Fractal Analysis of a Non-Newtonian Fluid Flow in a Rough-Walled Pipe

Area of Science:

• Fluid dynamics
• Rheology
• Surface science

Background:

• Understanding fluid flow in pipes is crucial for many industrial and natural processes.
• Non-Newtonian fluids exhibit complex flow behaviors not described by simple viscosity.
• Pipe wall roughness can significantly alter flow characteristics, affecting pressure drop and velocity profiles.

Purpose of the Study:

• To theoretically investigate the effect of fractal pipe surface roughness on non-Newtonian fluid flow.
• To analyze the influence of roughness on the velocity profile and Darcy friction factor.
• To compare the sensitivity of shear thinning, Newtonian, and shear thickening fluids to surface roughness.

Main Methods:

• Utilizing the power-law model to describe non-Newtonian fluid rheology.
• Characterizing pipe surface roughness using fractal dimensions.
• Developing theoretical models for laminar flow in rough-walled pipes.
• Analyzing velocity profiles and calculating Darcy friction factors.

Main Results:

• Pipe surface roughness demonstrably affects the velocity profile and Darcy friction factor.
• Shear thinning fluids are more sensitive to surface roughness than Newtonian or shear thickening fluids.
• An intersection point exists for a specific fractal dimension where all fluid types exhibit similar flow behavior.

Conclusions:

• Pipe surface roughness is a critical parameter in non-Newtonian fluid dynamics.
• The fractal nature of roughness provides a quantitative measure for its impact.
• Findings have implications for fluid dynamics in hydrology, biomedical engineering, and industrial applications.