Acoustic streaming of ink particles inside a water microdroplet generated by a surface acoustic wave (SAW) has been studied numerically using a finite volume numerical method and these results have been verified using experimental measurements. Effects of SAW excitation frequency, droplet volume, and radio-frequency (RF) power are investigated, and it has been shown that SAW excitation frequency influences the SAW attenuation length, l_SAW, and hence the acoustic energy absorbed by liquid. It has also been observed that an increase of excitation frequency generally enhances the SAW streaming behavior. However, when the frequency exceeds a critical value that depends on the RF power applied to the SAW device, weaker acoustic streaming is observed resulting in less effective acoustic mixing inside the droplet. This critical value is characterised by a dimensionless ratio of droplet radius to SAW attenuation length, i.e., R_d/l_SAW. With a mean value of R_d/l_SAW ≈ 1, a fast and efficient mixing can be induced, even at the lowest RF power of 0.05 mW studied in this paper. On the other hand, for the R_d/l_SAW ratios much larger than ∼1, significant decreases in streaming velocities were observed, resulting in a transition from regular (strong) to irregular (weak) mixing/flow. This is attributed to an increased absorption rate of acoustic wave energy that leaks into the liquid, resulting in a reduction of the acoustic energy radiated away from the SAW interaction region towards the droplet free surface. It has been demonstrated in this study that a fast and efficient mixing process with a smaller RF power could be achieved if the ratio of R_d/l_SAW ≤ 1 in the SAW-droplet based microfluidics.

This paper reports the numerical simulation and experimental characterization of three-dimensional acoustic streaming behavior of a liquid droplet subjected to a Rayleigh surface acoustic wave. The streaming behavior of the droplet was studied as a function of radio-frequency (RF) power, aperture of the interdigitated transducer, and size of the liquid droplet. The hydrodynamic flow field within the droplet was determined by solving the laminar incompressible Navier–Stoke’s equations. The numerical and experimental results are shown to be in good agreement over the range of parameters examined. The ratios of the position of butterfly central line (axis of rotation) to radius of the droplet are demonstrated to be fairly constant for moderate droplet volumes and to vary by less than 12% at large droplet volumes. Besides that, an increase in the RF power and a decrease in the droplet size result in an increased surface acoustic wave (SAW) streaming velocity. The numerical results also suggest that a maximum streaming velocity is achieved when the SAW width is approximately half of the droplet radius.

Pseudopotential lattice Boltzmann (LB) models have been recognized as efficient numerical tools to simulate complex fluid systems, including those at thermodynamic equilibrium states and with phase transitions. However, when the equation of state (EOS) of real fluids is implemented, the existing pseudopotential LB models suffer from thermodynamic inconsistency. This study presents a multipseudopotential interparticle interaction (MPI) scheme, which is fully consistent with thermodynamics and applicable to engineering applications. In this framework, multiple pseudopotentials are employed to represent dominant interaction potentials at different extents of the mean free path of particles. By simulating van der Waals and Carnahan-Starling fluids, it is demonstrated that the MPI scheme can correctly simulate the physical nature of two-phase systems on the lattice including the continuum predictions of liquid-vapor coexistence states and the sound speeds in liquid and vapor phases. It is also shown that the lattice interactions of the MPI scheme represent underlying molecular interactions as they vary in a broad range from strong short-distance repulsions to weak long-distance attractions during phase transitions. Consequently, the MPI is proved to be a reliable LB scheme as it avoids generating unphysical potentials in implementing the EOSs of real fluids and limiting the spurious velocities at the interface of two-phase systems. Additionally, a straightforward procedure is suggested and discussed to preset the MPI system with the two-phase properties of a selected fluid.