Tomlinson, Samuel D. ORCID: https://orcid.org/0000-0002-7180-9443 and Papageorgiou, Demetrios T. (2026) Laminar boundary layers over small-scale textured surfaces. Laminar boundary layers over small-scale textured surfaces, 40 (3):13. ISSN 0935-4964 (Print), 1432-2250 (Online) (doi:10.1007/s00162-026-00784-2)

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Abstract

We develop a model for steady, laminar boundary layers over small-scale textured surfaces. Although the texture is small relative to the boundary-layer thickness, it modifies the flow via a slip length. We use matched asymptotic expansions to simplify the problem, dividing the flow into outer, boundary-layer and inner regions. The far-field behaviour of the inner problem yields a slip boundary condition for the boundary layer. We derive an asymptotic solution valid when the slip length is small, and for arbitrary slip lengths, we develop a numerical method combining Chebyshev collocation and finite differences. We apply this framework to canonical small-scale textured surfaces, including superhydrophobic surfaces and riblets, and utilise existing analytical slip formulae. However, the framework is expected to extend to liquid-infused, porous, compliant or deformable surfaces with a variety of regular or random textures. We demonstrate how slip modifies the boundary layer’s velocity field, wall shear stress and displacement thickness across a range of surface configurations, and examine the linear stability of the resulting slip-modified boundary layers. Our approach enables computationally inexpensive modelling of a wide range of small-scale textured surfaces within laminar boundary-layer flows, providing predictive capability for drag, boundary-layer growth and transition across applications ranging from microfluidics to turbo-machinery and marine transport.

Item Type:	Article
Uncontrolled Keywords:	Laminar boundary layers, slip length, matched asymptotic expansions, superhydrophobic surfaces, riblets, drag reduction
Subjects:	Q Science > QA Mathematics > QA75 Electronic computers. Computer science
Faculty / School / Research Centre / Research Group:	Faculty of Engineering & Science Faculty of Engineering & Science > School of Computing & Mathematical Sciences (CMS)
Last Modified:	25 Aug 2026 16:14
URI:	https://gala.gre.ac.uk/id/eprint/54300

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