Combinatorial Aspects of the Splitting Number

We define the strong splitting number, prove that it equals s when exists, and put some restrictions on the possibility that s is a singular carcinal

The ultrafilter number for singular cardinals

We prove the consistency of a singular cardinal $\lambda$ with small value of the ultrafilter number $u_\lambda$, and arbitrarily large value of $2^\lambda$.Comment: 8 page

Strong polarized relations for the continuum

We prove that the strong polarized relation for the continuum holds for $\aleph_0$ and for every supercompact cardinal. We use iteration of Mathias forcing.Comment: 9 page

Emulsifiers as Additives in Fats: Effect on Polymorphic Transformations and Crystal Properties of Fatty Acids and Triglycerides

The role of emulsifiers in polymorphic transformations of fats and fatty acids is treated in this paper. Their effect as crystal modifiers in solution-mediated transformations (in fatty acids) is compared to that of a dynamic controller of polymorphic transformations in triglycerides. The importance of chemical structure both in the hydrophilic and in the hydrophobic moieties of the emulsifier for an inhibitory effect on phase transitions has been emphasized. The emulsifier solubility and crystallization behavior in different solvents are probably the main factors affecting its ability to interfere with the kinetics of solution-mediated transformations. On the other hand, certain requirements for a specific chemical structure of the emulsifier which provides good structure compatibility, must be met in order to affect the kinetics and mechanism of solid-solid or melt-mediated transformations. A mechanism of emulsifier incorporation in the fat and its effect in delaying the polymorphic transformation of tristearin is proposed. It has been concluded that the presence of the emulsifier does not dictate the formation of any preferred polymorph but rather controls the mobility of the molecules and their facility to undergo polymorphic transformations. The relationship between polymorphism in fats and presence of additives plays a major role in the food industry, because of the serious quality implications involved in phase transitions

Water Solubilization Using Nonionic Surfactants from Renewable Sources in Microemulsion Systems

In this study the effect of temperature, NaCl and oils (hydrocarbons: C8–C16) on the formation and solubilization capacity of the systems of oil/monoacylglycerols (MAG):ethoxylated fatty alcohols (CEO20)/propylene glycol (PG)/water was investigated. The effects of the surfactant mixture on the phase behavior and the concentration of water or oil in the systems were studied at three temperatures (50, 55, 60 °C) and with varied NaCl solutions (0.5; 2; 11%). Electrical conductivity measurement, FTIR spectroscopy and the DSC method were applied to determine the structure and type of the microemulsions formed. The dimension of the microemulsion droplets was characterized by dynamic light scattering. It has been stated that the concentration of CEO20 has a strong influence on the shape and extent of the microemulsion areas. Addition of a nonionic surfactant to the mixture with MAG promotes an increase in the area of microemulsion formation in the phase diagrams, and these areas of isotropic region did not change considerably depending on the temperature, NaCl solution and oil type. It was found that, depending on the concentration of the surfactant mixture, it was possible to obtain U-type microemulsions with dispersed particles size distribution ranging from 25 to 50 nm and consisting of about 30–32% of the water phase in the systems. The conditions under which the microemulsion region was found (electrolyte and temperature—insensitive, comparatively low oil and surfactant concentration) could be highly useful in detergency

Preparation of double emulsions using hybrid polymer/silica particles: New pickering emulsifiers with adjustable surface wettability

A facile route for the preparation of water-in-oil-in-water (w/o/w) double emulsions is described for three model oils, namely, n-dodecane, isopropyl myristate, and isononyl isononanoate, using fumed silica particles coated with poly(ethylene imine) (PEI). The surface wettability of such hybrid PEI/silica particles can be systematically adjusted by (i) increasing the adsorbed amount of PEI and (ii) addition of 1-undecanal to the oil phase prior to homogenization. In the absence of this long-chain aldehyde, PEI/silica hybrid particles (PEI/silica mass ratio = 0.50) produce o/w Pickering emulsions in all cases. In the presence of 1-undecanal, this reagent reacts with the primary and secondary amine groups on the PEI chains via Schiff base chemistry, which can render the PEI/silica hybrid particles sufficiently hydrophobic to stabilize w/o Pickering emulsions at 20 °C. Gas chromatography, 1H NMR and X-ray photoelectron spectroscopy provide compelling experimental evidence for this in situ surface reaction, while a significant increase in the water contact angle indicates markedly greater hydrophobic character for the PEI/silica hybrid particles. However, when PEI/silica hybrid particles are prepared using a relatively low adsorbed amount of PEI (PEI/silica mass ratio = 0.075) only o/w Pickering emulsions are obtained, since the extent of surface modification achieved using this Schiff base chemistry is insufficient. Fluorescence microscopy and laser diffraction studies confirm that highly stable w/o/w double emulsions can be achieved for all three model oils. This is achieved by first homogenizing the relatively hydrophobic PEI/silica hybrid particles (PEI/silica mass ratio = 0.50) with an oil containing 3% 1-undecanal to form an initial w/o emulsion, followed by further homogenization using an aqueous dispersion of relatively hydrophilic PEI/silica particles (PEI/silica mass ratio = 0.075). Dye release from the internal aqueous cores into the aqueous continuous phase was monitored by visible absorption spectroscopy. These studies indicate immediate loss of 12-18% dye during the high speed homogenization that is required for double emulsion formation, but no further dye release is observed at 20 °C for at least 15 days thereafter