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     

Criticality and phase transitions in ionic fluids

Recent experimental investigations of criticality and phase separation in ionic fluids have revealed behavior of great theoretical interest. In seeking to understand the experiments, some of which appear to exhibit argonlike criticality and some of which exhibit classical (mean-field) criticality, a convenient starting point is the restricted primitive model (RPM) of symmetrically charged hard spheres, all of equal diameter , each sphere bearing a positive or negative charge of magnitudeq. There is overall charge neutrality, so that the expected number densities of the anions and cations are equal, ₊= _-. Studies of RPM charge-charge and density-density correlation functions indicate that the fluctuation-suppressing mechanism that yields mean-field critical behavior in nonionic systems with long-range interparticle potentials is not operative in the RPM. On the basis of plausible assumptions, Ising-like behavior is instead expected. The above work is summarized. New work of Zhang and the author is outlined, showing that when one loses the RPM symmetry (through, e.g., different valence, diameter, or dipole moment of anions and cations) a strong coupling between charge-charge and density-density correlation ensues. The way in which this can be expected to give rise to mean-field or mean-field-like behavior is noted. Other new observations concern the mean-field analogy found by Høye and the author between the parameter 2/(d–2) (d is the dimensionality) in that model and the monomer number in high polymers, with respect to the coexistence-curve shape dependence on those parameters.     

Classical fluids of negative heat capacity

It is shown that new parametersX can be defined such that the heat capacity C_xT(S/T)_x is negative, even when the canonical ensemble [i.e., at fixed T=(U/S)_Y and YX] is stable. This implies an extension of the classical theory of polytropes from ideal gases to general fluids. As examples of negative heat capacity systems we treat blackbody radiation and general gas systems with nonsingular _T. For the case of a simple ideal gas we even exhibit an apparatus which enforces a constraint X(p, V)=const that makes C_x<0. We then show that it is possible to infer the statistical mechanics of canonicallyunstable systems-for which even the traditional heat capacities are negative-by imposing constraints that stabilize the associated noncanonical ensembles. Two explicit models are discussed.     

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.     

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.