Lie-group method solution for two-dimensional viscous flow between slowly expanding or contracting walls with weak permeability

The non-linear equations of motion describing the laminar, isothermal and incompressible flow in a rectangular domain bounded by two weakly permeable, moving porous walls, which enable the fluid to enter or exit during successive expansions or contractions, are considered. We apply Lie-group method for determining symmetry reductions of partial differential equations. Lie-group method starts out with a general infinitesimal group of transformations under which given partial differential equations are invariant, then, the determining equations are derived. The determining equations are a set of linear differential equations, the solution of which gives the infinitesimals of the dependent and independent variables. After the group has been determined, a solution to the given partial differential equation may be found from the invariant surface condition such that its solution leads to similarity variables that reduce the number of independent variables in the system. Effect of the permeation Reynolds number R_e and the dimensionless wall dilation rate α on self-axial velocity have been studied both analytically and numerically and the results are plotted.     

Separation of europium and thulium from mixed KI−H2SO4 solutions

The extraction of Tm with HDEHP from H₂SO₄, HCl and HBr is inversely proportional to the third power of the hydrogen ion concentration while the extraction is small with HDEHP, LA-2 and TBP from binary mixtures of acids. The extraction of both Eu and Tm with HDEHP from KI solutions decreases in the presence of small concentrations of H₂SO₄. The decrease is sharper in case of Eu leading to high separation factors between Eu and Tm from KI?H₂SO₄ mixtures.     

Aqueous polymerization of methyl methacrylate catalyzed by copper metal and some of its compounds

The aqueous polymerization of methyl methacrylate (MMA) with sodium bisulfite as initiator was carried out in a nitrogen atmosphere with and without inorganic substances like copper metal, cupric and cuprous oxides, and cupric sulfide. It was also done in the presence of organocopper compounds like copper phthalocyanine and copper biphthalocyanine. The catalytic effect of these compounds was studied. Mildly heated cupric sulfide proved to have a small catalytic effect on the polymerization process that may be attributed to the retarding effect of the released elementary sulfur. The catalytic effect of the different copper compounds and the copper metal equivalent contained in them was studied. The polymerization process revealed that cuprous and cupric oxides possess the highest catalytic influence. An attempt was made to investigate the role of the different anions on the polymerization process. It was found that an increase on the concentration of the copper compounds leads to a corresponding increase in the catalytic effect. It was also observed that the behavior of insoluble copper catalysts is different from that of the soluble. The effect of these catalysts on the average molecular weight of the poly(methyl methacrylate) (PMMA) produced was also examined.     

Emulsion polymerization of vinyl acetate initiated by potassium persulfate-cyclohexanone sodium bisulfite redox pair system

The emulsion polymerization of vinyl acetate using potassium persulfate and cyclohexanone sodium bisulfite as redox pair initiation system was studied. The rate of polymerization, maximum conversion, and the number of polymer particles produced were found to change with redox initiator, monomer and emulsifier concentrations, and temperature variation. The rate of polymerization was found to be dependent on the initiator, the monomer, and the emulsifier concentrations to the 0.88, 0.22, and 0.20 powers, respectively. The K₂S₂O₈–NaHSO₃ redox system was found to decrease maximum conversion and doesn't form a stable emulsion. The apparent arrhenius activation energy (E^a) estimated for the polymerization system was 65.6 kJ/mol. The viscosity average molecular weights for some obtained poly(vinyl acetate) were determined.     

Experiments on the flow past long circular cylinders in a shear flow

This paper describes an experimental investigation of the flow past circular cylinders, with the mean flow perpendicular to the cylinder axis, at conditions that yield a strong three-dimensional behaviour. The experiments were carried out in the subcritical regime. Long cylinders with end plates were subjected to shear flow with a linear velocity profile in the spanwise direction generated by means of a curved gauze. It was concluded that spanwise cellular structures of vortex shedding emerged in the wake, more clearly for some boundary conditions than others. These structures are characterised by a portion of spanwise length, a cell, having constant shedding frequency over a time average, which implies that there were no vortex dislocations inside that cell during that time. These features were studied using flow visualisation and hot-film anemometry. Spectra of the local shedding frequency are shown, revealing the effect of the shear parameter (=0.02 and 0.04) and aspect ratio L/D (=20.6 and 8) on the stability and geometry of the cells at several Reynolds numbers in the range of 3.13×10³Re_m1.25×10⁴.     

Some problems of simple finite deformation of viscoelastic bodies

Boltzmann's superposition principle is extended to large strains in the case where the principal strain axes do not change with time and are identically directed at all points of the body. The relations obtained are confirmed by experiment. On the basis of these relations the author examines the problem of large strains of a heated viscoelastic cylinder subjected to the action of time-dependent internal and external pressures, and the analogous problem in the presence of a reinforcing cylindrical shell. The solution of the solving nonlinear integral equation of the latter problem is unique and is obtained in the form of a convergent infinite series.Mekhanika Polimerov, Vol. 2, No. 4, pp. 508–518, 1966     

Ziziphus nummularia: A Comprehensive Review of Its Phytochemical Constituents and Pharmacological Properties

Ziziphus nummularia, a small bush of the Rhamnaceae family, has been widely used in traditional folk medicine, is rich in bioactive molecules, and has many reported pharmacological and therapeutic properties. Objective: To gather the current knowledge related to the medicinal characteristics of Z. nummularia. Specifically, its phytochemical contents and pharmacological activities in the treatment of various diseases such as cancer, diabetes, and cardiovascular diseases, are discussed. Methods: Major scientific literature databases, including PubMed, Scopus, ScienceDirect, SciFinder, Chemical Abstracts, Medicinal and Aromatic Plants Abstracts, Henriette’s Herbal Homepage, Dr. Duke’s Phytochemical and Ethnobotanical Databases, were searched to retrieve articles related to the review subject. General web searches using Google and Google scholar were also utilized. The search period covered articles published between 1980 and the end of October 2021.The search used the keywords ‘Ziziphus nummularia’, AND (‘phytochemical content’, ‘pharmacological properties, or activities, or effects, or roles’, ‘anti-inflammatory’, ‘anti-drought’, ‘anti-thermal’, ‘anthelmintic’, ‘antidiabetic’,’ anticancer’, ‘anticholinesterase’, ‘antimicrobial’, ‘sedative’, ‘antipyretic’, ‘analgesic’, or ‘gastrointestinal’). Results: This plant is rich in characteristic alkaloids, especially cyclopeptide alkaloids such as nummularine-M. Other phytochemicals, including flavonoids, saponins, glycosides, tannins, and phenolic compounds, are also present. These phytochemicals are responsible for the reported pharmacological properties of Z. nummularia, including anti-inflammatory, antioxidant, antimicrobial, anthelmintic, antidiabetic, anticancer, analgesic, and gastrointestinal activities. In addition, Z. nummularia has anti-drought and anti-thermal characteristics. Conclusion: Research into the phytochemical and pharmacological properties of Z. nummularia has demonstrated that this plant is a rich source of novel bioactive compounds. So far, Z. nummularia has shown a varied pharmacological profile (antioxidant, anticancer, anti-inflammatory, and cardioprotective), warranting further research to uncover the therapeutic potential of the bioactives of this plant. Taken together, Z. nummularia may represent a new potential target for the discovery of new drug leads.     

Origanum syriacum Phytochemistry and Pharmacological Properties: A Comprehensive Review

Herbal medicine has been gaining special interest as an alternative choice of treatment for several diseases, being generally accessible, cost-effective and safe, with fewer side-effects compared to chemically synthesized medicines. Over 25% of drugs worldwide are derived from plants, and surveys have shown that, when available, herbal medicine is the preferred choice of treatment. Origanum syriacum (Lamiaceae) is a widely used medicinal plant in the Middle East, both as a home and a folk remedy, and in the food and beverage industry. Origanum syriacum contains numerous phytochemical compounds, including flavonoids, phenols, essential oils, and many others. Because of its bioactive compounds, O. syriacum possesses antioxidant, antimicrobial, and antiparasitic capacities. In addition, it can be beneficial in the treatment of various diseases such as cancer, neurodegenerative disorders, and peptic ulcers. In this review, the chemical compositions of different types of extracts and essential oils from this herb will first be specified. Then, the pharmacological uses of these extracts and essential oils in various contexts and diseases will be discussed, putting emphasis on their efficacy and safety. Finally, the cellular and molecular mechanisms of O. syriacum phytochemicals in disease treatment will be described as a basis for further investigation into the plant’s pharmacological role.