Numerical Simulation of Piezoelectrically Agitated Surface Acoustic Waves on Microfluidic Biochips

  • Microfluidic biochips are biochemical laboratories on the microscale that are used for genotyping and sequencing in genomics, protein profiling in proteomics, and cytometry cell analysis. There are basically two classes of such biochips: active devices, where the solute transport on a network of channels on the chip surface is realized by external forces, and passive chips, where this is done using a specific design of the geometry of the channel network. Among the active biochips, current interest focuses on devices whose operational principle is based on piezoelectrically driven surface acoustic waves generated by interdigital transducers placed on the chip surface. In this paper, we are concerned with the numerical simulation of such piezoelectrically agitated surface acoustic waves relying on a mathematical model that describes the coupling of the underlying piezoelectric and elastomechanical phenomena. Since the interdigital transducers usually operate at a fixed frequency, weMicrofluidic biochips are biochemical laboratories on the microscale that are used for genotyping and sequencing in genomics, protein profiling in proteomics, and cytometry cell analysis. There are basically two classes of such biochips: active devices, where the solute transport on a network of channels on the chip surface is realized by external forces, and passive chips, where this is done using a specific design of the geometry of the channel network. Among the active biochips, current interest focuses on devices whose operational principle is based on piezoelectrically driven surface acoustic waves generated by interdigital transducers placed on the chip surface. In this paper, we are concerned with the numerical simulation of such piezoelectrically agitated surface acoustic waves relying on a mathematical model that describes the coupling of the underlying piezoelectric and elastomechanical phenomena. Since the interdigital transducers usually operate at a fixed frequency, we focus on the time-harmonic case. Its variational formulation gives rise to a generalized saddle point problem for which a Fredholm alternative is shown to hold true. The discretization of time-harmonic surface acoustic wave equations is taken care of by continuous, piecewise polynomial finite elements with respect to a nested hierarchy of simplicial triangulations of the computational domain. The resulting algebraic saddle point problems are solved by block-diagonally preconditioned iterative solvers with preconditioners of BPX-type. Numerical results are given both for a test problem documenting the performance of the iterative solution process and for a realistic surface acoustic wave device illustrating the properties of surface acoustic wave propagation on piezoelectric materials.show moreshow less

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Metadaten
Author:Andreas Gantner, Ronald H. W. HoppeGND, Daniel KösterGND, Kunibert G. SiebertGND, Achim WixforthORCiDGND
URN:urn:nbn:de:bvb:384-opus4-580
Frontdoor URLhttps://opus.bibliothek.uni-augsburg.de/opus4/85
Series (Serial Number):Preprints des Instituts für Mathematik der Universität Augsburg (2005-02)
Type:Preprint
Language:English
Publishing Institution:Universität Augsburg
Release Date:2005/10/25
Tag:Numerical Simulation; Surface Acoustic Waves; Biochip
GND-Keyword:Biochip; Numerische Mathematik; Direkte numerische Simulation
Institutes:Mathematisch-Naturwissenschaftlich-Technische Fakultät
Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik
Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Physik
Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik / Lehrstuhl für Numerische Mathematik
Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Physik / Lehrstuhl für Experimentalphysik I
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik