A finite element model of acoustic streaming phenomenon is presented in this work2. 2-D and 3-D FE models of SAW device based on YZ-LiNbO3 with a liquid loading are modeled. A micron-sized piezoelectric substrate with dimensions (400μm width x 1600μm propagation length x 500μm depth) was simulated to gain insights into the acoustic streaming in SAW devices. Two IDT finger pairs in each port were defined at the surface of Y-cut, Z-propagating LiNbO3 substrate. The fingers were defined with periodicity of 34.87 μm and aperture width of 200 μm. The IDT fingers were modeled as mass-less conductors and represented by a set of nodes coupled by voltage degrees of freedom (DOF). A total of approx. 150,000 elements (more than 250000 nodes) were generated. The model was created to ensure higher node density at the surface and throughout the middle of the device to study the different modes of surface acoustic waves and the use of tetragonal (solid) elements with 4 DOF ensured the same. Three DOF's provided the displacements in the longitudinal (x), normal (y), and the shear horizontal (z) directions and a fourth for the voltage.
Fluid is modeled as an incompressible, viscous, and Newtonian using the Navier-Stokes equation. The incompatibility of the Lagrangian frame of reference for solid modeling and Eulerian frame of reference for the fluid is overcome by using the arbitrary Lagrangian-Eulerian (ALE) method where the mesh is constantly updated without modifying the mesh topology. To account for the fluid-solid interaction, an interface is defined across which displacements are transferred from solid to fluid and pressure from fluid to solid. The fluid mesh is continuously updated as the piezoelectric substrate undergoes deformation. The Standard k-ε Model is used to study flow in the turbulent regime. The structure was simulated for a total of 100 nanoseconds (ns), with a time step of 1 ns. The excitation of the piezoelectric solid was provided by applying an AC voltage (with a peak value of 2.5 V and frequency of 100 MHz) on the transmitter IDT fingers.
The above models are utilized to investigate methods for increasing induced acoustic streaming velocity while minimizing the effect on antibody sensing layer in immuno-SAW sensors. Parameters studied in this model include intensity, frequency, density, and viscosity. The transient solutions generated from the model are used to predict trends in acoustic streaming velocity. In addition to the above parameters, the effect of various interdigital transducer (IDT) geometry/design on the streaming velocity is also investigated. Comparisons of model predicted trends with experimental data on non-specifically bound proteins will also be presented.
1. W. Nyborg, “Acoustic streaming” in Physical Acoustics. W Mason Ed. Vol. II B. New York, NY: Academic press Inc, 1965, ch. 11, 265-331.
2. ANSYS v.10 Trademark of ANSYS Inc. (www.ansys.com)