![]() ![]() Rayleigh–Schlichting streaming is generally treated within the incompressibility framework. This vorticity extends its influence beyond the VBL and in turn induces larger-scale eddies of width λ / 2 in the fluid bulk, where λ = c s f is the acoustic wavelength and c s the speed of sound. This vorticity appears in the form of an array of eddies pairs, denoted as inner vortices, along the channel walls. In Rayleigh–Schlichting streaming, a non-zero, time-averaged vorticity is generated inside the unsteady VBL of typical thickness δ = 2 ν ω 1 2, where ν is the kinematic viscosity and ω = 2 π f the acoustic angular frequency. The bulk acoustic streaming is denoted as Eckart streaming and becomes significant only with high frequencies (>MHz) or with very viscous liquids, so that the attenuation length is smaller than- or of the same order as-the vessel size. ![]() It is referred to Rayleigh–Schlichting streaming, and is different from that induced by acoustic attenuation in the bulk of fluid. Besides viscosity, the frequency also strongly influences the maximal streaming velocity.Īmongst different sorts of acoustic streaming, the one relevant in microfluidics situations usually involves viscous stress along walls or obstacles, generated by no-slip conditions and resulting in the presence of a viscous boundary layer (VBL). Globally, the streaming velocity is dramatically weakened by a higher viscosity, whereas the flow pattern and the disturbance distance remain similar regardless of viscosity. We then provide empirical scaling laws to quantify the influence of ν and f on the streaming velocity. As a characteristic streaming velocity, the maximal velocity is located at a distance of δ from the tip, and it increases as the square of the acoustic velocity. For all situations, the streaming flow appears as a main central jet from the tip, generating two lateral vortices beside the tip and outside the boundary layer. Both quantities supposedly influence the thickness of the viscous boundary layer δ = ν π f 1 / 2. We conducted experiments with particle image velocimetry to quantify this streaming flow through the influence of liquid viscosity ν, from 1 mm 2/s to 30 mm 2/s, and acoustic frequency f from 500 Hz to 3500 Hz. This sharp-edge streaming can be relatively intense, owing to the strongly focused inertial effect experienced by the acoustic flow near the tip. Acoustic streaming can be generated around sharp structures, even when the acoustic wavelength is much larger than the vessel size.
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