Development of a lattice Boltzmann model to investigate the interaction mechanism of surface acoustic wave on a sessile droplet

Abstract

This study focuses on the development of a three dimensional numerical model, based on the lattice Boltzmann method (LBM), for two-phase fluid flow dynamics employing a multiple-relaxation-time (MRT) pseudopotential scheme. The numerical model is applied in the investigation of acoustic interactions with microscale sessile droplets (1- 10 µl), under surface acoustic wave (SAW) excitation, through the introduction of additonal forcing terms in the LBM scheme. In the study, a range of resonant frequencies (61.7 - 250.1 MHz) are studied and quantatively compared to existing studies and experimental findings to verify the proposed model. The modelling predictions on the roles of forces (SAW, interfacial tension, inertia and viscosity) on the dynamics of mixing, pumping and jetting of a droplet are in good agreement with observations and experimental data. Further examination of the model, through parameter study, identified that the relaxation parameters considered free to tune in the MRT, play an important role in model stability, providing large reductions in spurious velocities, in both the liquid and gas phases, when the values are specified correctly. It has also been discovered that employing a dynamic contact angle hysteresis model increased the adhesion between the liquid droplet and the substrate, improving the agreement with experimental findings by up to 20%. Lastly, an investigation of various equation of state implementations revealed some fascinating differences in droplet dynamics and behaviours, owing primarily to the physical underpinning of which each is based upon. The developed model is successfully applied in the examination of various scenarios including SAW-droplet interactions on an inclined slope, droplet impact on flat (horizontal) and inclined surfaces with and without SAW interactions, and dual SAW interactions on a droplet at several configurations. The findings indicate the importance of applied SAW power, especially in inclined slope scenarios, to overcome the inertia and gravitational forces which act to counteract the droplet motion initiated by the acoustic wave direction of travel. Furthermore, a new multi-component multi-phase multi-pseudopotential (MCMP MPI) LB model is proposed. The study details initial model development and verification for classical benchmark cases, comparing to both the single-component (SCMP MPI) and publicised data. Similar to its SCMP MPI counterpart, the model displays excellent stability, even at high density ratios, and thermodynamic consistency. Comparison to the SCMP MPI model reveals lower spurious velocities are generated in the proposed MCMP model, approximately one order of magnitude lower. Close inspection of the interaction force implementation shows they are analogous whilst similar surface tension values are presented for both models. The proposed scheme signifies a new class of MPI model capable of simulating realistic fluid compositions for use in applications of scientific and engineering interest.