Imperial College London
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DrOrySchnitzer

Faculty of Natural Sciences, Department of Mathematics

Reader in Applied Mathematics
 
 
 
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Contact

 

+44 (0)20 7594 3833o.schnitzer Website

 
 
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Location

 

739Huxley BuildingSouth Kensington Campus

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Summary

 

Publications

Citation

BibTex format

@article{Schnitzer:2016:10.1103/PhysRevFluids.1.052101,
author = {Schnitzer, O},
doi = {10.1103/PhysRevFluids.1.052101},
journal = {Physical Review Fluids},
title = {Singular effective slip length for longitudinal flow over a dense bubble mattress},
url = {http://dx.doi.org/10.1103/PhysRevFluids.1.052101},
volume = {1},
year = {2016}
}
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RIS format (EndNote, RefMan)

TY  - JOUR
AB  - We consider the effective hydrophobicity of a periodically grooved surface immersed in liquid,with trapped shear-free bubbles protruding between the no-slip ridges at a π/2 contact angle.Specifically, we carry out a singular-perturbation analysis in the limit   1 where the bubbles areclosely spaced, finding the effective slip length (normalised by the bubble radius) for longitudinalflow along the the ridges as π/√2 − (12/π) ln 2 + (13π/24)√2 + o(√), the small parameter being the planform solid fraction. The square-root divergence highlights the strong hydrophobiccharacter of this configuration; this leading singular term (along with the third term) follows froma local lubrication-like analysis of the gap regions between the bubbles, together with generalmatching considerations and a global conservation relation. The O(1) constant term is found bymatching with a leading-order solution in the “outer” region, where the bubbles appear to betouching. We find excellent agreement between our slip-length formula and a numerical schemerecently derived using a “unified-transform” method (D. Crowdy, IMA J. Appl. Math., 80 1902,2015). The comparison demonstrates that our asymptotic formula, together with the diametric“dilute-limit” approximation (D. Crowdy, J. Fluid Mech., 791 R7, 2016), provides an elementaryanalytical description for essentially arbitrary no-slip fractions.
AU  - Schnitzer,O
DO  - 10.1103/PhysRevFluids.1.052101
PY  - 2016///
SN  - 2469-990X
TI  - Singular effective slip length for longitudinal flow over a dense bubble mattress
T2  - Physical Review Fluids
UR  - http://dx.doi.org/10.1103/PhysRevFluids.1.052101
UR  - http://hdl.handle.net/10044/1/39554
VL  - 1
ER  -
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