Fluid Flows of Mixed Regimes in Porous Media

In porous media, there are three known regimes of fluid flows, namely, pre-Darcy, Darcy and post-Darcy. Because of their different natures, these are usually treated separately in literature. To study complex flows when all three regimes may be present in different portions of a same domain, we use a single equation of motion to unify them. Several scenarios and models are then considered for slightly compressible fluids. A nonlinear parabolic equation for the pressure is derived, which is degenerate when the pressure gradient is either small or large. We estimate the pressure and its gradient for all time in terms of initial and boundary data. We also obtain their particular bounds for large time which depend on the asymptotic behavior of the boundary data but not on the initial one. Moreover, the continuous dependence of the solutions on initial and boundary data, and the structural stability for the equation are established.Comment: 33 page

Analysis of the Brinkman-Forchheimer equations with slip boundary conditions

In this work, we study the Brinkman-Forchheimer equations driven under slip boundary conditions of friction type. We prove the existence and uniqueness of weak solutions by means of regularization combined with the Faedo-Galerkin approach. Next we discuss the continuity of the solution with respect to Brinkman's and Forchheimer's coefficients. Finally, we show that the weak solution of the corresponding stationary problem is stable

Pore-scale numerical investigation of pressure drop behaviour across open-cell metal foams

The development and validation of a grid-based pore-scale numerical modelling methodology applied to five different commercial metal foam samples is described. The 3-D digital representation of the foam geometry was obtained by the use of X-ray microcomputer tomography scans, and macroscopic properties such as porosity, specific surface and pore size distribution are directly calculated from tomographic data. Pressure drop measurements were performed on all the samples under a wide range of flow velocities, with focus on the turbulent flow regime. Airflow pore-scale simulations were carried out solving the continuity and Navier–Stokes equations using a commercial finite volume code. The feasibility of using Reynolds-averaged Navier–Stokes models to account for the turbulence within the pore space was evaluated. Macroscopic transport quantities are calculated from the pore-scale simulations by averaging. Permeability and Forchheimer coefficient values are obtained from the pressure gradient data for both experiments and simulations and used for validation. Results have shown that viscous losses are practically negligible under the conditions investigated and pressure losses are dominated by inertial effects. Simulations performed on samples with varying thickness in the flow direction showed the pressure gradient to be affected by the sample thickness. However, as the thickness increased, the pressure gradient tended towards an asymptotic value

Jean-Baptiste Bélanger, hydraulic engineer, researcher and academic

Jean-Baptiste BÉLANGER (1790-1874) worked as a hydraulic engineer at the beginning of his career. He developed the backwater equation to calculate gradually-varied open channel flow properties for steady flow conditions. Later, as an academic at the leading French engineering schools (Ecole Centrale des Arts et Manufactures, Ecole des Ponts et Chaussées, and Ecole Polytechnique), he developed a new university curriculum in mechanics and several textbooks including a seminal text in hydraulic engineering. His influence on his contemporaries was considerable, and his name is written on the border of one of the four facades of the Eiffel Tower. BÉLANGER's leading role demonstrated the dynamism of practicing engineers at the time, and his contributions paved the way to many significant works in hydraulics

Modeling and Measuring Viscoelasticity with Dynamic Atomic Force Microscopy

peer reviewe

Unconfined Aquifer Flow Theory - from Dupuit to present

Analytic and semi-analytic solution are often used by researchers and practicioners to estimate aquifer parameters from unconfined aquifer pumping tests. The non-linearities associated with unconfined (i.e., water table) aquifer tests makes their analysis more complex than confined tests. Although analytical solutions for unconfined flow began in the mid-1800s with Dupuit, Thiem was possibly the first to use them to estimate aquifer parameters from pumping tests in the early 1900s. In the 1950s, Boulton developed the first transient well test solution specialized to unconfined flow. By the 1970s Neuman had developed solutions considering both primary transient storage mechanisms (confined storage and delayed yield) without non-physical fitting parameters. In the last decade, research into developing unconfined aquifer test solutions has mostly focused on explicitly coupling the aquifer with the linearized vadose zone. Despite the many advanced solution methods available, there still exists a need for realism to accurately simulate real-world aquifer tests

Syndromics: A Bioinformatics Approach for Neurotrauma Research

Substantial scientific progress has been made in the past 50 years in delineating many of the biological mechanisms involved in the primary and secondary injuries following trauma to the spinal cord and brain. These advances have highlighted numerous potential therapeutic approaches that may help restore function after injury. Despite these advances, bench-to-bedside translation has remained elusive. Translational testing of novel therapies requires standardized measures of function for comparison across different laboratories, paradigms, and species. Although numerous functional assessments have been developed in animal models, it remains unclear how to best integrate this information to describe the complete translational “syndrome” produced by neurotrauma. The present paper describes a multivariate statistical framework for integrating diverse neurotrauma data and reviews the few papers to date that have taken an information-intensive approach for basic neurotrauma research. We argue that these papers can be described as the seminal works of a new field that we call “syndromics”, which aim to apply informatics tools to disease models to characterize the full set of mechanistic inter-relationships from multi-scale data. In the future, centralized databases of raw neurotrauma data will enable better syndromic approaches and aid future translational research, leading to more efficient testing regimens and more clinically relevant findings