Effect of the permeability on the interaction between two spheres oscillating through Stokes-Brinkmann medium

Area of Science:

• Fluid Dynamics
• Continuum Mechanics
• Rheology

Background:

• Understanding fluid-viscous interactions is crucial in various engineering applications.
• The behavior of oscillating rigid bodies in fluids requires detailed analysis.
• Permeability's role in fluid-structure interaction is a key area of research.

Purpose of the Study:

• To investigate the influence of permeability on rectilinear oscillations of two rigid spheres.
• To analyze the forces acting on the spheres and visualize fluid flow patterns.
• To explore the limiting behaviors corresponding to Stokes and Darcy flows.

Main Methods:

• A collocation technique was utilized to solve the governing equations.
• Boundary conditions on the sphere surfaces were enforced using this method.
• Numerical simulations were performed to obtain forces and streamlines.

Main Results:

• In-phase and out-of-phase forces were calculated and presented graphically.
• Streamlines were plotted to illustrate fluid behavior around the spheres.
• The study provides insights into how permeability affects oscillatory motion.

Conclusions:

• Permeability significantly influences the dynamics of oscillating spheres in viscous fluids.
• The collocation method effectively captures the complex fluid-structure interactions.
• The findings contribute to a better understanding of fluid flow with porous boundaries.