17 research outputs found
Influence of the enclosed fluid on the flow over a microstructured surface in the Cassie state
Analytical expressions for the flow field as well as for the effective slip
length of a shear flow over a surface with periodic rectangular grooves are
derived. The primary fluid is in the Cassie state with the grooves being filled
with a secondary immiscible fluid. The coupling of both fluids is reflected in
a locally varying slip distribution along the fluid-fluid interface, which
models the effect of the secondary fluid on the outer flow. The obtained
closed-form analytical expressions for the flow field and effective slip length
of the primary fluid explicitly contain the influence of the viscosities of the
two fluids as well as the magnitude of the local slip, which is a function of
the surface geometry. They agree well with results from numerical computations
of the full geometry. The analytical expressions allow investigating the
influence of the viscous stresses inside the secondary fluid for arbitrary
geometries of the rectangular grooves. For classic superhydrophobic surfaces,
the deviations in the effective slip length compared to the case of inviscid
gas flow are are pointed out. Another important finding with respect to an
accurate modeling of flow over microstructured surfaces is that the local slip
length of a grooved surface is anisotropic.Comment: submitted to the Journal of Fluid Mechanic
Longitudinal and transversal flow over a cavity containing a second immiscible fluid
An analytical solution for the flow field of a shear flow over a rectangular
cavity containing a second immiscible fluid is derived. While flow of a
single-phase fluid over a cavity is a standard case investigated in fluid
dynamics, flow over a cavity which is filled with a second immiscible fluid,
has received little attention. The flow filed inside the cavity is considered
to define a boundary condition for the outer flow which takes the form of a
Navier slip condition with locally varying slip length. The slip-length
function is determined from the related problem of lid-driven cavity flow.
Based on the Stokes equations and complex analysis it is then possible to
derive a closed analytical expression for the flow field over the cavity for
both the transversal and the longitudinal case. The result is a comparatively
simple function, which displays the dependence of the flow field on the cavity
geometry and the medium filling the cavity. The analytically computed flow
field agrees well with results obtained from a numerical solution of the
Navier-Stokes equations. The studies presented in this article are of
considerable practical relevance, for example for the flow over
superhydrophobic surfaces.Comment: http://journals.cambridge.or
Rotation of an immersed cylinder sliding near a thin elastic coating
It is known that an object translating parallel to a soft wall in a viscous
fluid produces hydro- dynamic stresses that deform the wall, which, in turn,
results in a lift force on the object. Recent experiments with cylinders
sliding under gravity near a soft incline, which confirmed theoretical
arguments for the lift force, also reported an unexplained steady-state
rotation of the cylinders [Saintyves et al. PNAS 113(21), 2016]. Motivated by
these observations, we show, in the lubrication limit, that an infinite
cylinder that translates in a viscous fluid parallel to a soft wall at constant
speed and separation distance must also rotate in order to remain free of
torque. Using the Lorentz reciprocal theorem, we show analytically that for
small deformations of the elastic layer, the angular velocity of the cylinder
scales with the cube of the sliding speed. These predictions are confirmed
numerically. We then apply the theory to the gravity-driven motion of a
cylinder near a soft incline and find qualitative agreement with the
experimental observations, namely that a softer elastic layer results in a
greater angular speed of the cylinder.Comment: 16 pages, 4 figure
Axisymmetric Stokes flow due to a point-force singularity acting between two coaxially positioned rigid no-slip disks
We investigate theoretically on the basis of the steady Stokes equations for
a viscous incompressible fluid the flow induced by a Stokeslet located on the
centre axis of two coaxially positioned rigid disks. The Stokeslet is directed
along the centre axis. No-slip boundary conditions are assumed to hold at the
surfaces of the disks. We perform the calculation of the associated Green's
function in large parts analytically, reducing the spatial evaluation of the
flow field to one-dimensional integrations amenable to numerical treatment. To
this end, we formulate the solution of the hydrodynamic problem for the viscous
flow surrounding the two disks as a mixed-boundary-value problem, which we then
reduce into a system of four dual integral equations. We show the existence of
viscous toroidal eddies arising in the fluid domain bounded by the two disks,
manifested in the plane containing the centre axis through adjacent
counterrotating eddies. Additionally, we probe the effect of the confining
disks on the slow dynamics of a point-like particle by evaluating the
hydrodynamic mobility function associated with axial motion. Thereupon, we
assess the appropriateness of the commonly-employed superposition approximation
and discuss its validity and applicability as a function of the geometrical
properties of the system. Additionally, we complement our semi-analytical
approach by finite-element computer simulations, which reveals a good
agreement. Our results may find applications in guiding the design of
microparticle-based sensing devices and electrokinetic transport in small scale
capacitors
The flow of a fluid in Cassie state along a patterned surface and its effective slip length
Spreading dynamics on lithium niobate: An example of an intrinsically charged ferroelectric surface
Droplet wetting and manipulation are essential for the efficient functioning of many applications, ranging from microfluidic applications to electronic devices, agriculture, medical diagnosis, etc. As a means of manipulating droplet wetting, the effect of applying an external voltage or surface charge has been extensively exploited and is known as electrowetting. However, there also exist many materials which bear a quasi-permanent surface charge, like electrets, which are widely employed in sensors or energy storage. In addition, other materials in nature can acquire surface charge by the triboelectric effect, like human hair, natural rubber, and polymers. Nevertheless, there do not exist any studies on spreading on this class of charged surfaces. In our work, we for the first time investigate spreading dynamics on lithium niobate (LiNbO3) as an example of a ferroelectric material with strong instantaneous polarization (0.7C/m2). We find a spreading behavior that significantly differs from classic surfaces. Spreading times can be significantly enlarged compared to standard surfaces, up to hundreds of seconds. Furthermore, the classic Tanner’s law does not describe the spreading dynamics. Instead, the evolution of the droplet radius is dominated by an exponential law. Contact angles and spreading dynamics are also polarization-dependent. They are also influenced by adsorption layers, such as they are left behind by cleaning. Overall, all results indicate that adsorption layers play a significant role in the wetting dynamics of lithium niobate and possibly other charged materials, where such processes are very pronounced. Possible mechanisms are discussed. Our findings are essential for the understanding of wetting on charged surfaces like ferroelectric materials in general. The knowledge of surface charge-based wettability difference, surface charge specific adsorption and its impact on wettability can be utilized in applications like, printing, microfluidics, triboelectric nanogenerators, and to develop biocompatible components for tissue engineering