Nonlinear hydrodynamic effects induced by Rayleigh surface acoustic wave in sessile droplets

Area of Science:

• Fluid Dynamics
• Acoustics
• Microfluidics

Background:

• Acoustic streaming is a phenomenon driven by acoustic waves.
• The Stokes model is commonly used for acoustic streaming but may not capture nonlinear effects.
• Understanding fluid behavior in small droplets is crucial for various applications.

Purpose of the Study:

• To experimentally and numerically characterize three-dimensional acoustic streaming in small droplets induced by surface acoustic waves (SAW).
• To investigate the nonlinear nature of inertia in SAW-driven droplet flow.
• To determine the validity limits of the Stokes model and the necessity of the Navier-Stokes equation.

Main Methods:

• Experimental measurements of acoustic streaming in droplets (1-30 μl).
• Numerical simulations using the full Navier-Stokes equation.
• Definition and application of a new acoustic parameter, F{NA}, to quantify acoustic force versus surface tension.

Main Results:

• Quantitative evidence of strong nonlinear flow inertia in SAW-driven droplet streaming for F{NA} ≥ 0.01.
• The Stokes model introduces significant errors (up to 93%) in nonlinear regimes, while the Navier-Stokes equation provides accurate predictions.
• The Stokes model is only valid for very low acoustic power (≤1 μW, F{NA} < 0.002).
• Increased F{NA} (above 0.45) leads to internal streaming and droplet deformation.

Conclusions:

• The nonlinear inertia of flow is a critical factor in SAW-induced acoustic streaming within small droplets.
• Accurate modeling of this phenomenon requires the full Navier-Stokes equation, particularly in nonlinear regimes.
• The parameter F{NA} effectively characterizes the balance between acoustic force and surface tension, guiding the selection of appropriate models and predicting droplet deformation.