Turbulent flow of non-Newtonian substances

Summary A unique shear stress-shear rate relationship exists for laminar flow of any time independent substance in a tube, whereas this is not the case for turbulent flow. In order to obtain a unique relationship for turbulent flow, a new approach based on the elementary theoretical interpretation of experimental data is adopted in the present paper. In particular, wall shear stress is found to be a unique function of a new turbulent pseudo shear rate term. In this relationship therè are two parameters which characterize a given substance — the limiting viscosity at high shear rateµ _m and a factor _m which takes into account modification of turbulent structure by the non-Newtonian properties. Both of these parameters must be determined experimentally. Methods of predicting pressure gradients and of scaling up are outlined. In applying the approach to suspensions in which the solid phase has a density greater than that of the liquid medium, it may be important to determine the increment in shear stress equivalent to the energy required to maintain the solid particles in suspension.The validity of this approach is confirmed by data for the flow of a variety of substances including kaolin suspensions and Carbopol solutions in tubes ranging in diameter from 1.5 to 20 mm. Nomenclature C volume fraction solid in suspension - D tube diameter - f Darcy-Weisbach friction factor - g gravitational acceleration - K _s proportionality constant defined by eq. [10] - L length of tube - P pressure - Re Reynolds number - t exponent defined by eq. [1] - V mean velocity - V ^* volume of particles in pipe lengthL - W settling velocity of particles - _m factor defined by eq. [1] - shear rate - turbulent pseudo shear rate defined by eqs. [8] and [9] - _w wall shear stress - ( _w) _s increment in wall shear stress due to presence of settling particles - µ _m limiting viscosity at high rate of shear - ₁ density of carrier liquid - _m density of mixture - _s density of solid Professor of Chemical Engineering, University of Toronto and scientific advisor to Worthington (Canada) Ltd.With 8 figures     

Thermographic detection of adhesive-bond and interlaminar flaws in composites

This paper reports the development of a liquid-crystal passive thermographic technique for the detection of adhesive-bond-line and interlaminar flaws in composite materials. The technique was successfully used for the detection of flaws in three composite systems: E-glass/epoxy, graphite/epoxy and HMC. Thermographic results are compared to ultrasonic C-scan results to assess the relative effectiveness of the new technique. A photomicrographic study was also used to verify the detected flaws and to characterize the type and extent of the actual damage.     

Polymer contribution to the thermal conductivity and viscosity in a dilute solution (Fraenkel Dumbbell model)

The phase-space kinetic theory for polymeric liquid mixtures is used to obtain an expression for the polymer contribution to the thermal conductivity of a nonflowing, dilute solution of polymers, where the polymer molecules are modeled as Fraenkel dumbbells. This theory takes into account three mechanisms for the energy transport: diffusion of kinetic energy (including the Öttinger-Petrillo term), diffusion of intramolecular energy, and the work done against the intramolecular forces. This paper is an extension of previous developments for the Hookean dumbbell model and the finitely-extensible dumbbell model. A comparison among the dumbbell results suggests that the thermal conductivity increases with chain stiffness. In addition, the zero-shear-rate viscosity and first normal-stress coefficient are also given for the Fraenkel dumbbell model.Dedicated to Prof. John D. Ferry on the occasion of his 85th birthday.     

Viscosity Solutions of a Degenerate Parabolic-Elliptic System Arising in the Mean-Field Theory of Superconductivity

In a Type‐II superconductor the magnetic field penetrates the superconducting body through the formation of vortices. In an extreme Type‐II superconductor these vortices reduce to line singularities. Because the number of vortices is large it seems feasible to model their evolution by an averaged problem, known as the mean-field model of superconductivity. We assume that the evolution law of an individual vortex, which underlies the averaging process, involves the current of the generated magnetic field as well as the curvature vector. In the present paper we study a two‐dimensional reduction, assuming all vortices to be perpendicular to a given direction. Since both the magnetic field H and the averaged vorticity ω are curl‐free, we may represent them via a scalar magnetic potential q and a scalar stream function ψ, respectively. We study existence, uniqueness and asymptotic behaviour of solutions (ψ, q) of the resulting degenerate elliptic‐parabolic system (with curvature taken into account or not) by means of viscosity and weak solutions. In addition we relate (ψ, q) to solutions (ω, H) of the mean‐field equations without curvature. Finally we construct special solutions of the corresponding stationary equations with two or more superconducting phases. (Accepted August 8, 1997)     

Intermittency and Regularity Issues in 3<Emphasis Type="Italic">D</Emphasis> Navier-Stokes Turbulence

Two related open problems in the theory of 3D Navier-Stokes turbulence are discussed in this paper. The first is the phenomenon of intermittency in the dissipation field. Dissipation-range intermittency was first discovered experimentally by Batchelor and Townsend over fifty years ago. It is characterized by spatio-temporal binary behaviour in which long, quiescent periods in the velocity signal are interrupted by short, active ‘events’ during which there are violent fluctuations away from the average. The second and related problem is whether solutions of the 3D Navier-Stokes equations develop finite time singularities during these events. This paper shows that Leray’s weak solutions of the three-dimensional incompressible Navier-Stokes equations can have a binary character in time. The time-axis is split into ‘good’ and ‘bad’ intervals: on the ‘good’ intervals solutions are bounded and regular, whereas singularities are still possible within the ‘bad’ intervals. An estimate for the width of the latter is very small and decreases with increasing Reynolds number. It also decreases relative to the lengths of the good intervals as the Reynolds number increases. Within these ‘bad’ intervals, lower bounds on the local energy dissipation rate and other quantities, such as ||u(·, t)||_∞ and ||∇u(·, t)||_∞, are very large, resulting in strong dynamics at sub-Kolmogorov scales. Intersections of bad intervals for n≧1 are related to the potentially singular set in time. It is also proved that the Navier-Stokes equations are conditionally regular provided, in a given ‘bad’ interval, the energy has a lower bound that is decaying exponentially in time.Final version 17 March 05. Original version November 03.     

Development of a GC/Q-ToF-MS Method Coupled with Headspace Solid-Phase Microextraction to Evaluate the In Vitro Metabolism of β-Caryophyllene

Sample preparation remains both a challenging and time-consuming process in the field of bioanalytical chemistry. Many traditional techniques often require multi-step processes, which can introduce additional errors to the analytical method. Given the complexity of many biological matrices, thorough analyte extraction presents a major challenge to researchers. In the present study, a headspace solid-phase microextraction (HS-SPME) coupled with a GC/Q-ToF-MS method, was developed to quantify in vitro metabolism of β-caryophyllene by both human liver microsome (HLM) and S9 liver fractions. Validation of the method was demonstrated both in terms of linearity (R² = 0.9948) and sensitivity with a limit of detection of 3 ng/mL and a limit of quantitation of 10 ng/mL. In addition, the method also demonstrated both inter- and intra-day precision with the relative standard deviation (RSD) being less than 10% with four concentrations ranging from 50–500 ng/mL. Since this method requires no solvents and minimal sample preparation, it provides a rapid and economical alternative to traditional extraction techniques. The method also eliminates the need to remove salts or buffers, which are commonly present in biological matrices. Although this method was developed to quantify in vitro metabolism of one analyte, it could easily be adapted to detect or quantify numerous volatiles and/or semi-volatiles found in biological matrices.     

Lysinated Multiwalled Carbon Nanotubes with Carbohydrate Ligands as an Effective Nanocarrier for Targeted Doxorubicin Delivery to Breast Cancer Cells

Multiwalled carbon nanotubes (MWCNTs) are elongated, hollow cylindrical nanotubes made of sp2 carbon. MWCNTs have attracted significant attention in the area of drug delivery due to their high drug-loading capacity and large surface area. Furthermore, they can be linked to bioactive ligands molecules via covalent and noncovalent bonds that allow for the targeted delivery of anticancer drugs such as doxorubicin. The majority of methodologies reported for the functionalization of MWCNTs for drug delivery are quite complex and use expensive linkers and ligands. In the present study, we report a simple, cost-effective approach for functionalizing MWCNTs with the carbohydrate ligands, galactose (GA), mannose (MA) and lactose (LA), using lysine as a linker. The doxorubicin (Dox)-loaded functionalized MWCNTs were characterized using FT-IR, NMR, Raman, XRD and FE-SEM. The drug–loaded MWCNTs were evaluated for drug loading, drug release and cell toxicity in vitro, in breast cancer cells. The results indicated that the carbohydrate-modified lysinated MWCNTs had greater Dox loading capacity, compared to carboxylated MWCNTs (COOHMWCNTs) and lysinated MWCNTs (LyMWCNTs). In vitro drug release experiments indicated that the carbohydrate functionalized LyMWCNTs had higher Dox release at pH 5.0, compared to the physiological pH of 7.4, over 120 h, indicating that they are suitable candidates for targeting the tumor microenvironment as a result of their sustained release profile of Dox. Doxorubicin-loaded galactosylated MWCNTs (Dox-GAMWCNTs) and doxorubicin loaded mannosylated MWCNTs (Dox-MAMWCNTs) had greater anticancer efficacy and cellular uptake, compared to doxorubicin–loaded lactosylated MWCNTs (Dox-LAMWCNTs) and pure Dox, in MDA-MB231 and MCF7 breast cancer cells. However, neither the ligand conjugated multiwall blank carbon nanotubes (GAMWCNTs, MAMWCNTs and LAMWCNTs) nor the lysinated multiwalled blank carbon nanotubes produced significant toxicity in the normal cells. Our results suggest that sugar-tethered multiwalled carbon nanotubes, especially the galactosylated (Dox-GAMWCNTs) and mannosylated (Dox-MAMWCNTs) formulations, may be used to improve the targeted delivery of anticancer drugs to breast cancer cells.     

Tuning reactivity in trimetallic dual-atom alloys: molecular-like electronic states and ensemble effects

Single-atom alloys (SAAs) have drawn significant attention in recent years due to their excellent catalytic properties. Controlling the geometry and electronic structure of this type of localized catalytic active site is of fundamental and technological importance. Dual-atom alloys (DAAs) consisting of a heterometallic dimer embedded in the surface layer of a metal host would bring increased tunability and a larger active site, as compared to SAAs. Here, we use computational studies to show that DAAs allow tuning of the active site electronic structure and reactivity. Interestingly, combining two SAAs into a dual-atom site can result in molecular-like hybridization by virtue of the free-atom-like electronic d states exhibited by many SAAs. DAAs can inherit the weak d–d interaction between dopants and hosts from the constituent SAAs, but exhibit new electronic and reactive properties due to dopant–dopant interactions in the DAA. We identify many heterometallic DAAs that we predict to be more stable than either the constituent SAAs or homometallic dual-atom sites of each dopant. We also show how both electronic and ensemble effects can modify the strength of CO adsorption. Because of the molecular-like interactions that can occur, DAAs require a different approach for tuning chemical properties compared to what is used for previous classes of alloys. This work provides insights into the unique catalytic properties of DAAs, and opens up new possibilities for tailoring localized and well-defined catalytic active sites for optimal reaction pathways.

Creating dual-atom active sites in host metals allows tuning of chemical properties through electronic effects and ensemble effects. In particular, some dual-atom alloys feature molecular-like electronic states.