Mathematical Modelling of the Impact of Acoustic Waves on an Incompressible Fluid Flow through a Parallel Channel

This study investigates the impact of acoustic waves on fluid flow through a channel, and the channel is considered to be a pipe carrying incompressible fluid. The research focused on analysing the impact of an acoustic wave on the fluid flowing through the channel that could change the flow patterns and assessing how effective acoustic wave stimulation can be at disrupting the fluid flow. We modified the Navier-Stokes equation and incorporated the acoustic terms into the system and scaled it to be dimensionless. The scaled mathematical models were solved analytically, and we adopted Wolfram Mathematica, version 12, to perform the numerical computation and investigate the influence of acoustic wave propagation on fluid flow behaviour through the channel. Results: The simulated results reveal that the introduction of acoustic waves induces oscillatory velocity profiles and flow rates, indicating dynamic coupling between acoustic forcing and fluid motion. These oscillations are strongly dependent on acoustic wave parameters such as frequency and amplitude as well as pore geometry and fluid properties.The results suggest that acoustic fields can be strategically tuned to enhance fluid mobility, overcome capillary barriers, and promote redistribution of phases in porous networks.