Alghane M, Chen B X, Fu Y Q, Li Y, Desmulliez M P Y, Mohammed M I, Walton A J
School of Engineering and Physical Sciences, Heriot-Watt University, Edinburgh EH14 4AS, United Kingdom.
Phys Rev E Stat Nonlin Soft Matter Phys. 2012 Nov;86(5 Pt 2):056304. doi: 10.1103/PhysRevE.86.056304. Epub 2012 Nov 9.
We report an experimental and numerical characterization of three-dimensional acoustic streaming behavior in small droplets of volumes (1-30 μl) induced by surface acoustic wave (SAW). We provide a quantitative evidence of the existence of strong nonlinear nature of the flow inertia in this SAW-driven flow over a range of the newly defined acoustic parameter F{NA}=Fλ/(σ/R_{d})≥0.01, which is a measure of the strength of the acoustic force to surface tension, where F is the acoustic body force, λ is the SAW wavelength, σ is the surface tension, and R{d} is the droplet radius. In contrast to the widely used Stokes model of acoustic streaming, which generally ignores such a nonlinearity, we identify that the full Navier-Stokes equation must be applied to avoid errors up to 93% between the computed streaming velocities and those from experiments as in the nonlinear case. We suggest that the Stokes model is valid only for very small acoustic power of ≤1 μW (F{NA}<0.002). Furthermore, we demonstrate that the increase of F{NA} above 0.45 induces not only internal streaming, but also the deformation of droplets.
我们报告了由表面声波（SAW）诱导的小体积（1 - 30 μl）液滴中三维声流行为的实验和数值表征。我们提供了定量证据，表明在新定义的声学参数F{NA}=Fλ/(σ/R_{d})≥0.01的范围内，这种SAW驱动流中流动惯性具有很强的非线性性质，该参数衡量了声学力与表面张力的强度，其中F是声体力，λ是SAW波长，σ是表面张力，R{d}是液滴半径。与广泛使用的通常忽略这种非线性的声流斯托克斯模型不同，我们发现必须应用完整的纳维 - 斯托克斯方程，以避免在非线性情况下计算的声流速度与实验测量值之间出现高达93%的误差。我们认为斯托克斯模型仅在声功率≤1 μW（F{NA}<0.002）时才有效。此外，我们证明F{NA}超过0.45不仅会引起内部声流，还会导致液滴变形。
