Shallow Water equations for Non-Newtonian fluids

The purpose of this paper is to provide a consistent thin layer theory for some Non-Newtonian fluids that are incompressible and flowing down an inclined plane under the effect of gravity. We shall provide a better understanding of the derivation of Shallow Water models in the case of power-law fluids and Bingham fluids. The method is based on asymptotic expansions of solutions of the Cauchy Momentum equations in the Shallow Water scaling and in the neighbourhood of steady solutions so that we can close the average equations on the fluid height h and the total discharge rate q. Such a method has been first introduced in the case of Newtonian fluids where the computations are proved to be rigorous (Vila, in preparation [20]; Bresch and Noble, 2007 [9]) whereas the more complex case of arbitrary topography has been treated formally (Boutounet et al., 2008 [5]). The well posedness of the free surface Cauchy Momentum equations for these Non-Newtonian fluids is still an open problem: the computations carried out here are only formal.     

Designing micro-patterned Ti films that survive up to 10% applied tensile strain

Reducing the strain in brittle device layers is critical in the fabrication of robust flexible electronic devices. In this study, the cracking behavior of micro-patterned 500-nm-thick Ti films was investigated via uniaxial tensile testing by in situ SEM and 4-point probe measurements. Both visual observations by SEM and 4-pt resistance measurements showed that strategically patterned oval holes, off-set and rotated by 45°, had a significant effect on limiting the extent of cracking, specifically, in preventing cracks from converging. Failure with regard to electrical conduction was delayed from less than 2% to more than 10% strain.     

Liquid membrane transport: a survey

The literature pertaining to facilitated transport and liquid membrane separations is reviewed and summarized, especially work reported since 1977. Liquid membranes of all geometries are discussed, including immobilized liquid membranes and liquid surfactant or emulsion liquid membranes. Emphasis is placed on facilitated, or carrier-mediated transport in both configurations although other mechanisms such as coupled-transport and transport due to solubility differences are discussed. Mathematical modeling and analytical solutions for facilitated transport models are summarized. The possibility of industrial application of liquid membrane technology is mentioned and the most important experimental techniques for liquid membrane research are discussed. Also, directions for future research are recommended.     

Competitive facilitated transport through liquid membranes

A mathematical model is presented which solves the dimensionless, transient, non-linear partial differential equations governing the competitive facilitated transport of two gases through a liquid membrane. The model incorporates the mass transfer coefficients in the boundary conditions for the free gas concentrations. Several studies were carried out. A comparison of this model with a steady-state “equilibrium core” model was excellent. Through varying the dimensionless parameters, it was found that gas I would have a higher steady-state facilitation factor than gas 2 if k₁ >k₂ and k_-1k_-2. The boundary conditions and mass transfer coefficients were also varied to see their effects on the facilitation factors. The idea of pumping one of the gases against its concentration gradient was shown to be theoretically possible.     

Existence of Pulsating Roll-Waves for the Saint Venant System

The phenomenon of roll-waves occurs when shallow water flows down open inclined channels. This flow is described by the Saint Venant’s equations with a friction term due to Chezy. In the case of a flat bottom, their existence (as entropic and periodic travelling waves) follows from a classical work due to DRESSLER [6]. The aim of this paper is to prove the existence of roll-waves when the bottom is modulated by a small periodic perturbation. Following JIN and KATSOULAKIS [15], we first compute a Burgers-type equation which possesses “pulsating” roll-waves (the wave speed oscillates around an average velocity). We prove, in a mathematically rigorous fashion, the existence of these solutions.     

Identification of groundwater discharge in Cuddalore coast,Tamil Nadu using radium isotopes

For the optimal exploitation and management of coastal aquifers of Tamil Nadu, it is essential to evaluate the groundwater outflow into the sea also called as submarine groundwater discharge. In this study, radium isotopes (^223,224Ra) were employed to understand the groundwater discharge in coastal areas of Cuddalore district, Tamil Nadu. Sea water samples (100 L) were collected from various locations of Cuddalore coast in October 2011 and passed through Mn-impregnated acrylic fiber columns. These acrylic columns were analyzed for ^223,224Ra activities using radium delayed coincidence counter. The observed higher activities of ^223,224Ra excess (0.02 ± 0.001–3.28 ± 0.16 and 64 ± 3–380 ± 19 mBq/100 L respectively) indicate that groundwater discharge occurs in this coastal region.     

Magnetic field in a turbulent conducting fluid

The problem of magnetic field in conducting turbulent, incompressible fluid is considered. The velocity of the fluid is taken to be independent of the magnetic field and is described by a Gaussian field, ‘white noise’ in time with smooth space correlation. The main result is that no fast dynamo (by which is meant almost sure exponential growth of magnetic field) can exist for an incompressible fluid when the magnetic viscosity is positive. For d = 2, sharper results are obtained; the magnetic field dies out when the magnetic viscosity is strictly positive. Furthermore, when d = 2, existence and characterization of invariant measure are given for d = 2 when the magnetic viscosity is zero. The results are compared to those discussed by Baxendale and Rosovskii in [2]