the
first exact solutions to mass transport in multipolar microfluidics based on
the iterative conformal mapping of 2D advection-diffusion around a simple edge
into dipoles and multipolar geometries, revealing a rich landscape of transport
modes. The models were validated experimentally with a library of 3D printed
MFM devices and found in excellent agreement. Following a theory-guided design
approach, we further ideated and fabricated two new classes of spatiotemporally
reconfigurable MFM devices that are used for processing surfaces with
time-varying reagent streams, and to realize a multistep automated immunoassay.
Overall, the results set the foundations for exploring, developing, and
applying open-space MFMs.Comment: 16 pages, 5 figure
