arXiv subjects

Etienne Boulais

Publications and source records attributed to Etienne Boulais.

3 recordsLinked to original sources

arXiv2026

A Lego Block Approach to Flow in Complex Microfluidic Networks

We present a new way to construct analytical solutions for flow in complex microfluidic channel networks, as well as planar disordered media. Using a combination of Schwarz-Christoffel maps and segmentation techniques inspired by integrated circuit analysis, we build a library of base building blocks which can be reassembled to model complex geometries, in the style of ``Lego Blocks''. Our approach requires minimal numerical computation, and can then generate analytical solutions for any combination of inlet and outlet flow rates. Moreover, our method can tackle multiply connected domains which are usually difficult to model using typical conformal transform approaches. The solutions are developed for microfluidic Hele-Shaw cell devices, but also apply to ideal flow and Darcy flow in complex geometries, or any other flow problem adequately modeled by Laplace's equation. We end by showing how the procedure can be used to model complex disordered media, fractal-like flow geometries, as well as problems of steady advection-diffusion in microfluidic mixers.

physics.flu-dyn↗

arXiv2025

Radial Variations in Residence Time Distribution for Pipe Flows

Suspensions of low-diffusing particles in pipe flows exhibit a difference in age at different radial positions. Particles near the channel walls have higher residence times than the cross-sectional average. We quantify this effect using Monte-Carlo simulations, and show the existence of two different regimes: a "transitional" regime where delay compounds with channel length, and a "far-field" regime where diffusion counterbalances advection. The results presented therein can be used to quantify residence time distributions near the walls of the tube. This effect is important to consider in experiments involving the kinetics of nanometer-scale particles using modern inline analytical tools. This work also provide a radially resolved extension of classical Taylor dispersion results.

physics.flu-dyn↗

arXiv2020

2D Convection-Diffusion in Multipolar Flows

We present a complete analysis of the problem of convection-diffusion in low Re, 2-dimensional flows with distributions of singularities, such as those found in open-space microfluidics and in groundwater flows. Using Boussinesq transformations and solving the problem in streamline coordinates, we obtain concentration profiles in flows with complex arrangements of sources and sinks for both high and low Pe. These yield the complete analytical concentration profile at every point in applications that previously relied on material surface tracking, local lump models or numerical analysis such as microfluidic probes, groundwater heat pumps, or diffusive flows in porous media. Using conformal transforms, we generate families of symmetrical solutions from simple ones, and provide a general methodology that can be used to analyze any arrangement of source and sinks. The solutions obtained that contain the explicit dependence on the various parameters of the problems, such as Pe, the spacing of the apertures and their relative injection and aspiration rates. In particular, we show that the high Pe models can model problems with Pe as low as 1 with a maximum error committed of under $10\%$, and that this error decreases approximately as $Pe^{-1.5}$.

physics.flu-dyn↗