Applications of Group Analysis to the Three-Dimensional Equations of Fluids with Internal Inertia

Group classification of the three-dimensional equations describing flows of fluids with internal inertia, where the potential function $W= W(\rho,\dot{\rho})$, is presented. The given equations include such models as the non-linear one-velocity model of a bubbly fluid with incompressible liquid phase at small volume concentration of gas bubbles, and the dispersive shallow water model. These models are obtained for special types of the function $W(\rho,\dot{\rho})$. Group classification separates out the function $W(\rho,\dot{\rho})$ at 15 different cases. Another part of the manuscript is devoted to one class of partially invariant solutions. This solution is constructed on the base of all rotations. In the gas dynamics such class of solutions is called the Ovsyannikov vortex. Group classification of the system of equations for invariant functions is obtained. Complete analysis of invariant solutions for the special type of a potential function is given.Comment: This is a contribution to the Proc. of the Seventh International Conference ''Symmetry in Nonlinear Mathematical Physics'' (June 24-30, 2007, Kyiv, Ukraine), published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA

Optimization of enzyme-assisted microwave extraction of Zanthoxylum limonella essential oil using response surface methodology

Abstract Zanthoxylum limonella essential oil possesses potential antimicrobial activity and is of considerable interest as food flavouring and traditional herb. In this study, an enzymolysis-pretreatment-microwave-assisted extraction (EP-MAE) method was used to extract Z. limonella essential oil. The response surface methodology (RSM) with Plackett–Burman design (PBD) and Box-Behnken design (BBD) models were employed to optimize conditions in the EP-MAE method. Seven variables including water to plant ratio, enzyme amount, incubation temperature, incubation time, shaking speed, microwave time, and microwave power were selected to determine the optimal values for extracting Z. limonella essential oil. As the results, four variables including water to plant ratio, enzyme amount, microwave time and power were evaluated as significant variables affecting on yield and volatile compounds of Z. limonella essential oil from both PBD and BBD experiments. The optimum conditions of EP-MAE was obtained as follows: water to plant ratio (11.16 mL/g), enzyme amount (0.68%), microwave time (36.73 min), and power (1665 W). The Z. limonella essential oil composition and its yield from EP-MAE was compared to those extracted from MAE and hydrodistillation. The optimal extraction conditions in the EP-MAE method enhanced significantly higher essential oil yield (7.89 ± 0.08 mg/g) compared to those found by MAE (7.26 ± 0.04 mg/g) and hydrodistillation (7.04 ± 0.03 mg/g), respectively. Fifty-one volatile components were identified among these methods, with similar major compounds of limonene, β-pinene, and α-phellandrene, showing percentage ranging between 34.59–35.78%, 19.91–22.67%, 8.47–8.75%, respectively. However, an extremely higher content of compounds was detected using the EP-MAE method. This study demonstrates the significance of EP-MAE, which may be applied as a more potent extraction method for essential oils in aromatic plants compared to MAE and hydrodistillation

The removal of Pb2+ ion by MnFe2O4/waste tea leaves biochar and mechanism of adsorption

In order to transform waste tea leaves into a useful/valuable material for removal of Pb ^2+ ions from wastewater, MnFe _2 O _4 /biochar was synthesized. The tea waste was pyrolyzed at 500 °C to obtain the biochar. Effects of the composition of tea leaves on the physicochemical properties of biochar were evaluated. Biochar and MnFe _2 O _4 /biochar were mainly organic matter. Regarding inorganic components, aside from Fe and Mn there were considerable albeit small amounts of the mineral elements K and Ca in the MnFe _2 O _4 /biochar. The MnFe _2 O _4 /biochar is porous with a specific surface area of 24.38 m ^2 g ^−1 , and the surface is loaded with MnFe _2 O _4 and amorphous MnO _2 particles. Also carboxylic acid, hydroxyl, and carbonyl functional groups were formed on the MnFe _2 O _4 /biochar surfaces. The surface area and pore volume characteristics of the MnFe _2 O _4 /biochar were also increased compared with the baseline biochar, and the prepared MnFe _2 O _4 /biochar had mesostructure. The modification of biochar into MnFe _2 O _4 /biochar improved adsorption of Pb ^2+ ions with the removal increased to ∼98%. The Freundlich isotherm and the pseudo-second order kinetic models matched well Pb ^2+ adsorption onto the MnFe _2 O _4 /biochar