Water waves trapped by thin submerged cylinders in a two‐layer fluid: Discrete eigenvalue

Exact solutions of the linear water‐wave problem describing oblique water waves trapped by a submerged horizontal cylinder of small (but otherwise fairly arbitrary) cross‐section in a two‐layer fluid are constructed in the form of convergent series in powers of the small parameter characterising the “thinness” of the cylinder. The terms of this series are expressed through the solutions of the exterior Neumann problem for the Laplace equation describing the flow of unbounded fluid past the cylinder.     

Quasipatterns versus superlattices resulting from the superposition of two hexagonal patterns

We present a short review of the experimental observations and mechanisms related to the generation of quasipatterns and superlattices by the Faraday instability with two-frequency forcing. We show how two-frequency forcing makes possible triad interactions that generate hexagonal patterns, twelvefold quasipatterns or superlattices that consist of two hexagonal patterns rotated by an angle α relative to each other. We then consider which patterns could be observed when α does not belong to the set of prescribed values that give rise to periodic superlattices. Using the Swift–Hohenberg equation as a model, we find that quasipattern solutions exist for nearly all values of α. However, these quasipatterns have not been observed in experiments with the Faraday instability for $\alpha \ne \mathrm{\pi }/6$. We discuss possible reasons and mention a simpler framework that could give some hint about this problem.     

Simulating gas–liquid multiphase flow using meshless Lagrangian method

A multiphase flow model has been established based on a moving particle semi‐implicit method. A surface tension model is introduced to the particle method to improve the numerical accuracy and stability. Several computational techniques are employed to simplify the numerical procedure and further improve the accuracy. A particle fraction multiphase flow model is developed and verified by a two‐phase Poiseuille flow. The multiphase surface tension model is discussed in detail, and an ethanol drop case is introduced to verify the surface tension model. A simple dam break is simulated to demonstrate the improvements with various modifications in particle method along with a new boundary condition. Finally, we simulate several bubble rising cases to show the capacity of this new model in simulating gas–liquid multiphase flow with large density ratio difference between phases. The comparisons among numerical results of mesh‐based model, experimental data, and the present model, indicate that the new multiphase particle method is acceptable in gas–liquid multiphase fluids simulation. Copyright © 2014 John Wiley & Sons, Ltd.     

Membrane-based microchannel device for continuous quantitative extraction of dissolved free sulfide from water and from oil

Underground fluids are important natural sources of drinking water, geothermal energy, and oil-based fuels. To facilitate the surveying of such underground fluids, a novel microchannel extraction device was investigated for in-line continuous analysis and flow injection analysis of sulfide levels in water and in oil. Of the four designs investigated, the honeycomb-patterned microchannel extraction (HMCE) device was found to offer the most effective liquid–liquid extraction. In the HMCE device, a thin silicone membrane was sandwiched between two polydimethylsiloxane plates in which honeycomb-patterned microchannels had been fabricated. The identical patterns on the two plates were accurately aligned. The extracted sulfide was detected by quenching monitoring of fluorescein mercuric acetate (FMA). The sulfide extraction efficiencies from water and oil samples of the HMCE device and of three other designs (two annular and one rectangular channel) were examined theoretically and experimentally. The best performance was obtained with the HMCE device because of its thin sample layer (small diffusion distance) and large interface area. Quantitative extraction from both water and oil could be obtained using the HMCE device. The estimated limit of detection for continuous monitoring was 0.05 μM, and sulfide concentrations in the range of 0.15–10 μM could be determined when the acceptor was 5 μM FMA alkaline solution. The method was applied to natural water analysis using flow injection mode, and the data agreed with those obtained using headspace gas chromatography-flame photometric detection. The analysis of hydrogen sulfide levels in prepared oil samples was also performed. The proposed device is expected to be used for real time survey of oil wells and groundwater wells.     

Numerical simulations of negatively buoyant jets in an immiscible fluid using the Particle Finite Element Method

Negatively buoyant jets consist in a dense fluid injected vertically upward into a lighter ambient fluid. The numerical simulation of this kind of buoyancy‐driven flows is challenging as it involves multiple fluids with different physical properties. In the case of immiscible fluids, it requires, in addition, to track the motion of the interface between fluids and accurately represent the discontinuities of the flow variables. In this paper, we investigate numerically the injection of a negatively buoyant jet into a homogenous immiscible ambient fluid using the Particle Finite Element Method and compare the two‐dimensional numerical results with experiments on the injection of a jet of dyed water through a nozzle in the base of a cylindrical tank containing rapeseed oil. In both simulations and experiments, the fountain inlet flow velocity and nozzle diameter have been varied to cover a wide range of Froude Fr and Reynolds Re numbers ( 0.1 < Fr < 30, 8 < Re < 1350), reproducing both weak and strong laminar fountains. The flow behaviors observed for the different numerical simulations fit in the regime map based on the Re and Fr values of the experiments, and the maximum fountain height is in good agreement with the experimental observations, suggesting that particle finite element method is a useful tool for the study of immiscible two‐fluid systems. Copyright © 2011 John Wiley & Sons, Ltd.     

State space approach to magnetohydrodynamic flow of perfectly conducting micropolar fluid with stretch

In this work we introduce a model of the boundary layer equations for a perfect conducting micropolar fluid with stretch, bounded by an infinite vertical flat plane surface of a constant temperature. This model is applied to study the effects of free convection currents on the flow of the fluid in the presence of a constant magnetic field. The state space technique is adopted for the solution of a one‐dimensional problem for any set of boundary conditions. The resulting formulation together with the Laplace transform techniques are applied to a thermal shock problem. The inversion of the Laplace transforms is carried out using a numerical approach. Numerical results are given and illustrated graphically for the problem. Copyright © 2011 John Wiley & Sons, Ltd.     

Optimized Quantitative Method for Determining Isoflavones and Equol in Bovine Digestive Fluids and Feces

Many studies have been conducted on the impact of animal feed on isoflavones and their metabolite concentrations in bovine milk, but few studies have focused on the development and validation of analytical protocols for quantifying these compounds in biological matrices other than milk and plants. The purpose of this study was to develop a method that would enable four isoflavones and equol in cows’ feces and digestive fluids to be quantified simultaneously. The method is based on aglycones released by methanolic ultrasound-assisted extraction, followed by enzymatic hydrolysis and high-performance liquid chromatography tandem–mass spectrometry analysis. The sample preparation was optimized using the Box–Behnken design. The selected extraction conditions were 80°C, 10?min, and 50% methanol for digestive fluids and 70°C, 35?min, and 60% methanol for feces. For hydrolysis, the selected conditions were 37°C, 1?h, and a pH of 6 for both matrices. The analytical method showed a good linear regression model ranging from 5 to 125?ng?mL^?1. Both inter- and intraday accuracy (≤8.5 and ≤12.3%) and precision (≤11.1 and ≤15.2%) were suitable. No matrix effects were found. There was good repeatability and extract stability for at least 4 days of storage at???20 and 6°C. All recoveries were in the acceptable range of 70–120% for both matrices, except for biochanin A in feces, where the value was approximately 43%. This sensitive and reliable method will be useful for monitoring the passage of isoflavones and equol in the digestive system of ruminants.     

On power-law fluids with the power-law index proportional to the pressure

In this short note we study special unsteady flows of a fluid whose viscosity depends on both the pressure and the shear rate. Here we consider an interesting dependence of the viscosity on the pressure and the shear rate; a power-law of the shear rate wherein the exponent depends on the pressure. The problem is important from the perspective of fluid dynamics in that we obtain solutions to a technologically relevant problem, and also from the point of view of mathematics as the analysis of the problem rests on the theory of spaces with variable exponents. We use the theory to prove the existence of solutions to generalizations of Stokes’ first and second problem.     

Conditions of stability and instability for a pair of arbitrarily stratified compressible fluids in an arbitrary non-uniform gravity field

The work continues and develops authors’ previous investigation of stability in the small for a two-layer system of inhomogeneous compressible fluids in the uniform gravity field. Here we present a solution of a similar problem in the case of arbitrary non-uniform potential gravity field. The equilibrium stratification of both density and elastic properties of the fluids is supposed arbitrary, as well as the shape of open on top reservoir filled by the fluids. The problem of stability of equilibrium is analyzed as the corresponding problem for the non-linearly elastic bodies, basing on the static energy criterion with regard for the boundary conditions at all parts of the boundary. The crucial element of the analysis is conversion of the quadratic functional of second variation of total potential energy of the system into a “canonical” form that enables to determine its sign. Making use of this canonical form, we obtain almost coinciding with each other necessary and sufficient conditions for stability (those being valid also for an arbitrary number of layers).