Longitudinal flow in superhydrophobic channels with partially invaded grooves

Miyoshi, Hiroyuki; Rodriguez-Broadbent, Henry; Curran, Anna; Crowdy, Darren

doi:10.1007/s10665-022-10240-9

Cited by 8 publications

(2 citation statements)

References 28 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The contact lines of the liquid-air menisci are displaced a finite distance a ( > 0) into the grooves. Following earlier analyses (Crowdy 2021;Miyoshi et al 2022), we assume that the slats are infinitely thin; then, represents the solid fraction of the microstructure. The curved menisci adopt a cross-sectional shape of a circular arc; we consider here the idealised scenario of a 90 • protrusion angle, whereby a coincides with the bubble radius.…”

Section: Problem Formulationmentioning

confidence: 99%

Highly singular slip length for longitudinal shear flow over a dense bubble mattress

Yariv

2023

J. Fluid Mech.

View full text Add to dashboard Cite

Compound surfaces, consisting of periodic arrays of solid patches and free surfaces, exhibit hydrodynamic slipperiness which is quantified by their slip length. The limit of small solid fractions, where the slip length diverges, is of fundamental interest. This paper addresses longitudinal liquid flows over a periodic array of grooves which are partially invaded by the liquid. Assuming that the slats separating the grooves are infinitely thin, the solid fraction $\epsilon$ is set by the invasion depth. Inspired by the singular small-solid-fraction limit for non-invaded grooves (Schnitzer, Phys. Rev. Fluids, vol. 1, 2016, 052101R), we consider the idealised geometry of $90^{\circ }$ protrusion angles, where an integral force balance in the limit $\epsilon \to 0$ implies a slip length that scales as $\epsilon ^{-1}$ . The problem exhibits a nested structure, where the liquid domain is conceptually decomposed into four distinct regions: a unit-cell region on the scale of the period, where the wetted portion of the slat appears as a point singularity; two regions on the scale of the wetted slat, where the flow essentially varies in one dimension; and a transition region about the tip of the slat. Analysing these regions using matched asymptotic expansions and conformal mappings yields the ratio of slip length to semi-period as $2\epsilon ^{-1} - (10/{\rm \pi} )\ln 2 + \cdots$ .

show abstract

Section: Problem Formulationmentioning

confidence: 99%

Highly singular slip length for longitudinal shear flow over a dense bubble mattress

Yariv

2023

J. Fluid Mech.

View full text Add to dashboard Cite

show abstract

“…This property has made spiky coatings an attractive candidate for many practical applications (e.g., drag reduction of ships and drones [11], improvement of propeller performance [12], micro-pump design [1,13]) and stimulated many experimental and theoretical studies [14][15][16][17][18][19][20][21][22][23][24][25]. This is an active area of research with extensive literature, see [8,9,[26][27][28][29][30][31], and references therein.…”

mentioning

confidence: 99%

Slip length for a viscous flow over spiky surfaces

Skvortsov,

Grebenkov,

Chan

et al. 2023

EPL

View full text Add to dashboard Cite

For a model of a 3D coating composed of a bi-periodic system of parallel riblets with gaps we analytically derive an approximate formula for the effective slip length (an offset from the flat surface at which the flow velocity would extrapolate to zero) as a function of the geometry of the system (riblet period, riblet height, and relative gap size). This formula is valid for an arbitrary fraction of gaps (i.e., from narrow riblets to narrow gaps) and agrees with the known analytical results for the 2D periodic coating of riblets without gaps. We validate our analytical results with the numerical solution of the equations of the viscous (creeping) flow over the riblets with gaps.

show abstract

Numerical validation of analytical formulas for channel flows over liquid-infused surfaces

Miyoshi,

Rodriguez-Broadbent,

Crowdy

2024

J Eng Math

View full text Add to dashboard Cite

This paper provides numerical validation of some new explicit, asymptotically exact, analytical formulas describing channel flows over liquid-infused surfaces, an important class of surfaces of current interest in surface engineering. The new asymptotic formulas, reproduced here, were derived in a recent companion paper by the authors. The numerical validation is done by presenting a novel computational method for calculating longitudinal flow in a periodic channel involving finite-length closed liquid-filled grooves with a flat two-fluid interface, a challenging problem given the two-fluid nature of the flow. The formulas are asymptotically exact for wide channels where the grooves on the lower wall of the channel are well separated; the numerical method devised here, however, is subject to no such restrictions. Significantly, it is shown here that the asymptotic formulas remain good global approximants for the flow over a wide range of flow geometries, including those well outside the asymptotic parameter range for which they were derived. It is found that the formulas are more reliable for liquid-infused surfaces than for superhydrophobic surfaces.

show abstract

Longitudinal flow in superhydrophobic channels with partially invaded grooves

Cited by 8 publications

References 28 publications

Highly singular slip length for longitudinal shear flow over a dense bubble mattress

Highly singular slip length for longitudinal shear flow over a dense bubble mattress

Slip length for a viscous flow over spiky surfaces

Numerical validation of analytical formulas for channel flows over liquid-infused surfaces

Contact Info

Product

Resources

About