Sliding Drops: Ensemble Statistics from Single Drop Bifurcations

Ensembles of interacting drops that slide down an inclined plate show a dramatically different coarsening behavior as compared to drops on a horizontal plate: As drops of different size slide at different velocities, frequent collisions result in fast coalescence. However, above a certain size individual sliding drops are unstable and break up into smaller drops. Therefore, the long-time dynamics of a large drop ensemble is governed by a balance of merging and splitting. We employ a long-wave film height evolution equation and determine the dynamics of the drop size distribution towards a stationary state from direct numerical simulations on large domains. The main features of the distribution are then related to the bifurcation diagram of individual drops obtained by numerical path continuation. The gained knowledge allows us to develop a Smoluchowski-type statistical model for the ensemble dynamics that well compares to full direct simulations.

Dip-coating with prestructured substrates: transfer of simple liquids and Langmuir-Blodgett monolayers

When a plate is withdrawn from a liquid bath, either a static meniscus forms in the transition region between the bath and the substrate or a liquid film of finite thickness (a Landau-Levich film) is transferred onto the moving substrate. If the substrate is inhomogeneous, e.g. has a prestructure consisting of stripes of different wettabilities, the meniscus can be deformed or show a complex dynamic behavior. Here we study the free surface shape and dynamics of a dragged meniscus occurring for striped prestructures with two orientations, parallel and perpendicular to the transfer direction. A thin film model is employed that accounts for capillarity through a Laplace pressure and for the spatially varying wettability through a Derjaguin (or disjoining) pressure. Numerical continuation is used to obtain steady free surface profiles and corresponding bifurcation diagrams in the case of substrates with different homogeneous wettabilities. Direct numerical simulations are employed in the case of the various striped prestructures. The final part illustrates the importance of our findings for particular applications that involve complex liquids by modeling a Langmuir-Blodgett transfer experiment. There, one transfers a monolayer of an insoluble surfactant that covers the surface of the bath onto the moving substrate. The resulting pattern formation phenomena can be crucially influenced by the hydrodynamics of the liquid meniscus that itself depends on the prestructure on the substrate. In particular, we show how prestructure stripes parallel to the transfer direction lead to the formation of bent stripes in the surfactant coverage after transfer and present similar experimental results.

Locking of periodic patterns in Cahn-Hilliard models for Langmuir-Blodgett transfer

The influence of a periodic spatial forcing on the pattern formation in a generalized Cahn-Hilliard model describing Langmuir-Blodgett transfer is studied. The occurring locking effects enable a control mechanism for the pattern formation process. In the one-dimensional case the parameter range in which patterns are created is increased and the patterns' properties can be adjusted in a broader range. In two dimensions, one-dimensional stripe patterns can be destabilized, giving rise to a multitude of complex two-dimensional structures, including oblique and lattice patterns.

Nonuniversal power-law spectra in turbulent systems

Turbulence is generally associated with universal power-law spectra in scale ranges without significant drive or damping. Although many examples of turbulent systems do not exhibit such an inertial range, power-law spectra may still be observed. As a simple model for such situations, a modified version of the Kuramoto-Sivashinsky equation is studied. By means of semianalytical and numerical studies, one finds power laws with nonuniversal exponents in the spectral range for which the ratio of nonlinear and linear time scales is (roughly) scale independent.

Dissipation layers in Rayleigh-Bénard convection: a unifying view

Boundary layers play an important role in controlling convective heat transfer. Their nature varies considerably between different application areas characterized by different boundary conditions, which hampers a uniform treatment. Here, we argue that, independent of boundary conditions, systematic dissipation measurements in Rayleigh-Bénard convection capture the relevant near-wall structures. By means of direct numerical simulations with varying Prandtl numbers, we demonstrate that such dissipation layers share central characteristics with classical boundary layers, but, in contrast to the latter, can be extended naturally to arbitrary boundary conditions. We validate our approach by explaining differences in scaling behavior observed for no-slip and stress-free boundaries, thus paving the way to an extension of scaling theories developed for laboratory convection to a broad class of natural systems.

Wave-number-frequency spectrum for turbulence from a random sweeping hypothesis with mean flow

We derive the energy spectrum in wave-number-frequency space for turbulent flows based on Kraichnan's idealized random sweeping hypothesis with additional mean flow, which yields the instantaneous energy spectrum multiplied by a Gaussian frequency distribution. The model spectrum has two adjustable parameters, the mean flow velocity and the sweeping velocity, and has the property that the power-law index of the wave-number spectrum translates to the frequency spectrum, invariant for arbitrary choices of the mean velocity and sweeping velocity. The model spectrum incorporates both Taylor's frozen-in flow approximation and the random sweeping approximation in a natural way and can be used to distinguish between these two effects when applied to real time-resolved multipoint turbulence data. Evaluated in real space, its properties with respect to space-time velocity correlations are discussed, and a comparison to the recently introduced elliptic model is drawn.

Statistical analysis of global wind dynamics in vigorous Rayleigh-Bénard convection

Experimental and numerical studies of thermal convection have shown that sufficiently vigorous convective flows exhibit a large-scale thermal wind component sweeping along small-scale thermal boundary layer instabilities. A characteristic feature of these flows is an intermittent behavior in the form of irregular reversals in the orientation of the large-scale circulation. There have been several attempts toward a better understanding and description of the phenomenon of flow reversals, but so far most of these models are based on a statistical analysis of few-point measurements or on simplified theoretical assumptions. The analysis of long-term data sets (>5×10(5) turnover times τ(t)=d/u(rms)) obtained by numerical simulations of turbulent two-dimensional Rayleigh-Bénard convection allows us to get a more comprehensive view of the spatio-temporal flow behavior. By means of a global statistical analysis of the characteristic spatial modes of the flow we extract information about the stability of dominant large-scale modes as well as the reversal paths in state subspace. We examine probability density functions and drift vector fields of two-dimensional state subspaces spanned by different large-scale spatial modes. This also provides information about the coexistence of dominant modes.

Lagrangian particle statistics in turbulent flows from a simple vortex model

The statistics of Lagrangian particles in turbulent flows is considered in the framework of a simple vortex model. Here, the turbulent velocity field is represented by a temporal sequence of Burgers vortices of different circulation, strain, and orientation. Based on suitable assumptions about the vortices' statistical properties, the statistics of the velocity increments is derived. In particular, the origin and nature of small-scale intermittency in this model is investigated both numerically and analytically. We critically compare our results to experimental studies.

Lassa fever encephalopathy: Lassa virus in cerebrospinal fluid but not in serum

The pathogenesis of neurologic complications of Lassa fever is poorly understood. A Nigerian patient had fever, disorientation, seizures, and blood-brain barrier dysfunction, and Lassa virus was found in cerebrospinal fluid (CSF) but not in serum. The concentration of Lassa virus RNA in CSF corresponded to 1 x 10(3) pfu/mL, as determined by a quantitative real-time polymerase chain reaction assay. To characterize the Lassa virus in CSF, the 3.5-kb S RNA was sequenced. In the S RNA coding sequences, the CSF strain differed between 20% and 24.6% from all known prototype strains. These data suggest that Lassa virus or specific Lassa virus strains can persist in the central nervous system and thus contribute to neuropathogenesis. Lassa virus infection should be considered in West African patients or in travelers returning from this area who present only with fever and neurologic signs.

Paramecium--a model system for studying cellular graviperception

Experiments under varied gravitational accelerations as well as in density-adjusted media showed that sensation of gravity in protists may be linked to the known principles of mechanosensation. Paramecium, a ciliate with clear graviresponses (gravitaxis and gravikinesis) is an ideal model system to prove this hypothesis since the ciliary activity and thus the swimming behaviour is controlled by the membrane potential. It has also been assumed that the cytoplasmic mass causes a distinct stimulation of the bipolarly distributed mechano-sensitive K+ and Ca2+ ion channels in the plasma membrane in dependence of the spatial orientation of the cell. In order to prove this hypothesis, different channel blockers are currently under investigation. Gadolinium did not inhibit gravitaxis in Paramecium, showing that it does not specifically block gravireceptors. Further studies concentrated on the question of whether second messengers are involved in the gravity signal transduction chain. Exposure to 5 g for up to 10 min led to a significant increase in cAMP.