A Numerically Efficient Damping Model for Acoustic Resonances in Microfluidic Cavities

Abstract

Acoustofluidic damping is a crucial factor that limits the attainable acoustic amplitudes and therefore the effectiveness of acoustofluidic devices. It can be traced back to viscous and thermal dissipation in the bulk and in the boundary layers at cavity walls or suspended particles. However, numerical 3D simulations that include all relevant physics are prohibitively expensive since the acoustic boundary layers need to be resolved. We present a way to incorporate the dissipation effects into a synthetic acoustofluidic loss factor for the use in 3D device simulations. It comes at minimum numerical cost since boundary layers are resolved analytically. Our results and the validity of the physical assumptions we make in the derivation have been verified by analytical and numerical reference solutions. The acoustofluidic loss factor is easily incorporated in device models for a numerically feasible and quantitatively accurate prediction of acoustic amplitudes. In this sense, our work represents the missing link that allows to make not only qualitative but also quantitative predictions of acoustofluidic forces in realistic 3D devices.

Modeling of Microdevices for SAW-Based Acoustophoresis — A Study of Boundary Conditions

“…For simplicity, we often suppress the spatial and temporal variable and write a field simply as . Finally, following Hahn and Dual [ 41 ], we introduce damping in the fluid and the solid using the complex-valued frequency , where is the damping coefficient in the medium with the values listed in Table 2 . For simplicity, we used for both pyrex and PDMS, however this implies a damping length for PDMS longer than the 3 mm given in [ 36 ], so our model is only valid for PDMS devices with walls thinner than 3 mm.…”

Three-Dimensional Numerical Modeling of Acoustic Trapping in Glass Capillaries

“…Following the thorough analysis by Hahn and Dual [33], we introduce effective absorption in our equations by modifying the time derivative as ∂ t → −iωð1 þ iΓÞ, where Γ ≪ 1 is an effective absorption parameter, with values for the respective materials listed in Table I. The remaining details of the model are explained in the following subsections.…”

“…The fluid (water) with its acoustic pressure p, velocity v, density ρ fl , and sound speed c fl is modeled as pressure acoustics with absorption [33],…”

“…Examples of recent advances in modeling include Lei et al [29], who modeled the three-dimensional (3D) fluid domain without taking the solid domain into account; Muller and Bruus [32,39], who made detailed models in 2D of the thermoviscous and transient effects in the fluid domain; Gralinski et al [28], who modeled circular capillaries in 3D with fluid and glass domains without taking absorption and outgoing waves into account; Hahn and Dual [33], who calculated the acoustic field in a 3D model for a glass-silicon device (not a capillary system) and characterized the various loss mechanisms; and Garofalo et al [40], who studied a coupled transducer-silicon-glass-water system in 2D.…”

Multifunctional Composites

“…The first is measured directly. The second is associated with differences in thermo-mechanical properties between particles and a liquid medium, whereby the particles and liquid expand in ultrasonic field in different ways, creating a temperature gradient at the particle-liquid interface, as a result of which the ultrasonic energy at this interface is converted into heat [123,128]. Thermal part of attenuation in a liquid medium depends on thermal conductivity, thermal expansion, and heat capacity.…”