Modeling efficient fractal features to simulate the impact of porosity and viscosity on fluid interfacial stability

Efficient fractal theory is presented as a groundbreaking mathematical framework that precisely models the properties of porosity and viscosity in fluid flow, particularly for spinning ferrofluid columns in porous media. The novelty of this study lies in its demonstration that an inviscid fluid in fractal space replicates the behavior of a viscous fluid in traditional space, providing an entirely new perspective on fluid dynamics. This innovative approach leverages fractal theory to capture the intricate, fractal-like features within porous media and their influence on fluid flow under rotation and magnetic fields. The study’s contributions include the development of accurate characterizations for the system’s nonlinear dynamics, which were previously unattainable using traditional methods. A novel mathematical analysis establishes the stability criteria governing the behavior of viscous ferrofluids in porous media, offering key insights into their dynamics. Numerical validation further underscores the interplay between azimuthal magnetic field strength, angular rotation, and porosity, revealing that kinematic viscosity stabilizes the system when the inner fluid density is lower than the outer fluid’s. These findings not only enhance our theoretical understanding but also pave the way for practical advancements in applications involving ferrofluid stability in porous media, emphasizing the transformative potential of fractal theory in fluid dynamics.