The role of inertia for the rotation of a nearly spherical particle in a general linear flow

We analyse the angular dynamics of a neutrally buoyant nearly spherical particle immersed in a steady general linear flow. The hydrodynamic torque acting on the particle is obtained by means of a reciprocal theorem, regular perturbation theory exploiting the small eccentricity of the nearly spherical particle, and assuming that inertial effects are small, but finite.Comment: 7 pages, 1 figur

Elastic instability in stratified core annular flow

We study experimentally the interfacial instability between a layer of dilute polymer solution and water flowing in a thin capillary. The use of microfluidic devices allows us to observe and quantify in great detail the features of the flow. At low velocities, the flow takes the form of a straight jet, while at high velocities, steady or advected wavy jets are produced. We demonstrate that the transition between these flow regimes is purely elastic -- it is caused by viscoelasticity of the polymer solution only. The linear stability analysis of the flow in the short-wave approximation captures quantitatively the flow diagram. Surprisingly, unstable flows are observed for strong velocities, whereas convected flows are observed for low velocities. We demonstrate that this instability can be used to measure rheological properties of dilute polymer solutions that are difficult to assess otherwise.Comment: 4 pages, 4 figure

Stress balance in nano-patterned N/Cu(001) surfaces

We employ helium atom scattering (HAS) and density functional theory (DFT) based on the ultrasoft pseudopotential scheme and the plane-wave basis set to investigate the strain and stress balance in nano-patterned N/Cu(001) surfaces. HAS shows that, with increasing N coverage (and decreasing stripe widths), the stress-relief-driven lateral expansion of the averaged lattice parameter within finite-sized N-containing patches reduces from 3.5% to 1.8% and that, beyond a critical exposure, the lateral expansion of the patches increases again slightly, to 2.4%. The latter implies that in this higher coverage range the compressive stress is partially relieved via another mechanism, which turns out to be nucleation of Cu-vacancy trenches. In full agreement with the above and previous experimental observations, DFT calculations show that an optimized N-induced c(2\times2) structure has a net surface stress level of 4.2 N/m and such stress is effectively relieved when stripes of clean Cu(001) form along the direction or when trench-like steps of Cu atoms form along the direction. Additionally, the calculations demonstrate that (contrary to earlier suggestions) rumpling displacements within the outermost Cu layer do not act to relieve the compressive surface stress levels and that, while clock-like displacements could relieve stress levels, such displacements are energetically unstable

A new model for simulating colloidal dynamics

We present a new hybrid lattice-Boltzmann and Langevin molecular dynamics scheme for simulating the dynamics of suspensions of spherical colloidal particles. The solvent is modeled on the level of the lattice-Boltzmann method while the molecular dynamics is done for the solute. The coupling between the two is implemented through a frictional force acting both on the solvent and on the solute, which depends on the relative velocity. A spherical colloidal particle is represented by interaction sites at its surface. We demonstrate that this scheme quantitatively reproduces the translational and rotational diffusion of a neutral spherical particle in a liquid and show preliminary results for a charged spherical particle. We argue that this method is especially advantageous in the case of charged colloids.Comment: For a movie click on the link below Fig

Weak intermolecular interactions in an ionically bound molecular adsorbate: cyclopentadienyl=Cu(111)

The dissociative adsorption of cyclopentadiene (C5H6) on Cu(111) yields a cyclopentadienyl (Cp) species with strongly anionic characteristics. The Cp potential energy surface and frictional coupling to the substrate are determined from measurements of dynamics of the molecule together with density functional calculations. The molecule is shown to occupy degenerate threefold adsorption sites and molecular motion is characterized by a low diffusional energy barrier of 40 +/- 3 meV with strong frictional dissipation. Repulsive dipole-dipole interactions are not detected despite charge transfer from substrate to adsorbate

Ultra-high precision determination of site energy differences using a Bayesian method

Accurate experimental data of adsorbate potential energy landscapes are crucial as benchmarks for the evaluation of first-principles calculations. Here, we present a Bayesian method, analyzing the difference in forward and backward hopping rate in helium spin-echo measurements, that allows us to determine the binding-energy difference between two sites with unprecedented accuracy. Demonstrating the power of the method on the model system cyclopentadienyl/Cu(111), we find an energy difference between fcc and hcp hollow sites of (10.6±1.7) meV

Accurate light-time correction due to a gravitating mass

This work arose as an aftermath of Cassini's 2002 experiment \cite{bblipt03}, in which the PPN parameter $\gamma$ was measured with an accuracy $\sigma_\gamma = 2.3\times 10^{-5}$ and found consistent with the prediction $\gamma =1$ of general relativity. The Orbit Determination Program (ODP) of NASA's Jet Propulsion Laboratory, which was used in the data analysis, is based on an expression for the gravitational delay which differs from the standard formula; this difference is of second order in powers of $m$ -- the sun's gravitational radius -- but in Cassini's case it was much larger than the expected order of magnitude $m^2/b$, where $b$ is the ray's closest approach distance. Since the ODP does not account for any other second-order terms, it is necessary, also in view of future more accurate experiments, to systematically evaluate higher order corrections and to determine which terms are significant. Light propagation in a static spacetime is equivalent to a problem in ordinary geometrical optics; Fermat's action functional at its minimum is just the light-time between the two end points A and B. A new and powerful formulation is thus obtained. Asymptotic power series are necessary to provide a safe and automatic way of selecting which terms to keep at each order. Higher order approximations to the delay and the deflection are obtained. We also show that in a close superior conjunction, when $b$ is much smaller than the distances of A and B from the Sun, of order $R$, say, the second-order correction has an \emph{enhanced} part of order $m^2R/b^2$, which corresponds just to the second-order terms introduced in the ODP. Gravitational deflection of the image of a far away source, observed from a finite distance from the mass, is obtained to $O(m^2)$.Comment: 4 figure

Sedimentation and Flow Through Porous Media: Simulating Dynamically Coupled Discrete and Continuum Phases

We describe a method to address efficiently problems of two-phase flow in the regime of low particle Reynolds number and negligible Brownian motion. One of the phases is an incompressible continuous fluid and the other a discrete particulate phase which we simulate by following the motion of single particles. Interactions between the phases are taken into account using locally defined drag forces. We apply our method to the problem of flow through random media at high porosity where we find good agreement to theoretical expectations for the functional dependence of the pressure drop on the solid volume fraction. We undertake further validations on systems undergoing gravity induced sedimentation.Comment: 22 pages REVTEX, figures separately in uudecoded, compressed postscript format - alternatively e-mail '[email protected]' for hardcopies