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End date: 2022 × Start date: 2022 × Subject: Surface waves ×

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Now showing 1 - 2 of 2
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    A rigorous derivation and energetics of a wave equation with fractional damping
    (Basel : Springer, 2021) Mielke, Alexander; Netz, Roland R.; Zendehroud, Sina
    We consider a linear system that consists of a linear wave equation on a horizontal hypersurface and a parabolic equation in the half space below. The model describes longitudinal elastic waves in organic monolayers at the water–air interface, which is an experimental setup that is relevant for understanding wave propagation in biological membranes. We study the scaling regime where the relevant horizontal length scale is much larger than the vertical length scale and provide a rigorous limit leading to a fractionally damped wave equation for the membrane. We provide the associated existence results via linear semigroup theory and show convergence of the solutions in the scaling limit. Moreover, based on the energy–dissipation structure for the full model, we derive a natural energy and a natural dissipation function for the fractionally damped wave equation with a time derivative of order 3/2.
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    In situ surface acoustic wave field probing in microfluidic structures using optical transmission interferometry
    (Melville, NY : American Inst. of Physics, 2021) Weser, R.; Schmidt, H.
    The generation of mechanical driving forces in fluids at the microscale can be efficiently realized using acoustic actuators. For this purpose, bulk or surface acoustic waves (SAWs) are typically excited by an electroacoustic transducer, and the acoustic energy is subsequently coupled to the fluid. The resultant acoustic pressure field in the fluid allows for precise manipulation of immersed objects and also for the agitation of the fluid itself. In general, the fluidic actuation capability is mainly determined by the mechanical displacement amplitude at the interface between the fluid and the acoustically active surface. In the case of SAW-based actuators, the fluid most often is directly attached to the substrate surface along which the surface waves propagate. Hence, the lateral distribution of surface displacement amplitude, i.e., the surface acoustic wave field, at the fluid–substrate interface is of particular interest in order to achieve full control of the fluidic actuation. Here, we present a reliable experimental method for the in situ determination of the SAW field on fluid loaded substrate surfaces based on laser interferometry. The optical accessibility of the fluid–substrate interface is realized via transmission through the anisotropic, piezoelectric substrate material requiring only an additional calibration procedure in order to compensate the parasitic influence of effects based on different indices of refraction as well as on complex acousto-optic effects. Finally, the proposed method is demonstrated to yield reliable results of displacement amplitude on the fluid loaded surface and thus, to provide a valuable insight into acoustofluidic coupling that was not available so far.