Symmetrization in Geometry

The concept of an $i$-symmetrization is introduced, which provides a convenient framework for most of the familiar symmetrization processes on convex sets. Various properties of $i$-symmetrizations are introduced and the relations between them investigated. New expressions are provided for the Steiner and Minkowski symmetrals of a compact convex set which exhibit a dual relationship between them. Characterizations of Steiner, Minkowski and central symmetrization, in terms of natural properties that they enjoy, are given and examples are provided to show that none of the assumptions made can be dropped or significantly weakened. Other familiar symmetrizations, such as Schwarz symmetrization, are discussed and several new ones introduced.Comment: A chacterization of central symmetrization has been added and several typos have been corrected. This version has been accepted for publication on Advances in Mathematic

EVALUATION OF ELECTRODE SURFACE TREATMENTS IN SLUDGE ELECTRO-OSMOSIS DEWATERING”

The drying of sludge produced by Wastewater Treatment Plants (WWTPs) is a very hard process due to the presence of the colloid fraction. Electro-osmosis could be a suitable technique to reduce the water content of the final sludge. Electrical fields of 10 V/cm, 15 V/cm and 20 V/cm have been studied for electro-osmosis tests in a static or dynamic apparatus, obtaining a dry solids content up to 40-45%, with respect to 25-30% obtained by mechanical methods. In order to optimise the apparatus, the corrosion behaviour of the anodic material appears the main critical aspect, due to the high circulating current density. Moreover, wear may be detrimental for the surface of rotating electrodes. We then investigated the behaviour of materials used as electrodes mainly by evaluating the efficiency of the process and their surface aspect after treatment. The full understanding of the electrochemical reactions developed at the anode are a key factor for the material choice. We compared the efficiency and the corrosion resistance of anodes made of titanium MMO with respect to bare stainless steel (AISI 304) and stainless steel coated by PVD technique with TiN, AlTiN and DLC. Characterization of the anodes samples by roughness tests and by AFM show that corrosion resistance of the DSA was the most suitable for our application. However, efficiencies of the electro-osmosis process for all the materials used have been found comparable, in terms of developed current densities and total energy consumptions, for low-test duration

ADVANCES IN THE HYDROCARBON GAS-LIQUID EQUILIBRIUM UNDERSTANDING IN WATER AND OIL-BASED DRILLING FLUIDS

DETERMINATION OF C1-C5 HYDROCARBONS IN DRILLING MUDS Davide Doninelli, Jenny Rizzola, and Paolo Gronchi Politecnico di Milano - Chemistry, Material and Chemical Engineering Dept. “G. Natta”; P.za Leonardo da Vinci, 32 20133 Milano, Italy. E-mail: [email protected]. The aim of this work was to evaluate the amount of C1-C5 gases dissolved in the drilling muds through the definition of a analytical model of the partition coefficient between the hydrocarbon concentration in the gas phase and in the muddy. The conveniences of the work may be: • to verify the convenience of a possible gas recover; • to evaluate the environmental impact of the degassing treatment unit associated to the gas discharge in atmosphere; • to evaluate the desorption times in order to optimize the mud treatment process. The method is centered on the calculation of the partition coefficient starting from the analysis of gas phase at the equilibrium with a known amount of dissolved hydrocarbon. A laboratory apparatus was built, constituted by a heated jacketed reactor, with temperature control, to simulate the absorption of the hydrocarbon gas during the drilling and a second vessel for the gas desorption until equilibrium. The study is divided in two parts as the operations were performed at 303 K and at 323 K temperatures. The first part (at 303K) included the study of the absorption and desorption of C1-C4 gases in different muds: aqueous-based muds (PHPA and HPWBM) and oil-based (LTOBM). The choice of the sludge was made in reason to emulate in a laboratory, the properties of most drilling fluids. In the second part we examined pentane too. Pentane is a liquid hydrocarbon at ambient condition (boiling point 310 K) but could be used as gas at 323K . The right technology for the use pentane in gas phase must takes into account the vapor-liquid equilibrium when injected as liquid for the absorption into the muds. We observed that the partition coefficient decreases increasing molecular weight up to butane with all the mud, with pentane instead we have two different behaviors for water and the oil based muds: with the PHPA and HPWBM (water-based) the constant decreases instead in the LTOBM (oil-based) it remains constant. As regards the trend with the temperature we observed two different behaviors: with the aqueous mud the constant increases with temperature, and for the oil mud remains constant. Discussion about relation between mud composition and the gas concentrations are tentatively reported. Acknowledgements The authors would like to acknowledge financial support from GEOLOG S.p.A. (Ital

Extracorporeal support for pulmonary resection: current indications and results.

Extracorporeal assistances are exponentially used for patients, with acute severe but reversible heart or lung failure, to provide more prolonged support to bridge patients to heart and/or lung transplantation. However, experience of use of extracorporeal assistance for pulmonary resection is limited outside lung transplantation. Airways management with standard mechanical ventilation system may be challenging particularly in case of anatomical reasons (single lung), presence of respiratory failure (ARDS), or complex tracheo-bronchial resection and reconstruction. Based on the growing experience during lung transplantation, more and more surgeons are now using such devices to achieve good oxygenation and hemodynamic support during such challenging cases. We review the different extracorporeal device and attempt to clarify the current practice and indications of extracorporeal support during pulmonary resection

ELECTRO-OSMOTIC DEWATERING OF SEWAGE SLUDGE: PRELIMINARY RESULTS

About half of the organic pollution load treated by the activated sludge process is oxidised and converted into water and carbon dioxide, while the remaining is converted into biomass, called “excess biological sludge” or “waste sludge”. At present, this technique is the cheapest way to remove colloidal and soluble organic pollutants from sewage, but it produces a huge amount of liquid waste sludge, with a dry solid (DS) content of less than 2%, rich in organic substances, mostly biodegradable. Therefore, it needs further processes to reduce its volume, by reducing its water content, and to reduce its polluting potential, due to its high content of biodegradable organic matter. However, sludge produced by Wastewater Treatment Plants (WWTPs) usually has a poor dewaterability. Industrially, mechanical dewatering is the method employed to increase the dry solids (DS) of sewage sludge. The aim of dewatering is the decrease of transport and disposal costs, but the efficiency of the mechanical dehydration methods is low. Electro-osmosis could be a suitable technique to reduce water content of the final sludge by the application of an electric field. Studies about electro-dewatering reported that the DS could increase to values around 40-45%, with respect to 25-30% obtained by mechanical methods, such as centrifuge, filter press and belt press. Aim Here, we investigated the parameters affecting pressure-driven electro-dewatering, with a static and a dynamic device, starting from types of sludge mechanically pre-dehydrated. We focused on the optimization of operating conditions to achieve the best results in terms of solids percentage at the minimum energy consumption. Methods Experiments have been performed by means of a lab-scale device able to produce both a mechanical pressure and an electric field. The use of both these systems could be efficient to increase the amount of dry solids in the final sludge. This device, as illustrated in Figure 1, consists of: • Cylindrical glass vessel (h=176 mm, Ø=80 mm) • Cooling water-jacket • Compressed air system (1-4.5 bar) • Double effect cylinder (200 mm stroke) SMC-CP96 (piston) • DC power supply (30 V-5 A) • Anode: DSA Ti (MMO), fixed to the piston • Cathode: stainless steel mesh (AISI 304) • Cloth: PTT (polytrimethyleneterephthalate) Figure 1-Equipment schematic of electro-dewatering device. Main Results The applied voltage has been set at 10 V, 15 V and 20 V and pressures at 3 bar. The results confirmed values of final DS around 40%. Initial DS and sludge conductivity, together with the applied electric field, are the key factors of electro-osmosis tests. The rotating piston highlighted that a mixing of sludge during the potential application could slightly increase the sludge conductivity, but cakes must be kept under 1.5 cm of thickness in order to achieve a good dewatering. In conclusion, in this paper we assess the feasibility of the electro-osmosis dewatering. It is a promising technique to remove water from sewage sludge, since it is able to increase DS of 15% on average with respect industrial mechanical dewatering. Moreover, this work proved that the treatment of a high DS cake is more difficult than a non-dewatered sludge due to a lower conductivity during the process

Influence of sludge characteristics on pressure-driven electro-dewatering of stabilized sewage sludge

The feasibility of the pressure-driven electro-dewatering (EDW) on aerobically and anaerobically stabilised sludge samples, taken from four different wastewater treatment plants around the metropolitan area of Milan (Italy), has been assessed. First, sewage sludges were characterized by measuring DS content, VS/DS ratio, pH, conductivity, zeta potential and capillary suction time (CST) of the liquid fraction. Then, after a preliminary centrifugation of the sludge samples in the laboratory, pressure-driven EDW tests have been performed in a lab-scale device, under the application of 300 kPa of pressure and an applied voltage of 15 V. The DS content increased up to 18.4-31.1%, (with an increase of 8.6% to 23.0% from the initial DS value) depending on the characteristics of the sludge samples and the polymer dosage. If compared with EDW tests, the increase due to the sole effect of pressure ranged from 3 to 10% and strictly depended on polymer dosage. The characteristics of sludge that affect the increase of the DS content were investigated during both the pressure-driven stage and the EDW stage. Polyelectrolyte addition (4 and 8 g/kgDS) mainly affected the pressure-driven phase of the tests. However, the VS/DS ratio was the main factor affecting the pressure-driven stage on the unconditioned aerobically stabilised samples. CST values could also reliably predict the efficiency of this stage during experiments

Pressure-driven electro-dewatering applied for sludge: Economic & environmental life cycle assessment

Dewatering plays an important role in sludge minimization and reuse. In this study, pressure-driven electro-dewatering (EDW) was investigated using a lab device and various operating parameters were optimised. Furthermore, the EDW system’s economic and environmental performances were evaluated using Life Cycle Assessment. These results can be interesting for the stakeholders within the WWTP industry who are considering upgrading from the conventional mechanical dewatering to the EDW