Analytic modelling of passive microfluidic mixers
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Published:2022
Issue:4
Volume:19
Page:3892-3908
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ISSN:1551-0018
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Container-title:Mathematical Biosciences and Engineering
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language:
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Short-container-title:MBE
Author:
Bonament Alexi1, Prel Alexis1, Sallese Jean-Michel2, Lallement Christophe1, Madec Morgan1
Affiliation:
1. Laboratory of Engineer Sciences, Computer Science and Imagine (ICube), UMR 7357 (UniversitȦ de Strasbourg/Centre National de Recherche Scientifique), Strasbourg, France 2. STI-IEL-Electronics Laboratory, Ecole Polytechnique FȦdȦrale de Lausanne (EPFL), Lausanne, Switzerland
Abstract
<abstract>
<p>This paper deals with a new analytical model for microfluidic passive mixers. Two common approaches already exist for such a purpose. On the one hand, the resolution of the advection-diffusion-reaction equation (ADRE) is the first one and the closest to physics. However, ADRE is a partial differential equation that requires finite element simulations. On the other hand, analytical models based on the analogy between microfluidics and electronics have already been established. However, they rely on the assumption of homogeneous fluids, which means that the mixer is supposed to be long enough to obtain a perfect mixture at the output. In this paper, we derive an analytical model from the ADRE under several assumptions. Then we integrate these equations within the electronic-equivalent models. The resulting models computed the relationship between pressure and flow rate in the microfluidic circuit but also takes the concentration gradients that can appear in the direction perpendicular to the channel into account. The model is compared with the finite element simulation performed with COMSOL Multiphysics in several study cases. We estimate that the global error introduced by our model compared to the finite element simulation is less than 5% in every use case. In counterparts, the cost in terms of computational resources is drastically reduced. The analytical model can be implemented in a large range of modelling and simulation languages, including SPICE and hardware description language such as Verilog-AMS. This feature is very interesting in the context of the <italic>in silico</italic> prototyping of large-scale microfluidic devices or multi-physics devices involving microfluidic circuits, <italic>e.g.</italic> lab-on-chips.</p>
</abstract>
Publisher
American Institute of Mathematical Sciences (AIMS)
Subject
Applied Mathematics,Computational Mathematics,General Agricultural and Biological Sciences,Modeling and Simulation,General Medicine
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