Ultrasound-induced emulsification of subcritical carbon dioxide/water with and without surfactant as a strategy for enhanced mass transport

Pulsed ultrasound was used to disperse a biphasic mixture of CO₂/H₂O in a 1 dm³ high-pressure reactor at 30 °C/80 bar. A view cell positioned in-line with the sonic vessel allowed observation of a turbid emulsion which lasted approximately 30 min after ceasing sonication. Within the ultrasound reactor, simultaneous CO₂-continuous and H₂O-continuous environments were identified. The hydrolysis of benzoyl chloride was employed to show that at similar power intensities, comparable initial rates (1.6 ± 0.3 × 10^–3 s^–1 at 95 W cm^–2) were obtained with those reported for a 87 cm³ reactor (1.8 ± 0.2 × 10^–3 s^–1 at 105 W cm^–2), demonstrating the conservation of the physical effects of ultrasound in high-pressure systems (emulsification induced by the action of acoustic forces near an interface). A comparison of benzoyl chloride hydrolysis rates and benzaldehyde mass transport relative to the non-sonicated, ‘silent’ cases confirmed that the application of ultrasound achieved reaction rates which were over 200 times faster, by reducing the mass transport resistance between CO₂ and H₂O. The versatility of the system was further demonstrated by ultrasound-induced hydrolysis in the presence of the polysorbate surfactant, Tween, which formed a more uniform CO₂/H₂O emulsion that significantly increased benzoyl chloride hydrolysis rates. Finally, pulse rate was employed as a means of slowing down the rate of hydrolysis, further illustrating how ultrasound can be used as a valuable tool for controlling reactions in CO₂/H₂O solvent mixtures.     

Transmural pressure effects on the stability of clamped cylindrical shells subjected to internal fluid flow: Theory and experiments

An experimental and theoretical parametric study is undertaken to investigate the effect of transmural pressure on the non-linear dynamics and stability of circular cylindrical shells with clamped ends subjected to internal fluid flow. The theoretical structural model is based on the Donnell non-linear shallow shell theory, and potential flow theory is employed to describe the fluid-structure interaction. It is found that, for low transmural pressures in the range investigated, the shell loses stability by static subcritical divergence, while for higher transmural pressures the loss of stability is supercritical. In addition, there are ranges of flow velocity in which the shell exhibits quasi-periodic or even chaotic behaviour.     

Isolation of ceramide fractions from skin sample by subcritical chromatography with packed silica and evaporative light scattering detection

Separative method of lipid classes from the stratum corneum was developed with packed silica and supercritical CO2 containing 10% of methanol at 15 degrees C, 15 MPa and 3 ml min(-1). The elution order of lipid classes was first esterified cholesterol, triglycerides, squalene co-eluted in a single peak, then free fatty acids, free cholesterol, ceramides and finally glycosylceramides. The ceramides were eluted in several fractions which depended on the number of hydroxyl groups in the molecule, i.e. more hydroxyl groups were contained in ceramides, more important was the retention. Moreover, the retention was not altered by the presence of carbon double bond and variation of the alkyl chain length. The ceramide response with the evaporative light scattering detector was improved by turning the influence of the solvent nature on the response to advantage. Therefore, addition of various solvents with or without triethylamine and formic acid were tested in post-column due to the incompatibility of such modifiers with silica stationary phase. Thereby the solvent conditions for the separation and the detection can be adjusted almost independently. The response was greatly increased by post-column addition of 1% (v/v) triethylamine and its equivalent amount of formic acid in dichloromethane introduced at 0.1 ml min(-1) into the mobile phase. This device had allowed the detection of 400 ng of ceramide with a S/N = 21, whereas no peak was observed in absence of the post-column addition. Finally, the method was applied to the treatment of skin sample which led to highly enriched ceramide fraction.     

Sub- and supercritical glycolysis of polyethylene terephthalate (PET) into the monomer bis(2-hydroxyethyl) terephthalate (BHET)

Sub- and supercritical glycolysis of polyethylene terephthalate (PET) with ethylene glycol (EG) to bis(2-hydroxyethyl) terephthalate (BHET) was investigated for the purpose of developing a PET recycling process. Supercritical glycolysis was carried out at 450 °C and 15.3 MPa while subcritical glycolysis was carried out at 350 °C and 2.49 MPa or at 300 °C and 1.1 MPa. High yields (gt; 90%) of the monomer BHET were obtained in both super- and subcritical cases. For the same PET/EG weight ratio of about 0.06, the optimum reaction time was 30 min for supercritical glycolysis and 75 and 120 min for two cases of subcritical glycolysis. GPC, RP-HPLC, ¹H NMR and ¹³C NMR, and DSC were used to characterize the polymer and reaction products. Supercritical glycolysis will be suitable to a process requiring a high throughput due to its short reaction time.     

Sharp conditions of global existence and scattering for a focusing energy-critical Schrödinger equation

We consider a focusing energy-critical Schrödinger equation with subcritical perturbations and address question related to the sharp criterion of global existence and scattering. By analyzing the variational characteristics of this equation, we established two types of invariant flows. Then approximating this equation by the energy-critical nonlinear Schrödinger equations with the same initial data and combining the properties of the invariant flows, we obtain the sharp conditions of global existence for this equation. Moreover, when the solution is globally defined, we prove the scattering.     

Probing a subcritical instability with an amplitude expansion: An exploration of how far one can get

We explore methods to locate subcritical branches of spatially periodic solutions in pattern forming systems with a nonlinear finite-wavelength instability. We do so by means of a direct expansion in the amplitude of the linearly least stable mode about the appropriate reference state which one considers. This is motivated by the observation that for some equations fully nonlinear chaotic dynamics has been found to be organized around periodic solutions that do not simply bifurcate from the basic (laminar) state. We apply the method to two model equations, a subcritical generalization of the Swift–Hohenberg equation and a novel extension of the Kuramoto–Sivashinsky equation that we introduce to illustrate the abovementioned scenario in which weakly chaotic subcritical dynamics is organized around periodic states that bifurcate “from infinity” and that can nevertheless be probed perturbatively. We explore the reliability and robustness of such an expansion, with a particular focus on the use of these methods for determining the existence and approximate properties of finite-amplitude stationary solutions. Such methods obviously are to be used with caution: the expansions are often only asymptotic approximations, and if they converge their radius of convergence may be small. Nevertheless, expansions to higher order in the amplitude can be a useful tool to obtain qualitatively reliable results.     

On the breakup of bubbles at high Reynolds numbers and subcritical Weber numbers

In this paper we propose a simplified two-dimensional model to describe some aspects of the turbulent breakage of bubbles at subcritical Weber numbers. In particular we focus on the breakup of bubbles owing to their interaction with an array of successive eddies, modeled by a train of straining flows. Our simulations show that, under certain conditions, a bubble accumulates energy due to its interaction with a sequence of turbulent structures until it eventually breaks, even if none of the eddies is sufficiently energetic to split the particle by itself. It is also shown that the different strain directions of the eddies acting on the surface of the bubble, and the resonance effect between their characteristic frequency and the natural oscillation frequency of the bubble immersed into the straining flow are the two key factors in the bubble deformation, and subsequent breakup mechanism. Moreover, the breakup patterns obtained from our simulations seem to agree qualitatively well with the experimental observations.     

Existence of solution for a nonvariational elliptic system with exponential growth in dimension two

We prove existence of solution for an elliptic system on a bounded domain in dimension two. We use the Galerkin scheme in the product of Hilbert spaces. The nonlinearities may have subcritical or critical exponential growth.     

Cu(I)-mediated lactone formation in subcritical water: a benign synthesis of benzopyranones and urolithins A–C

Benzopyranones were successfully synthesized using Cu(I)-mediated C–O bond formation in subcritical water. A number of benzopyranone derivatives including polymethoxy benzopyranones, benzopyranopyridones, chromenoindolones, and furochromenones were synthesized in satisfactory yield. This methodology was further applied to synthesize the intestinal microbial metabolites, urolithins A, B, and C, which were found to exhibit potent antioxidant activity.