Geometric transition in friction for flow over a bubble mattress

By Anthony M. J. Davis, Eric Lauga. 2008

184 citations recorded by the source corpus.

Laminar flow over a bubble mattress is expected to experience a significant reduction in friction since the individual surfaces of the bubbles are shear-free. However, if the bubbles are sufficiently curved, their protrusion into the fluid and along the flow direction can lead to an increase in friction as was recently demonstrated experimentally and computationally. We provide in this paper a simple model for this result. We consider a shear flow at low Reynolds number past a two-dimensional array of bubbles and calculate analytically the effective slip length of the surface as a function of the bubble geometry in the dilute limit. Our model is able to reproduce quantitatively the relationship between effective friction and bubble geometry obtained in numerical computations and, in particular, (a) the asymmetry in friction between convex and concave bubbles and (b) the existence of a geometric transition from reduced to enhanced friction at a critical bubble protrusion angle.

Subfields: Computational Mechanics, Surfaces, Coatings and Films

View Paper: https://www.semanticscholar.org/paper/5a7e4eb652d2120043a51cc148717fe285f2a798

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In Computational Mechanics

In Surfaces, Coatings and Films

Citations in the corpus

On the mechanism of turbulent drag reduction with super-hydrophobic surfaces (2015, background): “The magnitude of DR or DI is dependent upon the meniscus shape, its protrusion angle, the SH surface micro-pattern, and the flow regime (Steinberger et al. 2007; Davis & Lauga 2009; Rothstein 2010; Karatay et al. 2013).”
Superhydrophobic drag reduction in laminar flows: a critical review (2016, methodology): “In Exp Fluids (2016) 57:176 1 3 Page 11 of 20 176 agreement with their numerical simulation as well as the theoretical prediction by Davis and Lauga (2009b), their measured slip lengths (1–5 µm) decreased rapidly when the protrusion angle increased beyond 10°.”
Effective slip in pressure-driven flow past super-hydrophobic stripes (2009, background): “One reason is the possible meniscus curvature, which has been clarified in some recent works (Sbragaglia & Prosperetti 2007; Hyväluoma & Harting 2008; Davis & Lauga 2009) and another reason is viscous dissipation taking place in the underlying gas phase.”
Influence of the enclosed fluid on the flow over a microstructured surface in the Cassie state (2013, methodology): “Although such a fluid is obviously non-existent, this assumption has been widely used in the modelling of water–air interfaces, for instance at superhydrophobic surfaces (Lauga & Stone 2003; Sbragaglia & Prosperetti 2007b; Davis & Lauga 2009; Crowdy 2010; Davis & Lauga 2010).”