Microfluidic multipoles theory and applications

Abstract

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 microfluidic multipole is constrained by the lack of simple, accurate models to predict mass transport within them. In this work, we introduce the complete 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 are validated experimentally with a library of 3D printed devices and found in excellent agreement. Following a theory-guided design approach, we further ideate and fabricate two classes of spatiotemporally reconfigurable multipolar 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 microfluidic multipoles.

Fig. 1

From dipoles and quadrupoles to multipoles. Theoretical streamlines (a–d) and fluorescence micrograph (e–h). Positive and negative sign, respectively, represent injection and aspiration apertures. To facilitate comparison between theory and experiment, green and red background were superposed on flow fields to highlight the expected areas of confinement not captured by streamlines. a, e Microfluidic dipole. b, f Microfluidic quadrupole. c, g MFM with rotational symmetry. d, h 12-aperture MFM with translational symmetry. Scale bars represent 500 μm

Fig. 2

Theoretical model. Solutions for a leading edge in a no-slip plane flow (Pe = 100) is first obtained (a) and then transformed via the complex potential to obtain the dipole concentration profile (b). This solution can then be further transformed to obtain symmetrical configurations such as the “flower multipole” (c). Similar steps can be taken to obtain solutions for a variety of problems. Pictured here are (d) the microfluidic quadrupole (e) the “poppy” alternating multipole and (f) a multicolor “flower multipole” with different injected reagents. Black and white maps in inset represent the mapping of the upper complex plane and lower complex plane of solution (a), respectively. Checkerboard insets demonstrate how the transform used affects a regular grid. The red line corresponds to the line of concentration 1/2 and separates the “interior” and “exterior” domains

Fig. 3

Experimental setup and side-by-side comparison between theory and experiments. a Schematics of a fixed MFM setup. The MFM is precisely positioned over the surface with a gap controlled by the spacers. b Picture of the experimental setup with holder and MFM clamped atop of an inverted microscope. c–f Side-by-side comparison between analytical and experimental results for various multipolar configurations. The top half of each subfigure is the theoretical concentration profile while the bottom half is a micrograph of a fluorescent dye injected using the MFM (Pe ∼10², Reynolds number ∼10⁻³). c Microfluidic dipole. d Microfluidic quadrupole. e Polygonal multipole (f) 4-petal axisymmetric “flower” multipole (g) 8-petal axisymmetric “flower” multipole (h) Asymmetric impinging flows of different concentrations. Scale bars = 500 µm

Fig. 4

Microfluidic multipole devices. a Fluorescence micrograph showing the confinement pattern of a rMFM device. b Graph representing the periodic exposure to reagents for each confinement area of a rMFM used as a chemical stroboscope. c Fluorescence micrographs showing 28 different confinement patterns made with a 12-aperture tMFM during a single experiment lasting less than 2 min. Scale bar represents 500 µm

Fig. 5

Immunofluorescence assay experiment using a microfluidic multipole. a–c Workflow of an immunofluorescence assay using a staggered tMFM. a The device is used as a 6-sided rMFM device to expose the capture antibody to 6 different concentrations of antigen. b The corner apertures are then used to expose the previous areas with detection antibodies. c The last aperture is used to wash the slide. d Micrograph of the detection antibody of the immunoassay made with the tMFM device. e Experimental binding curve of the immunoassay. Error bars represent the standard deviation over 6 spots