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

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

Steady streaming confined between three-dimensional wavy surfaces

We present a theoretical and numerical study of three-dimensional pulsatile confined flow between two rigid horizontal surfaces separated by an average gap h, and having three-dimensional wavy shapes with arbitrary amplitude σ h where σ ∼ O(1), but long-wavelength variations λ, with h/λ 1. We are interested in pulsating flows with moderate inertial effect arising from the Reynolds stress due to the cavity non-parallelism. We analyse the inertial steady-streaming and the second harmonic flows in a lubrication approximation. The dependence of the three-dimensional velocity field in the transverse direction is analytically obtained for arbitrary Womersley numbers and possibly overlapping Stokes layers. The horizontal dependence of the flow is solved numerically by computing the first two pressure fields of an asymptotic expansion in the small inertial limit. We study the variations of the flow structure with the amplitude, the channel’s wavelength and the Womersley number for various families of three-dimensional channels. The steady-streaming flow field in the horizontal plane exhibits a quadrupolar vortex, the size of which is adjusted to the cavity wavelength. When increasing the wall amplitude, the wavelengths characterizing the channel or the Womersley number, we find higher-order harmonic flow structures, the origin of which can either be inertially driven or geometrically induced. When some of the channel symmetries are broken, a steady-streaming current appears which has a quadratic dependence on the pressure drop, the amplitude of which is linked to the Womersley number

Averaged Reynolds Equation for Flows between Rough Surfaces in Sliding Motion

The flow between rough surfaces in sliding motion with contacts between these surfaces, is analyzed through the volume averaging method. Assuming a Reynolds (lubrication) approximation at the roughness scale, an average flow model is obtained combining spatial and time average. Time average, which is often omitted in previous works, is specially discussed. It is shown that the effective transport coefficients, traditionally termed ‘flow factors’ in the lubrication literature, that appear in the average equations can be obtained from the solution to two closure problems. This allows for the numerical determination of flow factors on firmer bases and sheds light on some arguments to the literature. Moreover, fluid flows through fractures form an important subset of problems embodied in the present analysis, for which macroscopisation is given

Sliding lubricated anisotropic rough surfaces

The object of this paper is to study the effects of lubricant film flow, pressurized and sheared between two parallel rough surfaces in sliding motion. The influence of microscopic surface roughness on lubricant film flow macroscopic behavior is described through five nondimensional parameters called flow factors. These macroscopic transport parameters are related to the local geometry of apertures and surfaces. Short- and long-range-correlated surface roughnesses display very different macroscopic behaviors when surfaces are close to contact. These behaviors are related to underlying surface roughness parameters such as the correlation length and the self-affine Hurst exponent. The problem is numerically studied, and results are compared to some analytical asymptotic results

Nonuniversal conductivity exponents in continuum percolating Gaussian fractures

We study the electrical and hydraulic conductivity percolation exponents in a Gaussian fracture using the method proposed in Plouraboué et al. [Phys. Rev. E 73, 036305, 2006]. Nonuniversal conductivity percolation exponents are found: they differ from the theoretical predictions for infinite system size for frozen power-law distributions of local conductivities, as with their finite size corrections. In the hydraulic case, we also find that the probability density function of the conductivity follows a power-law distribution near the percolation threshold