134 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
The influence of incompressible surfactant on drag in flow along an array of gas-filled grooves
Surfactants can have a detrimental effect on the drag reduction in shear flow
over superhydrophobic surfaces in Cassie state. While surfactant-free
gas-liquid interfaces are often well approximated as shear-free, surfactants
can impede the flow by stacking up in front of obstacles. We study shear-flow
along an array of narrow gas-filled grooves of finite length embedded in an
otherwise planar surface, with the gas-liquid interface protruding slightly
above or below the plane. Assuming immiscible surfactants forming an
incompressible, inviscid surfactant phase at the gas-liquid interfaces we
employ a recently proposed model [Baier and Hardt, J.Fluid Mech., 949 (2022)]
for addressing this situation. Using a domain perturbation technique together
with the Lorentz reciprocal theorem we obtain the slip length characterizing
the flow over such surfaces to second order in the maximal interface deflection
as a small parameter. We find that within the range of moderate interface
deflections studied, the slip length for flow over such surfaces is negative
(positive) for surfaces protruding above (below) the surface and is much
smaller than for flow over a corresponding surfactant-free interface. Thus,
contrary to expectations of reduced drag in flow over superhydrophobic surfaces
in Cassie state, surfactant covered interfaces can even be detrimental for drag
reduction in the limit where surfactants act as an effectively incompressible
surface-fluid. This has important implications for the appropriate design of
superhydrophobic surfaces for reducing flow resistance.Comment: 14 pages, 4 figures; Revised versio
Thermocapillary Flow on Superhydrophobic Surfaces
A liquid in Cassie-Baxter state above a structured superhydrophobic surface
is ideally suited for surface driven transport due to its large free surface
fraction in close contact to a solid. We investigate thermal Marangoni flow
over a superhydrophobic array of fins oriented parallel or perpendicular to an
applied temperature gradient. In the Stokes limit we derive an analytical
expression for the bulk flow velocity above the surface and compare it with
numerical solutions of the Navier-Stokes equation. Even for moderate
temperature gradients comparatively large flow velocities are induced,
suggesting to utilize this principle for microfluidic pumping.Comment: 4 pages, 4 figure
Knudsen pump inspired by Crookes radiometer with a specular wall
A rarefied gas is considered in a channel consisting of two infinite parallel
plates between which an evenly spaced array of smaller plates is arranged
normal to the channel direction. Each of these smaller plates is assumed to
possess one ideally specularly reflective and one ideally diffusively
reflective side. When the temperature of the small plates differs from the
temperature of the sidewalls of the channel, these boundary conditions result
in a temperature profile around the edges of each small plate which breaks the
reflection symmetry along the channel direction. This in turn results in a
force on each plate and a net gas flow along the channel. The situation is
analysed numerically using the direct simulation Monte Carlo (DSMC) method and
compared with analytical results where available. The influence of the ideally
specularly reflective wall is assessed by comparing with simulations using a
finite accommodation coefficient at the corresponding wall. The configuration
bears some similarity with a Crookes radiometer, where a non-symmetric
temperature profile at the radiometer vanes is generated by different
temperatures on each side of the vane, resulting in a motion of the rotor. The
described principle may find applications in pumping gas on small scales driven
by temperature gradients
Sample dispersion in isotachophoresis with Poiseuille counterflow
A particular mode of isotachophoresis (ITP) employs a pressure-driven flow
opposite to the sample electromigration direction in order to anchor a sample
zone at a specific position along a channel or capillary. We investigate this
situation using a two-dimensional finite-volume model based on the
Nernst-Planck equation. The imposed Poiseuille flow profile leads to a
significant dispersion of the sample zone. This effect is detrimental for the
resolution in analytical applications of ITP. We investigate the impact of
convective dispersion, characterized by the area-averaged width of a sample
zone, for various values of the sample P\'{e}clet-number, as well as the
relative mobilities of the sample and the adjacent electrolytes. A
one-dimensional model for the area-averaged concentrations based on a
Taylor-Aris-type effective axial diffusivity is shown to yield good agreement
with the finite-volume calculations. This justifies the use of such simple
models and opens the door for the rapid simulation of ITP protocols with
Poiseuille counterflow
Page switching in mixed-device web surveys: prevalence and data quality
As a self-administered survey mode, web surveys allow respondents to temporarily leave the survey page and switch to another web page in a
different browser tab or to another window/app. This form of sequential multitasking has the potential to disrupt the response process and reduce
data quality if respondents become distracted (Krosnick, 1991; Sendelbah et al., 2016). Browser data indicating respondents leaving the survey
page allow non-reactive measurement of their multitasking. We investigated the prevalence of page switching, number of switching events and
time spent absent per event with respect to respondents’ characteristics and devices used. Furthermore, we analysed the association with data
quality (item missing, differentiation in grid questions and number of characters to open-ended questions). The results indicate that the
prevalence of page switching is relatively low and the durations of page switching events are rather short. Also, respondents using a PC/tablet are
more likely to leave the survey page than those using a smartphone. As to data quality, we did not find any correlation between page switching
and the quality of the answers. Thus, this study provides no evidence that multitasking poses a threat to data quality. The findings are discussed
with respect to the delimitations of multitasking using browser paradata
Shear flow over a surface containing a groove covered by an incompressible surfactant phase
We study shear-driven liquid flow over a planar surface with an embedded
gas-filled groove, with the gas-liquid interface protruding slightly above or
below the planar surface. The flow direction is along the groove, taken to be
much longer than wide, and the gas-liquid interface is assumed to be covered by
an incompressible surface fluid, representing a surfactant phase. Using the
incompressiblity condition for the surface fluid, the equations of motion and
corresponding boundary conditions for the liquid phase are obtained by
minimizing the dissipation rate. Assuming a moderate deformation of the
interface, a domain perturbation technique with the maximal deformation as
small parameter is employed. The Stokes equation in the liquid phase under
corresponding boundary conditions is solved to second order in the deformation
using the Keldysh-Sedov formalism. The obtained analytical results are compared
with numerical calculations of the same problem, allowing an assessment of the
limits of validity of the expansion. While on a planar gas-liquid interface no
flow is induced, a recirculating flow is observed on an interface protruding
slightly above or below the planar surface. The study sheds light onto the
mobility of curved gas-liquid interfaces in the presence of surfactants acting
as an incompressible surface fluid.Comment: 13 pages, 4 figure
Propulsion Mechanisms for Leidenfrost Solids on Ratchets
We propose a model for the propulsion of Leidenfrost solids on ratchets based
on viscous drag due to the flow of evaporating vapor. The model assumes
pressure-driven flow described by the Navier-Stokes equations and is mainly
studied in lubrication approximation. A scaling expression is derived for the
dependence of the propulsive force on geometric parameters of the ratchet
surface and properties of the sublimating solid. We show that the model results
as well as the scaling law compare favorably with experiments and are able to
reproduce the experimentally observed scaling with the size of the solid
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