Effective mobilities for thin-film flows on micropillar arrays

Area of Science:

• Fluid dynamics
• Surface science
• Materials science

Background:

• Micropillar-textured surfaces are vital for controlling fluid behavior in applications such as thermal management and microfluidics.
• Existing models lack a unified framework for analyzing both capillary-driven and Marangoni-driven transport across diverse film thicknesses on these surfaces.

Purpose of the Study:

• To develop a unified thin-film modeling framework for wetting dynamics on periodic micropillar arrays.
• To derive explicit analytical mobility expressions for lubrication-based modeling.
• To capture both capillary-driven and Marangoni-driven transport across arbitrary film thicknesses.

Main Methods:

• Utilized an equivalent microchannel formulation.
• Employed a Fourier series solution of the Stokes equations.
• Derived exact analytical mobilities for pressure-driven and Marangoni-driven flows.

Main Results:

• Obtained analytical mobility expressions valid for film thicknesses below and above the pillar height.
• Developed a unified framework connecting confined transport, overtopped films, and effective slip.
• Demonstrated that Marangoni-driven transport saturates more strongly with increasing pillar height than pressure-driven transport.

Conclusions:

• The derived mobility laws provide a constitutive ingredient for extending lubrication theory to complex wetting dynamics on textured substrates.
• The framework successfully captures the interplay between film thickness, pillar height, and lateral confinement.
• The findings offer a comprehensive approach to understanding fluid transport on engineered textured surfaces.