Multi-scale roughness transfer in cold metal rolling

We report on a comparative Atomic Force Microscope (AFM) multi-scale roughness analysis of cold rolled Al alloy and steel roll, in order to characterize the roughness transfer from the steel roll to the workpiece in cold strip rolling processes. More than three orders of length-scale magnitudes were investigated from 100 microns to 50 nanometers on both types of surfaces. The analysis reveals that both types of surfaces are anisotropic self-affine surfaces. Transverse and longitudinal height profiles exhibit a different roughness exponent (Hurst exponent) z֊=0.93±0.03 and zʈ=0.5±0.05 Different length-scale cut-offs are obtained in each direction lsup=50mm, lsupՆ100mm. Height and slope distributions are also computed to complement this study. The above mentionned self-affine characteresitics are found to be very similar for the roll and the strip surfaces, which suggest that roughness transfer takes place from the macroscopic (100 µm) to the very small scale (50 nm)

Capillary pinching in a pinched microchannel

We report a study of the capillary pinching of a gas bubble by a wetting liquid inside a pinched channel. The capillary pinching induces very reproducible bubbling, at a very well-defined frequency. There are two regimes associated with drip and jet bubbling. In the latter, we show that highly monodispersed bubbles are formed by our pinched channel. The dynamics of the bubble formation also shows two distinct regimes: a long-duration elongation of the air bubble and a rapid relaxation of the interface after interface breakup. The slow regime depends on the flux imposed and the channel geometry. The rapid deformation dynamic regime depends very weakly on the boundary conditions. Scaling arguments are proposed in the context of the lubrication approximation to describe the two regimes

Stationary convection-diffusion between two co-axial cylinders

In this note, we examine the high Peclet number limit of the stationary extended Graetz problem for which two families of real and imaginary eigenvalues are associated, respectively, with a downstream convective relaxation and the upstream diffusive establishment. The asymptotic behavior of both families of eigenvalues is studied, in the limit of large Peclet number and thin wall, which bring to the fore a single parameter dependence, previously mentioned in the literature from numerical investigations [M.A. Cotton, J.D. Jackson, in: R.W. Lewis, K. Morgan (Eds.), Numerical Methods in Thermal Problems, vol. IV, Pineridge Press, Swansea, 1985, pp. 504–515]. The fully developed region is specifically studied thanks to the first eigenvalue dependence on the Peclet number, on the thermal conductivity coefficients and on the diameter ratio of the cylinders. The effective transport between the fluid and the solid is investigated through the evaluation of the fully developed Nusselt number and experimental measurements

Symmetry breaking and electrostatic attraction between two identical surfaces

By allowing the surface charge of one surface to affect the adsorption equilibrium of the other, we establish the existence of a long-range attractive interaction between two identical surfaces in an electrolyte containing polyvalent counterions with a mean-field Poisson-Boltzmann approach. A Stern electrostatic condition from linearization of the mass-action adsorption isotherm is used to capture how polyvalent ion condensation affects and reverses the surface charge. We furthermore establish a direct mapping between this Stern-layer condition and previously derived modified mean-field formulations associated with correlated fluctuations theory. For a sufficiently potential-sensitive isotherm, antisymmetric charge inversion can occur to produce an attractive force that increases with decreasing ionic strengths. Analyses of a mass-action isotherm produce force-separation relations, including an exponential far-field force decay distinct but consistent with previously proposed correlated fluctuation theories and in quantitative agreement with experimental data

Kelvin–Helmholtz instability in a Hele-Shaw cell

A linear stability analysis is presented for the Kelvin–Helmholtz instability in a Hele-Shaw cell, an analysis based on the Navier–Stokes equation to improve on the previous Euler–Darcy study that Gondret and Rabaud [Phys. Fluids 9, 3267 (1997)] made of their own experiments

Kelvin–Helmholtz instability in a Hele-Shaw cell: Large effect from the small region near the meniscus

In an attempt to improve the poor prediction of our previous theory, we examine corrections from the small region in a Hele-Shaw cell near the meniscus where the flow is three dimensional. At larger Reynolds numbers, we find an O(1) change to the effective boundary condition for mass conservation which is to be applied to the large scale flow outside the small region

Generalized Lagrangian Coordinates for Transport and Two-Phase Flows in Heterogeneous Anisotropic Porous Media

We show how Lagrangian coordinates provide an effective representation of how difficult non-linear, hyperbolic transport problems in porous media can be dealt with. Recalling Lagrangian description first, we then derive some basic but remarkable properties useful for the numerical com- putation of projected transport operators. We furthermore introduce new generalized Lagrangian coordinates with their application to the Darcy–Muskat two-phase flow models. We show how these generalized Lagrangian coordinates can be constructed from the global mass conservation, and that they are related to the existence of a global pressure previously defined in the literature about the subject. The whole representation is developed in two or three dimensions for numerical purposes, for isotropic or anisotropic heterogeneous porous media

Gap Filling of 3-D Microvascular Networks by Tensor Voting

We present a new algorithm which merges discontinuities in 3-D images of tubular structures presenting undesirable gaps. The application of the proposed method is mainly associated to large 3-D images of microvascular networks. In order to recover the real network topology, we need to fill the gaps between the closest discontinuous vessels. The algorithm presented in this paper aims at achieving this goal. This algorithm is based on the skeletonization of the segmented network followed by a tensor voting method. It permits to merge the most common kinds of discontinuities found in microvascular networks. It is robust, easy to use, and relatively fast. The microvascular network images were obtained using synchrotron tomography imaging at the European Synchrotron Radiation Facility. These images exhibit samples of intracortical networks. Representative results are illustrated

Conductances between confined rough walls

Two- and three-dimensional creeping flows and diffusion transport through constricted and possibly rough surfaces are studied. Asymptotic expansions of conductances are derived as functions of the constriction local geometry. The validity range of the proposed theoretical approximations is explored through a comparison either with available exact results for specific two-dimensional aperture fields or with direct numerical computations for general three-dimensional geometries. The large validity range of the analytical expressions proposed for the hydraulic conductivity (and to a lesser extent for the electrical conductivity) opens up interesting perspectives for the simulation of flows in highly complicated geometries with a large number of constrictions

A New Approach to Model Confined Suspensions Flows in Complex Networks: Application to Blood Flow

The modeling of blood flows confined in micro-channels or micro-capillary beds depends on the interactions between the cell-phase, plasma and the complex geometry of the network. In the case of capillaries or channels having a high aspect ratio (their longitudinal size is much larger than their transverse one), this modeling is much simplified from the use of a continuous description of fluid viscosity as previously proposed in the literature. Phase separation or plasma skimming effect is a supplementary mechanism responsible for the relative distribution of the red blood cell’s volume density in each branch of a given bifur- cation. Different models have already been proposed to connect this effect to the various hydrodynamics and geometrical parameters at each bifurcation. We discuss the advantages and drawbacks of these models and compare them to an alternative approach for modeling phase distribution in complex channels networks. The main novelty of this new formulation is to show that albeit all the previous approaches seek for a local origin of the phase segre- gation phenomenon, it can arise from a global non-local and nonlinear structuration of the flow inside the network. This new approach describes how elementary conservation laws are sufficient principles (rather than the complex arametric models previously proposed) to provide non local phase separation. Spatial variations of the hematocrit field thus result from the topological complexity of the network as well as nonlinearities arising from solving a new free boundary problem associated with the flux and mass conservation. This network model approach could apply to model blood flow distribution either on artificial micro-models, micro-fluidic networks, or realistic reconstruction of biological micro-vascular networks