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@article{Schnitzer:2019:10.1017/jfm.2019.177,
author = {Schnitzer, O and Yariv, E},
doi = {10.1017/jfm.2019.177},
journal = {Journal of Fluid Mechanics},
pages = {212--243},
title = {Stokes resistance of a solid cylinder near a superhydrophobic surface. Part 1. Grooves perpendicular to cylinder axis},
url = {http://dx.doi.org/10.1017/jfm.2019.177},
volume = {868},
year = {2019}
}

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TY  - JOUR
AB  - An  important  class  of  canonical  problems  which  is  employed  in  quantifying  the  slip-periness of microstructured superhydrophobic surfaces is concerned with the calculationof the hydrodynamic loads on adjacent solid bodies whose size is large relative to themicrostructure period. The effect of superhydophobicity is most pronounced when thelatter  period  is  comparable  with  the  separation  between  the  solid  probe  and  the  su-perhydrophobic surface. We address the above distinguished limit, considering a simpleconfiguration  where  the  superhydrophobic  surface  is  formed  by  a  periodically  groovedarray, in which air bubbles are trapped in a Cassie state, and the solid body is an in-finite cylinder. In the present Part, we consider the case where the grooves are alignedperpendicular to the cylinder and allow for three modes of rigid-body motion: rectilinearmotion  perpendicular  to  the  surface;  rectilinear  motion  parallel  to  the  surface,  in  thegrooves direction; and angular rotation about the cylinder axis. In this scenario, the flowis periodic in the direction parallel to the axis. Averaging over the small-scale periodicityyields a modified lubrication description where the small-scale details are encapsulatedin two auxiliary two-dimensional cell problems which respectively describe pressure- andboundary-driven longitudinal flow through an asymmetric rectangular domain, boundedby a compound surface from the bottom and a no-slip surface from the top. Once theintegral flux and averaged shear stress associated with each of these cell problems arecalculated  as  a  function  of  the  slowly  varying  cell  geometry,  the  hydrodynamic  loadsexperienced  by  the  cylinder  are  provided  as  quadratures  of  nonlinear  functions  of  thelatter distributions over a continuous sequence of cells.
AU  - Schnitzer,O
AU  - Yariv,E
DO  - 10.1017/jfm.2019.177
EP  - 243
PY  - 2019///
SN  - 0022-1120
SP  - 212
TI  - Stokes resistance of a solid cylinder near a superhydrophobic surface. Part 1. Grooves perpendicular to cylinder axis
T2  - Journal of Fluid Mechanics
UR  - http://dx.doi.org/10.1017/jfm.2019.177
UR  - http://hdl.handle.net/10044/1/68083
VL  - 868
ER  -

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