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Updated: May 23, 2026
11:03
An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
Published on: December 4, 2017
Hydrodynamics of fractal continuum flow
Alexander S Balankin1, Benjamin Espinoza Elizarraraz
1Grupo Mecánica Fractal, Instituto Politécnico Nacional, México Distrito Federal, México 07738.
Summary
This study introduces a fractal continuum flow model using local fractional differential operators. It derives fundamental conservation laws and hydrodynamic equations, revealing implications of long-range correlations in fractal flows.
Area of Science:
- Fluid dynamics
- Fractal geometry
- Non-integer calculus
Background:
- Fractal continua exhibit complex flow behaviors not fully described by classical physics.
- Existing models often struggle to capture the intricate dynamics of fractal systems.
- Understanding these flows is crucial for various scientific and engineering applications.
Purpose of the Study:
- To develop a novel mathematical model for fractal continuum flow.
- To generalize key theorems in fluid mechanics to fractal continua.
- To derive and analyze hydrodynamic equations for anisotropic fractal flows.
Main Methods:
- Employing local fractional differential operators to model fractal flow.
- Generalizing the Green-Gauss divergence theorem for fractal continua.
- Generalizing the Reynolds transport theorem for fractal continua.
Main Results:
- A new model for fractal continuum flow is proposed.
- Generalizations of fundamental fluid dynamics theorems are presented.
- Hydrodynamic equations for anisotropic fractal continuum flow are derived.
Conclusions:
- The proposed fractal continuum flow model provides a framework for analyzing complex fluid dynamics.
- The derived equations offer insights into the behavior of anisotropic fractal flows.
- Isotropic fractal continuum flow obeying specific rules can be described by conventional hydrodynamic equations.
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