392 research outputs found
Hydrodynamic friction of fakir-like super-hydrophobic surfaces
A fluid droplet located on a super-hydrophobic surface makes contact with the
surface only at small isolated regions, and is mostly in contact with the
surrounding air. As a result, a fluid in motion near such a surface experiences
very low friction, and super-hydrophobic surfaces display strong drag-reduction
in the laminar regime. Here we consider theoretically a super-hydrophobic
surface composed of circular posts (so called fakir geometry) located on a
planar rectangular lattice. Using a superposition of point forces with suitably
spatially-dependent strength, we derive the effective surface slip length for a
planar shear flow on such a fakir surface as the solution to an infinite series
of linear equations. In the asymptotic limit of small surface coverage by the
posts, the series can be interpreted as Riemann sums, and the slip length can
be obtained analytically. For posts on a square lattice, our analytical results
are in excellent quantitative agreement with previous numerical computations
Effective velocity boundary condition at a mixed slip surface
This paper studies the nature of the effective velocity boundary conditions
for liquid flow over a plane boundary on which small free-slip islands are
randomly distributed. It is found that, to lowest order in the area fraction
covered by free-slip regions with characteristic size , a
macroscopic Navier-type slip condition emerges with a slip length of the order
of . The study is motivated by recent experiments which suggest that
gas nano-bubbles may form on solid walls and may be responsible for the
appearance of a partial slip boundary conditions for liquid flow. The results
are also relevant for ultra-hydrophobic surfaces exploiting the so-called
``lotus effect''.Comment: 14 pages, 1 figur
Electro-osmosis on anisotropic super-hydrophobic surfaces
We give a general theoretical description of electro-osmotic flow at striped
super-hydrophobic surfaces in a thin double layer limit, and derive a relation
between the electro-osmotic mobility and hydrodynamic slip-length tensors. Our
analysis demonstrates that electro-osmotic flow shows a very rich behavior
controlled by slip length and charge at the gas sectors. In case of uncharged
liquid-gas interface, the flow is the same or inhibited relative to flow in
homogeneous channel with zero interfacial slip. By contrast, it can be
amplified by several orders of magnitude provided slip regions are uniformly
charged. When gas and solid regions are oppositely charged, we predict a flow
reversal, which suggests a possibility of huge electro-osmotic slip even for
electro-neutral surfaces. On the basis of these observations we suggest
strategies for practical microfluidic mixing devices. These results provide a
framework for the rational design of super-hydrophobic surfaces.Comment: 4 pages, 4 figures; submitted to PRL Revised version: several
references added, typos corrected. Supplementary file was restructured, the
second part of the original EPAPS was removed and is supposed to be published
as a separate pape
Enhanced diffusion by reciprocal swimming
Purcell's scallop theorem states that swimmers deforming their shapes in a
time-reversible manner ("reciprocal" motion) cannot swim. Using numerical
simulations and theoretical calculations we show here that in a fluctuating
environment, reciprocal swimmers undergo, on time scales larger than that of
their rotational diffusion, diffusive dynamics with enhanced diffusivities,
possibly by orders of magnitude, above normal translational diffusion.
Reciprocal actuation does therefore lead to a significant advantage over
non-motile behavior for small organisms such as marine bacteria
Statics and dynamics of a cylindrical droplet under an external body force
We study the rolling and sliding motion of droplets on a corrugated substrate
by Molecular Dynamics simulations. Droplets are driven by an external body
force (gravity) and we investigate the velocity profile and dissipation
mechanisms in the steady state. The cylindrical geometry allows us to consider
a large range of droplet sizes. The velocity of small droplets with a large
contact angle is dominated by the friction at the substrate and the velocity of
the center of mass scales like the square root of the droplet size. For large
droplets or small contact angles, however, viscous dissipation of the flow
inside the volume of the droplet dictates the center of mass velocity that
scales linearly with the size. We derive a simple analytical description
predicting the dependence of the center of mass velocity on droplet size and
the slip length at the substrate. In the limit of vanishing droplet velocity we
quantitatively compare our simulation results to the predictions and good
agreement without adjustable parameters is found.Comment: Submitted to the Journal of Chemical Physic
Gas Enrichment at Liquid-Wall Interfaces
Molecular dynamics simulations of Lennard-Jones systems are performed to
study the effects of dissolved gas on liquid-wall and liquid-gas interfaces.
Gas enrichment at walls is observed which for hydrophobic walls can exceed more
than two orders of magnitude when compared to the gas density in the bulk
liquid. As a consequence, the liquid structure close to the wall is
considerably modified, leading to an enhanced wall slip. At liquid-gas
interfaces gas enrichment is found which reduces the surface tension.Comment: main changes compared to version 1: flow simulations are included as
well as different types of gase
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