Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Drag force on a sphere moving towards an anisotropic super-hydrophobic
  plane   We analyze theoretically a high-speed drainage of liquid films squeezed
between a hydrophilic sphere and a textured super-hydrophobic plane, that
contains trapped gas bubbles. A super-hydrophobic wall is characterized by
parameters $L$ (texture characteristic length), $b_1$ and $b_2$ (local slip
lengths at solid and gas areas), and $\phi_1$ and $\phi_2$ (fractions of solid
and gas areas). Hydrodynamic properties of the plane are fully expressed in
terms of the effective slip-length tensor with eigenvalues that depend on
texture parameters and $H$ (local separation). The effect of effective slip is
predicted to decrease the force as compared with expected for two hydrophilic
surfaces and described by the Taylor equation. The presence of additional
length scales, $L$, $b_1$ and $b_2$, implies that a film drainage can be much
richer than in case of a sphere moving towards a hydrophilic plane. For a large
(compared to $L$) gap the reduction of the force is small, and for all textures
the force is similar to expected when a sphere is moving towards a smooth
hydrophilic plane that is shifted down from the super-hydrophobic wall. The
value of this shift is equal to the average of the eigenvalues of the
slip-length tensor. By analyzing striped super-hydrophobic surfaces, we then
compute the correction to the Taylor equation for an arbitrary gap. We show
that at thinner gap the force reduction becomes more pronounced, and that it
depends strongly on the fraction of the gas area and local slip lengths. For
small separations we derive an exact equation, which relates a correction for
effective slip to texture parameters. Our analysis provides a framework for
interpreting recent force measurements in the presence of super-hydrophobic
surface.

26
The categories of this paper are: bayes-an
31
The categories of this paper are: ao-sci
5
The categories of this paper are: gr-qc
30
The categories of this paper are: q-alg
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The categories of this paper are: adap-org
11
The categories of this paper are: hep-lat
28
The categories of this paper are: alg-geom
13
The categories of this paper are: quant-ph
1
The categories of this paper are: cs
29
The categories of this paper are: funct-an
23
The categories of this paper are: solv-int
0
The categories of this paper are: hep-ph
10
The categories of this paper are: q-bio
9
The categories of this paper are: nlin
14
The categories of this paper are: math-ph
22
The categories of this paper are: chao-dyn