Flow and Transport in Coupled Channel-Matrix Systems
A variety of natural and industrial processes are characterized by flow and transport within porous- or (micro) textured-walled channels and fractures. Some examples include contaminant transport in fractured rocks, flows over sediments beds, vegetation and slippery liquid-infused porous surfaces, and ultrafiltration of colloids, just to mention a few. Examples of flows over micropatterns in form of, e.g., villi, posts, riblets, etc., include nutrient uptake from roots, flows above carbon nanotube forests and superhydrophobic surfaces, nutrient delivery in micro-fluidic bioreactor devices and chaotic mixing in microchannels. While seemingly different, these systems share some unique features: their overall macroscopic response is regulated by the exchange of mass and momentum through the shared channel-obstruction interface and by the obstruction topology. Yet, relating the (pore-scale) obstruction topology to the response function at the system scale remains largely unaddressed.
Direct numerical simulations, which explicitly resolve the obstruction topology, are often too computationally intensive when a great disparity of scales between the micropattern and the device (or system) exists. When direct numerical simulations do not represent a viable option due to their computational cost, effective medium models could be potentially employed to represent the average behavior of the patterned layer, as sketched in Figure.
Figure 1: Conceptualization of micropatterns as a porous medium [Credit: Bowen Ling].
The main question is whether a few layers of discrete obstacles can be modeled as an effective continuum, and consequently, whether or not microfluidics experiments in microchannels with textured/patterned walls could be both employed as surrogates of more complex channel-matrix coupled systems, and used to validate existing theories. We use a combination of numerical simulations, theoretical modeling (upscaling methods) and microfluidic experiments to understand, quantify and predict mass and momentum transfer at the boundaries of thin and thick porous layers in contact with free fluid. We apply our techniques to investigate a wide range of applications including passive and reactive transport in fractured rocks, flow above vegetated layers, and engineered patterned surfaces. We are particularly interested in configurations in which the layer permeability and advective mass transport across the channel/porous medium interface cannot be neglected.
Figure 2: 3D numerical simulations of passive transport (bottom) in the fabricated microfluidic chip (top). Such simulations are used to assess different upscaling approximations [Credit: Bowen Ling].
References
B. Ling, G. Rizzo, I. Battiato, F. de Barros, ‘On transport in channel-matrix systems via integral transforms’, Accepted, Phys. Rev. Fluids, selected by the editors of PRFluids to be an Editors’ Suggestion (2021).
B. Ling, Oostrom, M., Tartakovsky, A. M., Battiato(c), I., ‘Hydrodynamic dispersion in thin porous channels with controlled microtexture’, Phys. Fluids, 30, 076601, Editor’s Pick (2018).
S. Rubol, Ling, B., Battiato, I., ‘Universal scaling-law for flow resistance over canopies with complex morphology’, Nature Scientific Reports, 8:4430, DOI:10.1038/s41598- 018-22346-1 (2018).
B. Ling, Tartakovsky, A. M., Battiato, I., ‘Dispersion controlled by permeable surfaces: surface properties and scaling’, J. Fluid Mech., 801, pp. 13-42 (2016).
S. Rubol, Battiato, I., De Barros, F., ‘Vertical dispersion in obstructed shear flows’, Water Resour. Res., doi: 10.1002/2016WR018907 (2016).
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Battiato, I., Rubol, S., ‘Single-parameter model of vegetated aquatic flows’, Water Resour. Res., 50, doi:10.1002/2013WR015065, (2014).
Papke, A., Battiato, I., ‘A reduced complexity model for dynamic similarity in obstructed shear flows’, Geophys. Res. Lett., 40, pp. 1-5, (2013).
Battiato, I., ‘Self-similarity in coupled Brinkman/Navier-Stokes flows’ J. Fluid Mech., 699, pp. 94-114, (2012).
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