Numerical approximation of generalized Newtonian fluids using Powell–Sabin–Heindl elements: I. theoretical estimates

In this paper we consider the numerical approximation of steady and unsteady generalized Newtonian fluid flows using divergence free finite elements generated by the Powell–Sabin–Heindl elements. We derive a priori and a posteriori finite element error estimates and prove convergence of the method of successive approximations for the steady flow case. A priori error estimates of unsteady flows are also considered. These results provide a theoretical foundation and supporting numerical studies are to be provided in Part II. Copyright © 2003 John Wiley & Sons, Ltd.     

Detecting instabilities in flows of viscoelastic fluids

There is a growing interest in developing numerical tools to investigate the onset of physical instabilities observed in experiments involving viscoelastic flows, which is a difficult and challenging task as the simulations are very sensitive to numerical instabilities. Following a recent linear stability analysis carried out in order to better understand qualitatively the origin of numerical instabilities occurring in the simulation of flows viscoelastic fluids, the present paper considers a possible extension for more complex flows. This promising method could be applied to track instabilities in complex (i.e. essentially non‐parallel) flows. In addition, results related to transient growth mechanism indicate that it might be responsible for the development of numerical instabilities in the simulation of viscoelastic fluids. Copyright © 2003 John Wiley & Sons, Ltd.     

Analysis of plane and axisymmetric flows of incompressible fluids with the stream tube method: Numerical simulation by trust-region optimization algorithm

New concepts for the study of incompressible plane or axisymmetric flows are analysed by the stream tube method. Flows without eddies and pure vortex flows are considered in a transformed domain where the mapped streamlines are rectilinear or circular. The transformation between the physical domain and the computational domain is an unknown of the problem. In order to solve the non-linear set of relevant equations, we present a new algorithm based on a trust region technique which is effective for non-convex optimization problems. Experimental results show that the new algorithm is more robust compared to the Newton-Raphson method.     

Production of superfine fibers by the electrospinning method

Weakly conducting fluid flows in an electric field in the presence of phase interfaces are investigated theoretically and experimentally. The object of the investigation is an axisymmetric jet. The analysis is carried out within the framework of electrohydrodynamics (EHD) with allowance for surface charge transfer on mobile interfaces. The jet shape is calculated at large distances from the outflow point. The theoretical and experimental data are compared for Newtonian and polymeric fluids.     

Analysis and finite element simulations of a second‐order fluid model in a bounded domain

This article is concerned with the equations governing the steady motion of a viscoelastic incompressible second‐order fluid in a bounded domain. A new proof of existence and uniqueness of strong solutions is given. In addition, using appropriate finite element methods to approximate a coupled equivalent problem, sharp error estimates are obtained using a fixed point argument. The method is applied to the two‐dimensional lid‐driven cavity problem, at low Reynolds number and in a certain range of values of the viscoelastic parameters, to analyze the combined effects of inertia and viscoelasticity on the flow. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2007     

Physicochemical Principles of Extraction with Supercritical Gases

The present review considers some physicochemical properties of fluid mixtures that are of importance for fluid extraction and supercitical fluid chromatography (SFC). Firstly, the important types of phase diagrams are treated, the occurrence of solid phases also being considered in some simple cases. Specific examples are given of mixtures of a highly volatile component I (e.g. CO₂, C₂H₆) with a relatively involatile component II (e.g. squalane) of very different molecular size, shape, structure, and/or polarity, and it is shown how the rather complicated types of phase diagrams can be calculated and correlated. The importance of fluid mixtures extends far beyond the fields of science and technology reviewed.     

Chromatography with Supercritical Fluids

Chromatography with supercritical fluids unites the features of both gas chromatography and liquid chromatography, yet retains special characteristics of its own. The diffusion coefficient and particularly the viscosity of fluid phases may approach values for low-pressure gases, while the solvent power may be similar to that of liquids. However, with supercritical fluids it is possible to control chromatographic separations very effectively by pressure programming, since the solubility increases with increasing density. Temperature programming, on the other hand, can have the opposite effect to that in gas- or liquid-chromatography since the density decreases with increasing temperature at a given pressure. Supercritical fluid chromatography is primarily of interest for the separation of higher molecular weight compounds. The efficiency of this method of separation is demonstrated on several homologous series. Thus, a styrene oligomer with nominal M_w=2200 can be resolved by a pressure and temperature program into 40 species.     

Supercritical Propanol-Water Synthesis and Comprehensive Size Characterisation of Highly Crystalline anatase TiO2 Nanoparticles

Highly crystalline anatase TiO₂ nanoparticles have been synthesised in less than 1 min in a supercritical propanol-water mixture using a continuous flow reactor. The synthesis parameter space (T, P, concentration) has been explored and the average particle size can be accurately controlled within 10-18 nm with narrow size distributions (2-3 nm). At subcritical conditions amorphous products are obtained, whereas a broad range of T and P in the supercritical regime gives 11-14 nm particles. At high temperature and pressure, the particles size increase to 18 nm. The nanoparticles have been extensively characterised with powder X-ray diffraction (PXRD), transmission electron microscopy (TEM) and small-angle X-ray scattering (SAXS) with excellent agreement on size and size distribution parameters. The SAXS analysis suggests disk-shaped particles with diameters that are approximately double the height. For comparison, a series of conventional autoclave sol-gel syntheses have been carried out. These also produce phase-pure anatase nanoparticles, but with much broader size distributions and at much longer synthesis times (hours). The study demonstrates that synthesis in supercritical fluids is a very promising method for manipulating the size and size distribution of nanoparticles, thus removing one of the key limitations in many applications of nanomaterials.     

Solubility Optimization of Loxoprofen as a Nonsteroidal Anti-Inflammatory Drug: Statistical Modeling and Optimization

Industrial-based application of supercritical CO₂ (SCCO₂) has emerged as a promising technology in numerous scientific fields due to offering brilliant advantages, such as simplicity of application, eco-friendliness, and high performance. Loxoprofen sodium (chemical formula C₁₅H₁₈O₃) is known as an efficient nonsteroidal anti-inflammatory drug (NSAID), which has been long propounded as an effective alleviator for various painful disorders like musculoskeletal conditions. Although experimental research plays an important role in obtaining drug solubility in SCCO₂, the emergence of operational disadvantages such as high cost and long-time process duration has motivated the researchers to develop mathematical models based on artificial intelligence (AI) to predict this important parameter. Three distinct models have been used on the data in this work, all of which were based on decision trees: K-nearest neighbors (KNN), NU support vector machine (NU-SVR), and Gaussian process regression (GPR). The data set has two input characteristics, P (pressure) and T (temperature), and a single output, Y = solubility. After implementing and fine-tuning to the hyperparameters of these ensemble models, their performance has been evaluated using a variety of measures. The R-squared scores of all three models are greater than 0.9, however, the RMSE error rates are 1.879 × 10⁻⁴, 7.814 × 10⁻⁵, and 1.664 × 10⁻⁴ for the KNN, NU-SVR, and GPR models, respectively. MAE metrics of 1.116 × 10⁻⁴, 6.197 × 10⁻⁵, and 8.777 × 10⁻⁵errors were also discovered for the KNN, NU-SVR, and GPR models, respectively. A study was also carried out to determine the best quantity of solubility, which can be referred to as the (x₁ = 40.0, x₂ = 338.0, Y = 1.27 × 10⁻³) vector.     

Living fluids

One of the major emerging fields of research of the beginning of this century concerns living fluids. By “living fluids”, we mean two major categories of complex fluids: (i) fluids which are essential to life, like blood, and (ii) active fluids made of particles that are able to propel themselves in the suspending fluid by converting a form of their energy into mechanical motion. Studies on active fluids have known a considerable interest since the last decade. Blood might be viewed as an old topic, but the progresses in experimental techniques, analytical concepts and numerics, have contributed nowadays to a dramatic renewal of the interest in this field, with a great potential towards understanding physical and mechanical factors in cardiovascular diseases. These fields have considerably strengthened interdisciplinary research. The series of reviews of this dossier focus on the tremendous recent progress achieved in research on living fluids both from the experimental and theoretical points of views. These reviews present also the major open issues, making of this dossier a unique guide for future research in these fields. This project grew up thanks to the international summer school that we organized on the topic “living fluids” at the IES (Institut dʼétudes scientifiques) of Cargèse (Corsica) in 2012.