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

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

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

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

Smoke Testing for Machine Learning: Simple Tests to Discover Severe Defects

Machine learning is nowadays a standard technique for data analysis within software applications. Software engineers need quality assurance techniques that are suitable for these new kinds of systems. Within this article, we discuss the question whether standard software testing techniques that have been part of textbooks since decades are also useful for the testing of machine learning software. Concretely, we try to determine generic and simple smoke tests that can be used to assert that basic functions can be executed without crashing. We found that we can derive such tests using techniques similar to equivalence classes and boundary value analysis. Moreover, we found that these concepts can also be applied to hyperparameters, to further improve the quality of the smoke tests. Even though our approach is almost trivial, we were able to find bugs in all three machine learning libraries that we tested and severe bugs in two of the three libraries. This demonstrates that common software testing techniques are still valid in the age of machine learning and that considerations how they can be adapted to this new context can help to find and prevent severe bugs, even in mature machine learning libraries.Comment: Accepted at Empirical Software Engineering, Springe