Investigation of droplet size distribution for liquid-liquid emulsions in Taylor-Couette flows

In this paper, we investigate oil-in-water emulsions in a Taylor-Couette flow. A high-speed camera was employed to record the formation of those emulsions, and image processing was used to obtain the diameter of the droplets. No surfactants were added in order to study the pure effect of the fluid dynamical forces on the droplets. The results for three different oil-in-water emulsions show that the Sauter mean diameter considerably depends on the local shear rate and the material properties and that the droplet size distribution follows a log-normal distribution. We, therefore, propose to express the Sauter mean diameter normalized by Prandtl mixing length in terms of a correlation, which is based on the Kolmogorov turbulence theory. This correlation subsequently depends on the local shear rate and the material properties such as viscosity, density, and interfacial tension. The predictions of the correlation show fairly good agreement with the experimental measurement the Sauter mean diameter. Finally, comparing the predictions of the correlation to the data presented by Eskin et al. [Chem. Eng. Sci. 161 36–47; 2017] shows excellent agreement in the case, where the droplets are larger than the Kolmogorov length scale.     

Template-based growth of titanium dioxide nanorods by a particulate sol-electrophoretic deposition process

TiO 2 nanorods have been successfully grown into a track-etched polycarbonate (PC) membrane by a particulate sol-electrophoretic deposition from an aqueous medium.The prepared sols had a narrow particle size distribution around 17 nm and excellent stability against aging,with zeta potentials in the range of 47-50 mV at pH 2.It was found that TiO 2 nanorods were grown from dilute aqueous sol with a low,0.1-M concentration.Fourier transform infrared spectroscopy (FT-IR) analysis confirmed that a full conversi...     

Evaluation of linear and nonlinear convection schemes on multidimensional non‐orthogonal grids with applications to KVLCC2 tanker

Almost all evaluations of convection schemes reported in the literature are conducted using simple problems on uniform orthogonal grids; thus, having limited contribution when solving industrial computational fluid dynamics (CFD), where the grids are usually non‐orthogonal with distortions. Herein, several convection schemes are assessed in uniform and distorted non‐orthogonal grids with emphasis on industrial applications. Linear and nonlinear (TVD) convection schemes are assessed on analytical benchmarks in both uniform and distorted grids. To evaluate the performance of the schemes, four error metrics are used: dissipation, phase and L₁ errors, and the schemes' effective order of accuracy. Qualitative and quantitative deterioration of these error metrics as a function of the grid distortion metrics are investigated, and rigorous verifications are performed. Recommendations for effective use of the convection schemes based on the range of grid aspect ratio (AR), expansion ratio (ER) and skewness (Q) are included. A ship hydrodynamics case is studied, involving a Reynolds averaged Navier–Stokes simulation of a bare‐hull KVLCC2 tanker using linear and nonlinear convection schemes coupled with isotropic and anisotropic Reynolds‐stress (ARS) turbulence models using CFDShip‐Iowa v4. Predictions of local velocities and turbulent quantities from the midships to the nominal wake plane are compared with experimental fluid dynamics (EFD), and rigorous verification and validation analyses for integral forces and moments are performed for 0° and 12° drift angles. Best predictions are observed when coupling a second‐order TVD scheme with the anisotropic turbulence model. Further improvements are observed in terms of prediction of the vortical structures for 30° drift when using TVD2S‐ARS coupled with DES. Copyright © 2009 John Wiley & Sons, Ltd.     

A New Model for Prediction of One Electron Reduction Potential of Nitroaryl Compounds

This paper introduces a simple model for prediction of one electron reduction potential [E(RNO₂/R ^? NO₂^–)] of various nitroaryl compounds. The new method uses energy difference between highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) in gas phase at the B3LYP/6‐311++G** level (ΔE_HOMO‐LUMO) and some structural parameters. It was used for 35 nitroaryl compounds including nitrobenzenes, nitrofurans, 2‐nitroimidazoles, 4‐nitroimidazoles, 5‐ninuintidazoles, nitroazaindoles, nitroacridines, and miscellaneous nitroaryl compounds. The root mean square (rms) percent deviation and the average absolute error of predictions of E(RNO₂/R ^? NO₂^–) relative to experiment were decreased from 12.4 % and 0.42 V to 3.5 % and 0.11 V, respectively, upon consideration of several structural parameters. Increment of the value of ΔE_HOMO‐LUMO and inclusion of specific polar groups can increase thermodynamic stability of these compounds.     

Synthesis of a PEG-PNIPAm thermosensitive dendritic copolymer and investigation of its self-association

A Novel thermosensitive dendritic copolymer based on polyethylene glycol(PEG) and poly(Nisopropylacrylamide)(PNIPAm) with a cloud point(CP) around 36 ?C was successfully synthesized by preparation of a dendritic polyol and followed by atom transfer radical polymerization(ATRP) of N-isopropylacrylamide. The dendritic copolymer was characterized using gel-permeation chromatography(GPC), FTIR and 1H-NMR spectroscopy. The selfassociation behavior of the copolymer in aqueous medium was investigated by dynamic light scattering(DLS) and transmission electron microscopy(TEM). These investigations confirmed that the dendritic copolymer showed different association behaviors at various temperatures.     

Preparation and characterization of a novel water soluble amino chitosan (amino-CS) derivative for facilitated transport of CO<Subscript>2</Subscript>

With the goal of obtaining a water soluble polymeric carrier for preparation of fixed facilitated transport membranes, a water soluble amino containing chitosan derivative was prepared through Michael-addition reaction between chitosan and ethyl acrylate followed by amidation of the ester groups with an appropriate diamine. This derivative was characterized using ¹H-NMR spectroscopy. Then, facilitated transport membranes were prepared by casting a thin layer of chitosan derivative/poly(vinyl alcohol) blend on a porous polysolfune support; and the effect of fixed carrier’s content, feed temperature and feed pressure on the CO₂ permeance, and CO₂/CH₄ selectivity of produced membranes were studied. A facilitated transport mechanism for CO₂ through this membrane was concluded.     

Exploring students' mathematical performance,metacognitive experiences and skills in relation to fundamental theorem of calculus

Several studies have explored students’ understanding of the relationships between definite integrals and areas under curve(s). So far, however, there has been less attention to students’ understanding of the Fundamental Theorem of Calculus (FTC). In addition, students’ metacognitive experiences and skills whilst solving FTC questions have not previously been explored. This paper explored students’ mathematical performance, metacognitive experiences and metacognitive skills in relation to FTC questions by interviewing nine university and eight Year 13 students. The findings show that several students had difficulty solving questions related to the FTC and that students’ metacognitive experiences and skills could be further developed.     

Revised Bloom's taxonomy and integral calculus: unpacking the knowledge dimension

In this paper, the knowledge dimension for Revised Bloom's taxonomy (RBT) is unpacked for integral calculus. As part of this work, the 11 subtypes of the knowledge dimension are introduced, and through document analysis of chapter 4 of the RBT handbook, these subtypes are defined. Then, by consulting materials frequently used for teaching integral calculus, each subtype is exemplified. The developed dimension may enable or enhance opportunities for dialogue between lecturers, teachers, and researchers about how to develop and align educational objectives, teaching activities, and assessments in integral calculus, or how metacognition and metacognitive knowledge could be used to support teaching and learning.     

On smoothing,regularization, and averaging in stochastic approximation methods for stochastic variational inequality problems

Traditionally, most stochastic approximation (SA) schemes for stochastic variational inequality (SVI) problems have required the underlying mapping to be either strongly monotone or monotone and Lipschitz continuous. In contrast, we consider SVIs with merely monotone and non-Lipschitzian maps. We develop a regularized smoothed SA (RSSA) scheme wherein the stepsize, smoothing, and regularization parameters are reduced after every iteration at a prescribed rate. Under suitable assumptions on the sequences, we show that the algorithm generates iterates that converge to the least norm solution in an almost sure sense, extending the results in Koshal et al. (IEEE Trans Autom Control 58(3):594–609, 2013) to the non-Lipschitzian regime. Additionally, we provide rate estimates that relate iterates to their counterparts derived from a smoothed Tikhonov trajectory associated with a deterministic problem. To derive non-asymptotic rate statements, we develop a variant of the RSSA scheme, denoted by aRSSA\(_r\), in which we employ a weighted iterate-averaging, parameterized by a scalar r where \(r = 1\) provides us with the standard averaging scheme. The main contributions are threefold: (i) when \(r<1\) and the parameter sequences are chosen appropriately, we show that the averaged sequence converges to the least norm solution almost surely and a suitably defined gap function diminishes at an approximate rate \(\mathcal{O}({1}\slash {\root 6 \of {k}})\) after k steps; (ii) when \(r<1\), and smoothing and regularization are suppressed, the gap function admits the rate \(\mathcal{O}({1}\slash {\sqrt{k}})\), thus improving the rate \(\mathcal{O}(\ln (k)/\sqrt{k})\) under standard averaging; and (iii) we develop a window-based variant of this scheme that also displays the optimal rate for \(r < 1\). Notably, we prove the superiority of the scheme with \(r < 1\) with its counterpart with \(r=1\) in terms of the constant factor of the error bound when the size of the averaging window is sufficiently large. We present the performance of the developed schemes on a stochastic Nash–Cournot game with merely monotone and non-Lipschitzian maps.     

Relative T -Injective Modules and Relative T -Flat Modules

Let T be a Wakamatsu tilting module. A module M is called (n, T)-copure injective (resp. (n, T)-copure flat) if ɛ _T ¹ (N, M) = 0 (resp. Γ₁ ^T (N, M) = 0) for any module N with T-injective dimension at most n (see Definition 2.2). In this paper, it is shown that M is (n, T)-copure injective if and only if M is the kernel of an I _n (T)-precover f: A → B with A ∈ Prod T. Also, some results on Prod T-syzygies are presented. For instance, it is shown that every nth Prod T-syzygy of every module, generated by T, is (n, T)-copure injective.