On the influence of wavy riblets on the slip behaviour of viscous fluids

Bonnivard, Matthieu; Suárez‐Grau, Francisco J.; Tierra, Giordano

doi:10.1007/s00033-015-0614-y

Cited by 7 publications

(2 citation statements)

References 23 publications

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“…At the bottom we consider a surface covered by periodically distributed riblets with low amplitude, associated with a small parameter 𝜀, where 𝜀 𝛿 is the amplitude and 𝜀 ℓ is the period, where 𝛿 > ℓ > 1. This type of rough surface has been treated in [17,24,64,65] for fluid flows with Navier slip boundary conditions.…”

Section: Introductionmentioning

confidence: 99%

A generalized Reynolds equation for micropolar flows past a ribbed surface with nonzero boundary conditions

2022

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Inspired by the lubrication framework, in this paper we consider a micropolar fluid flow through a rough thin domain, whose thickness is considered as the small parameter ε while the roughness at the bottom is defined by a periodical function with period of order εℓ and amplitude εδ, with δ> ℓ >1. Assuming nonzero boundary conditions on the rough bottom and by means of a version of the unfolding method, we identify a critical case δ = 3/2ℓ − 1/2 and obtain three macroscopic models coupling the effects of the rough bottom and the nonzero boundary conditions. In every case we provide the corresponding micropolar Reynolds equation. We apply these results to carry out a numerical study of a model of squeeze-film bearing lubricated with a micropolar fluid. Our simulations reveal the impact of the roughness coupled with the nonzero boundary conditions on the performance of the bearing, and suggest that the introduction of a rough geometry may contribute to enhancing the mechanical properties of the device.

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Section: Introductionmentioning

confidence: 99%

A generalized Reynolds equation for micropolar flows past a ribbed surface with nonzero boundary conditions

2022

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“…when it has rows of riblets, pillars or periodic patterns, the effective slip condition is anisotropic, i.e., direction-dependent. Examples of flows over such surfaces have been studied by analytical and numerical methods [16,17,18,19]. However, these studies only consider flows in the directions perpendicular to and parallel to the rows of riblets.…”

Section: Introductionmentioning

confidence: 99%