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.