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A new self-excited chemo-fluidic oscillator based on stimuli-responsive hydrogels: Mathematical modeling and dynamic behavior

Reference

Joseph Páez Chávez, Andreas Voigt, Jörg Schreiter, Uwe Marschner, Stefan Siegmund, Andreas Richter, "A new self-excited chemo-fluidic oscillator based on stimuli-responsive hydrogels: Mathematical modeling and dynamic behavior" , In Applied Mathematical Modelling, vol. 40, no. 23–24, pp. 9719-9738, 2016. [doi]

Abstract

Abstract This work concerns the modeling and dynamical study of a chemo-fluidic oscillator with the ability of coupling chemical and fluidic domains. The coupling is made possible by means of stimuli-responsive (also referred to as smart) hydrogels, which are able to change their volume under small variations of special thermodynamic parameters, in a reversible and reproducible manner. The paper presents a piecewise-smooth dynamical system describing the behavior of this chemo-fluidic oscillator. Specialized path-following algorithms are applied to study the periodic response of the system under parameter variations. Our investigation reveals that the origin of the oscillatory behavior is connected to the presence of a Hopf bifurcation in the system. Furthermore, the effect of several system parameters on the frequency of oscillation is studied in detail.

Bibtex

@article{PáezChávez20169719,
title = "A new self-excited chemo-fluidic oscillator based on stimuli-responsive hydrogels: Mathematical modeling and dynamic behavior ",
journal = "Applied Mathematical Modelling ",
volume = "40",
number = "23–24",
pages = "9719 - 9738",
year = "2016",
note = "",
issn = "0307-904X",
doi = "https://doi.org/10.1016/j.apm.2016.06.038",
url = "http://www.sciencedirect.com/science/article/pii/S0307904X16303493",
author = "Joseph Páez Chávez and Andreas Voigt and Jörg Schreiter and Uwe Marschner and Stefan Siegmund and Andreas Richter",
keywords = "Chemo-fluidic oscillator",
keywords = "Phase transition polymer",
keywords = "Microfluidic circuit",
keywords = "Non-smooth dynamical system",
keywords = "Numerical continuation",
keywords = "Bifurcation ",
abstract = "Abstract This work concerns the modeling and dynamical study of a chemo-fluidic oscillator with the ability of coupling chemical and fluidic domains. The coupling is made possible by means of stimuli-responsive (also referred to as smart) hydrogels, which are able to change their volume under small variations of special thermodynamic parameters, in a reversible and reproducible manner. The paper presents a piecewise-smooth dynamical system describing the behavior of this chemo-fluidic oscillator. Specialized path-following algorithms are applied to study the periodic response of the system under parameter variations. Our investigation reveals that the origin of the oscillatory behavior is connected to the presence of a Hopf bifurcation in the system. Furthermore, the effect of several system parameters on the frequency of oscillation is studied in detail. "
}

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