Supplementary Information
Computational details
Structural model
FE structural models of a SAW device based on LGS substrate, with dimensions 1600 μm length x 1600 μm depth x 200 μm height, were developed. Figure 1a in the main manuscript shows a schematic diagram of the simulated SAW device with orthogonal IDT configuration integrated with delay path modification, in the form of microcavities. IDT finger pairs with periodicity 40 μm, were defined on the surface for each port along (0, 22, 0) and (0, 22, 90) Euler directions. The piezoelectric domain was meshed using coupled field tetragonal solid elements with four degrees of freedom accounting for the three translations and voltage. High mesh densities were ensured near the surface. Impulse response analysis was performed during 190 ns by applying an impulse voltage of 100 V at the input IDT and employing a time step of 0.95 ns^{1}. Subsequently, an ac analysis was carried out using a peak voltage of 2.5 V with the device frequency obtained from impulse response analysis for each of the propagation directions.
Fluid structure interaction model
The fluid region, with 50 μm height, was modeled as an infinite reservoir of Newtonian, incompressible fluid on top of the piezoelectric domain, subject to stress free boundary condition at the free surface (i.e. P =0). The piezoelectric domain was meshed using tetragonal solid elements with four DOF to account for the three translations and the voltage. The fluid domain was meshed using eight node fluid elements and discretized employing an Arbitrary Lagrangian Eulerian (ALE) frame for the kinematical description. The FSI model contained millions of nodes and elements: 2, 217, 889 nodes and 2, 085, 525 elements. Numerical solutions were obtained by sequential solution of the generalized NavierStokes equation for the fluid domain and acoustoelectric equations for the piezoelectric motion^{ }^{2}, employing the iterative sequential coupling algorithm^{3}. In this algorithm, the governing equations for the two domains are solved separately and the solver iteration between the two domains continues till convergence of the load transferred across the interface is achieved.
Best case microcavities
To obtain the best microcavity configuration for sensing, 20 microcavities of λ/2 square cross sections with varying depths were etched on the device surface along the delay path with IDTs along the (0, 22, 90) direction. These microcavities were filled with a waveguide material polystyrene (PS) to provide increased entrapment of acoustic energy near the device surface^{4}. Based on our simulated node translation data, we find that Love waves incident on a shallow groove or cavity on the surface of a piezoelectric substrate filled with another elastically isotropic material such as polystyrene are weakly scattered with a part of the energy contained in the reflected and the transmitted Love waves and the other part converted into the bulk shear waves that propagate into the substrate. Our simulations indicate that PS filled microcavities with dimensions λ/2 x λ/2 x λ/2 exhibit the highest energy transmission and smallest insertion loss (lesser by 2 dB compared to the next best PS filled λ/2 x λ/2 x λ/8 microcavities) (Fig. 1S) Our analyses of displacement profiles for each of the simulated microcavity designs indicate that these improvements are brought about by a larger coherent reflection of the incident Love wave and subsequent reduced conversions into bulk shear modes which radiate into the substrate (Fig. 1b). Details of the passbands are shown in Fig. IS where a 21.8 dB increase in energy transmission is clearly shown for the best case microcavity (λ/2 x λ/2 x λ/2) over the SAW sensor with unidirectional IDTs along the (0, 22, 90) Euler direction and no delay path modifications (standard SAW). Therefore, 20 PSfilled microcavities with dimensions λ/2 x λ/2 x λ/2 were incorporated in the delay path of a SAW device with orthogonallyoriented, mutuallyinteracting IDTs along the (0, 22, 0) and (0, 22, 90) Euler directions.
(Color Online) Figure 1s: Comparison of transmitted energies for empty and PSfilled microcavities with /2 square cross section and depths of /4, /4 and /2 with standard LGS SAW delayline device and an optimized LW device. Std LGS refers to a device with unidirectional IDTs and no delay path modifications. PS filled microcavities with dimensions λ/2 x λ/2 x λ/2 exhibit the highest energy transmission and smallest insertion loss and form the best case configuration.
Computation of streaming force and device sensitivity
Biofouling elimination in the simulated SAW devices due to mixed mode waves propagating along (0, 22, 0) Euler direction is dependent on the magnitude of the induced acoustic streaming forces computed as^{5, 6}:
(1)
Here, and k_{i}_{ }refer to the attenuation constant and leaky SAW wave number, respectively, and are obtained using a perturbation approach^{7, 8},_{ } refers to the angular frequency and A refers to the acoustic wave displacement, which are obtained using FE simulations.
The device sensitivity was computed using the perturbation theory utilizing the mass sensitivity equation applicable to all types of surface acoustic devices independent of the type of acoustic modes ^{9}:
(2)
To calculate the mass sensitivity, the values of mode center frequency f_{0}, angular frequency , average area density of wave energy U, and displacements u_{x}, u_{y}, and u_{z} were derived from the finite element simulations.
The computed time averaged streaming velocities for the microcavity based orthogonal device are compared with those for the unidirectional standard SAW device in Fig. 2S.
(Color Online) Figure 2S: Comparison of time averaged streaming velocity profiles in the three principal directions along the fluid film thickness, for (a) standard SAW device with IDTs along (0, 22, 0) and (b) orthogonal SAW device with microcavities in delay path.
References
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