Fractal Model for Drag Reduction on Multiscale Nonwetting Rough Surfaces

Area of Science:

• Fluid dynamics
• Surface science
• Tribology

Background:

• Rough surfaces create alternating no-slip and free shear boundary conditions, potentially reducing fluid drag.
• The Cassie state of wettability depends on the balance between dynamic and capillary pressures, influencing drag reduction.

Purpose of the Study:

• Develop an analytical model using fractal geometry to quantify Cassie state stability and drag reduction.
• Investigate the impact of surface fractal parameters and Reynolds number on drag reduction and friction factor for laminar flow.

Main Methods:

• Utilized a fractal representation of rough surface topography to develop an analytical model.
• Conducted a systematic study on drag reduction and friction factor for laminar flow in a rectangular channel.
• Extended the classical Moody diagram to include hydrophobic and superhydrophobic surfaces.

Main Results:

• Quantified the stability of the Cassie state and its relation to drag reduction.
• Developed friction factor curves and regime maps for hydrophobic and superhydrophobic surfaces.
• Demonstrated that superhydrophobic surfaces do not consistently provide optimal drag reduction.

Conclusions:

• The fractal model provides a method to predict drag reduction on rough, nonwetting surfaces.
• Regime maps guide the selection of surfaces for effective drag reduction.
• The model's applicability to fabricated surfaces like copper, aluminum, and zinc oxide is discussed.