[paper] Analytic Modeling of Passive Microfluidic Mixers

Alexi Bonament¹, Alexis Prel¹, Jean-Michel Sallese², Christophe Lallement¹, 

and Morgan Madec¹

Analytic modelling of passive microfluidic mixers

Mathematical Biosciences and Engineering (2022)

Vol. 19, No. 4: 3892-3908

DOI: 10.3934/mbe.2022179

   
1. ICube, UMR 7357, Universite de Strasbourg/CRNS (F)
2. STI-IEL-Electronics Laboratory, EPFL (CH)

Abstract: 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 in silicon prototyping of large-scale microfluidic devices or multi-physics devices involving microfluidic circuits, e.g. lab-on-chips.

Fig:  Schematic of the Y-shaped passive mixer. The device is composed of two inlets (here, one is the water and the other is a dye) and one outlet. As we can see on this cartoon (which is purely illustrative and not a simulation result), the mixing is established along the channel and, for a short channel, the dye concentration is not homogeneous in the x direction.

Acknowledgments: This research was supported by the European Regional Development Fund (ERDF) and the Interreg V Upper Rhine Offensive Sciences Program (Project 3.14 – Water Pollution Sensor).

[paper] RTN and BTI statistical compact modeling

G.Pedreira^a, J.Martin-Martinez^a, P.Saraza-Canflanca^b, R.Castro Lopez^b, R.Rodriguez^a, E.Roca^b, F.V.Fernandez^b, M.Nafria^a 

Unified RTN and BTI statistical compact modeling from a defect-centric perspective

Solid-State Electronics

Available online 25 June 2021, 108112

In Press, Journal Pre-proof

DOI: 10.1016/j.sse.2021.108112

a Universitat Autònoma de Barcelona (UAB), Electronic Engineering Department, REDEC group. Barcelona, Spain
b Instituto de Microelectrónica de Sevilla, IMSE-CNM, CSIC and Universidad de Sevilla, Spain

Abstract: In nowadays, deeply scaled CMOS technologies, time-dependent variability effects have become important concerns for analog and digital circuit design. Transistor parameter shifts caused by Bias Temperature Instability and Random Telegraph Noise phenomena can lead to deviations of the circuit performance or even to its fatal failure. In this scenario extensive and accurate device characterization under several test conditions has become an unavoidable step towards trustworthy implementing the stochastic reliability models. In this paper, the statistical distributions of threshold voltage shifts in nanometric CMOS transistors will be studied at near threshold, nominal and accelerated aging conditions. Statistical modelling of RTN and BTI combined effects covering the full voltage range is presented. 

The results of this work suppose a complete modelling approach of BTI and RTN that can be applied in a wide range of voltages for reliability predictions.