1,934 research outputs found
'Gas cushion' model and hydrodynamic boundary conditions for superhydrophobic textures
Superhydrophobic Cassie textures with trapped gas bubbles reduce drag, by
generating large effective slip, which is important for a variety of
applications that involve a manipulation of liquids at the small scale. Here we
discuss how the dissipation in the gas phase of textures modifies their
friction properties. We propose an operator method, which allows us the mapping
of the flow in the gas subphase to a local slip boundary condition at the
liquid/gas interface. The determined uniquely local slip length depends on the
viscosity contrast and underlying topography, and can be immediately used to
evaluate an effective slip of the texture. Besides superlubricating Cassie
surfaces our approach is valid for rough surfaces impregnated by a
low-viscosity 'lubricant', and even for Wenzel textures, where a liquid follows
the surface relief. These results provide a framework for the rational design
of textured surfaces for numerous applications.Comment: 8 pages, 6 figure
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 (texture characteristic length), and (local slip
lengths at solid and gas areas), and and (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 (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, , and , 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 ) 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.Comment: 9 pages, 5 figures, submitted to PRE; EPAPS file include
Flow past superhydrophobic surfaces with cosine variation in local slip length
Anisotropic super-hydrophobic surfaces have the potential to greatly reduce
drag and enhance mixing phenomena in microfluidic devices. Recent work has
focused mostly on cases of super-hydrophobic stripes. Here, we analyze a
relevant situation of cosine variation of the local slip length. We derive
approximate formulae for maximal (longitudinal) and minimal (transverse)
directional effective slip lengths that are in good agreement with the exact
numerical solution and lattice-Bolzmann simulations for any surface slip
fraction. The cosine texture can provide a very large effective (forward) slip,
but it was found to be less efficient in generating a transverse flow as
compared to super-hydrophobic stripes.Comment: 8 pages, 6 figure
Effective slip boundary conditions for arbitrary one-dimensional surfaces
In many applications it is advantageous to construct effective slip boundary
conditions, which could fully characterize flow over patterned surfaces. Here
we focus on laminar shear flows over smooth anisotropic surfaces with arbitrary
scalar slip , varying in only one direction. We derive general
expressions for eigenvalues of the effective slip-length tensor, and show that
the transverse component is equal to a half of the longitudinal one with twice
larger local slip, . A remarkable corollary of this relation is that the
flow along any direction of the 1D surface can be easily determined, once the
longitudinal component of the effective slip tensor is found from the known
spatially nonuniform scalar slip.Comment: 10 pages, 2 figures, submitted to J. Fluid Mec
Ferrofluid Valve Operated By the Magnetic Field of a Straight Current-carrying Wire
Integrated valves produce increased control and make up an essential part of different devices, especially in microfluidics. The use of ferrofluid in valves is one of actuation methods. Different magnetic fields could be used to operate a ferrofluid valve. In the present paper, we propose to use the magnetic field created by a straight current-carrying wire to operate a ferrofluid valve which can open the channel formed by two coaxial cones and a cylinder. Numerical modelling of the valve behaviour for different values of ferrofluid volumes and currents in the wire is done for two cases: when the ferrofluid wets and does not wet surrounding solid boundaries. It is shown that the presence of limiting cones allows the ferrofluid to sustain the pressure drop which is much bigger in case of non-wetting than in case of wetting. In case of wetting the ferrofluid cannot sustain any pressure drop at small currents, but in case of non-wetting the ferrofluid can do it even at zero current. It is found that in case of non-wetting spasmodic and hysteresis phenomena are possible for some values of ferrofluid volumes and currents in the wire
Effective slip-length tensor for a flow over weakly slipping stripes
We discuss the flow past a flat heterogeneous solid surface decorated by
slipping stripes. The spatially varying slip length, , is assumed to be
small compared to the scale of the heterogeneities, , but finite. For such
"weakly" slipping surfaces, earlier analyses have predicted that the effective
slip length is simply given by the surface-averaged slip length, which implies
that the effective slip-length tensor becomes isotropic. Here we show that a
different scenario is expected if the local slip length has step-like jumps at
the edges of slipping heterogeneities. In this case, the next-to-leading term
in an expansion of the effective slip-length tensor in powers of
becomes comparable to the leading-order term, but
anisotropic, even at very small . This leads to an anisotropy of the
effective slip, and to its significant reduction compared to the
surface-averaged value. The asymptotic formulae are tested by numerical
solutions and are in agreement with results of dissipative particle dynamics
simulations.Comment: 11 pages, 4 figures, submitted to Phys. Rev.
Effective hydrodynamic boundary conditions for microtextured surfaces
We report measurements of the hydrodynamic drag force acting on a smooth
sphere falling down under gravity to a plane decorated with microscopic
periodic grooves. Both surfaces are lyophilic, so that a liquid (silicone oil)
invades the surface texture being in the Wenzel state. A significant decrease
in the hydrodynamic resistance force as compared with that predicted for two
smooth surfaces is observed. To quantify the effect of roughness we use the
effective no-slip boundary condition, which is applied at the imaginary smooth
homogeneous isotropic surface located at an intermediate position between top
and bottom of grooves. Such an effective condition fully characterizes the
force reduction measured with the real surface, and the location of this
effective plane is related to geometric parameters of the texture by a simple
analytical formula.Comment: 4 pages, submitted to Phys. Rev.
Effective slippage on superhydrophobic trapezoidal grooves
We study the effective slippage on superhydrophobic grooves with trapezoidal
cross-sections of various geometries (including the limiting cases of triangles
and rectangular stripes), by using two complementary approaches. First,
dissipative particle dynamics (DPD) simulations of a flow past such surfaces
have been performed to validate an expression [E.S.Asmolov and O.I.Vinogradova,
J. Fluid Mech. \textbf{706}, 108 (2012)] that relates the eigenvalues of the
effective slip-length tensor for one-dimensional textures. Second, we propose
theoretical estimates for the effective slip length and calculate it
numerically by solving the Stokes equation based on a collocation method. The
comparison between the two approaches shows that they are in excellent
agreement. Our results demonstrate that the effective slippage depends strongly
on the area-averaged slip, the amplitude of the roughness, and on the fraction
of solid in contact with the liquid. To interpret these results, we analyze
flow singularities near slipping heterogeneities, and demonstrate that they
inhibit the effective slip and enhance the anisotropy of the flow. Finally, we
propose some guidelines to design optimal one-dimensional superhydrophobic
surfaces, motivated by potential applications in microfluidics.Comment: 11 pages, 8 figures, submitted to J. Chem. Phy
- …