Dilute Solution Model Research Articles

Measurement of Solution Composition as an Alternative to Titration for Evaluating the Hydrolytic Resistance of Glass.

The measurement of solution composition is proposed as an alternative to titration to determine titration volume, which is the figure of merit for evaluating the hydrolytic resistance of glass containers for pharmaceutical packaging. In the new method, instead of titrating the sample and blank solutions, their compositions are measured by inductively coupled plasma mass spectrometry, and these compositions are converted to titration volume using a set of coefficients and a simple equation. The coefficients were derived using the well-developed thermodynamic data and models for dilute aqueous solutions, which make it possible to calculate pH from solution composition and then simulate a titration as a series of pH calculations as titrant is progressively added to the solution. In this paper we explain how a titration can be simulated, describe how the set of coefficients was derived, and provide experimental evidence that the titration volume from the new method is equivalent to that from titration. Since the new method is more difficult and expensive, it is not meant as a replacement for titration in the standard and pharmacopeial methods. Its value lies in enabling previously impossible hydrolytic resistance studies, supplying additional information about the composition of the hydrolytic solution which reveals important aspects of glass corrosion, and providing insights about titration which point to possible improvements in the standard titration procedures.

Viscoelastic simulations using the closed-form Adaptive Length Scale (ALS-C) model

In this paper we employ the closed-form of the Adaptive Length Scale Model (ALS-C) [Ghosh et al., “A new model for dilute polymer solutions in flows with strong extensional components”, J. Rheol. 46, 1057–1089 (2002)] and we investigate its characteristics and potential to more accurately capture pressure-drop in contraction flows of viscoelastic fluids. The ALS-C model was originally derived based on purely homogeneous elongational flows in order to model coil-stretch hysteresis. However, in its originally proposed form we reveal a number of numerical issues which have not been analysed previously and are reported here considering both standard rheological flows, simple channel flows and complex flows within a 4:1 contraction. We demonstrate a new approach for evaluating the instantaneous change in the adaptive length scale as a result of instantaneous changes in the flow field, overcoming the need to employ other root-finding approaches. Guidelines are provided for the correct use of the employed local Weissenberg number and a modified approach is considered for the evolution equation of the actual extensibility, allowing its efficient use in complex numerical simulations. We illustrate that a suitable combination of the model parameters can produce behaviours that are found experimentally in viscoelastic fluids and we find that pressure-drop enhancements in flows within 4:1 contractions observed experimentally are achievable.

A constitutive equation for Rouse model modified for variations of spring stiffness, bead friction, and Brownian force intensity under flow

We derived a constitutive equation for the Rouse model (the most frequently utilized bead-spring model) with its spring constant κ, bead friction coefficient ζ, and the (squared) Brownian force intensity B being allowed to change under flow. Specifically, we modified the Langevin equation of the original Rouse model by introducing time (t)-dependent κ, ζ, and B (of arbitrary t dependence), which corresponded to the decoupling and preaveraging approximations often made in bead-spring models. From this modified Langevin equation, we calculated time evolution of second-moment averages of the Rouse eigenmode amplitudes and further converted this evolution into a constitutive equation. It turned out that the equation has a functional form, σ(t)=∫−∞tdt′{κ(t)/κ(t′)}M(t,t′)C−1(t,t′), where σ(t) and C−1(t,t′) are the stress and Finger strain tensors, and M(t,t′) is the memory function depending on κ(t′), ζ(t′), and B(t′) defined under flow. This equation, serving as a basis for analysis of nonlinear rheological behavior of unentangled melts, reproduces previous theoretical results under specific conditions, the Lodge–Wu constitutive equation for the case of t-independent κ, ζ, and B [A. S. Lodge and Y. Wu, “Constitutive equations for polymer solutions derived from the bead/spring model of Rouse and Zimm,” Rheol. Acta 10, 539 (1971)], the finite extensible nonlinear elastic (FENE)-Peterlin mean-Rouse formulation for the case of t-dependent changes of the only κ reported by Wedgewood and co-workers [L. E. Wedgewood et al., “A finitely extensible bead-spring chain model for dilute polymer solutions,” J. Non-Newtonian Fluid Mech. 40, 119 (1991)], and analytical expression of steady state properties for arbitrary κ(t), ζ(t), and B(t) reported by ourselves [H. Watanabe et al., “Revisiting nonlinear flow behavior of Rouse chain: Roles of FENE, friction reduction, and Brownian force intensity variation,” Macromolecules 54, 3700 (2021)]. It is to be added that a constitutive equation reported by Narimissa and Wagner [E. Narimissa and M. H. Wagner, “Modeling nonlinear rheology of unentangled polymer melts based on a single integral constitutive equation,” J. Rheol. 64, 129 (2020)] has a significantly different functional form and cannot be derived from the Rouse model with any simple modification of the Rouse–Langevin equation.

Balance between strength and ductility of dilute Fe2B by high-throughput first-principles calculations

In boride ceramics, Fe2B typically functions as the primary wear-resistant phase owing to its high hardness, but the elastic and ductile-brittle properties of Fe2B greatly influence its wear resistance and industrial application. First-principles calculations using density functional theory (DFT) were utilized to systematically investigate the effects of Al, Si, and transition elements (including 3d, 4d, and 5d transition elements) on the mechanical properties and electronic structure of Fe31MB16 with a dilute solution model. The bulk modulus (B), shear modulus (G), and Young's modulus (E) were calculated through the stress-strain method. The Vickers hardness (HV) and fracture toughness (KIC) were calculated by semi-empirical models. The electronic structures and chemical bonding were analyzed using the charge density difference, electron localization function, and Mulliken bond population. Overall, Fe31YB16 had the largest moduli (B, G, and E) among all the Fe31MB16 compounds that were investigated, while Fe31CrB16 had the highest hardness. Compared with pure Fe2B, the ductility of Fe31MB16 improved to varying degrees according to the B/G and Poisson's ratio (σ) criteria, respectively. However, adding alloying elements in this concentration did not change the intrinsic brittleness of Fe2B. Moreover, the trends in the calculated KIC of Fe31MB16 (M = Cr, Mn, Mo, and W respectively) were consistent with those of experiments. The electronic structure and Mulliken population analysis showed that the differences in the mechanical properties of the Fe31MB16 compounds were primarily determined by the M-B and B–B bonds because the alloying element M replaced Fe. These results provide guidance for improving the ductility of Fe2B and its industrial application.

A charged finitely extensible dumbbell model: Explaining rheology of dilute polyelectrolyte solutions

A robust non-Newtonian fluid model of dilute polyelectrolyte solutions is derived from kinetic theory arguments. Polyelectrolyte molecules are modeled as finitely elongated nonlinear elastic dumbbells, where effective charges (interacting through a simple Coulomb force) are added to the beads in order to model the repulsion between the charged sections of polyelectrolyte chains. It is shown that the relative strength of this repulsion is regulated by the electric-to-elastic energy ratio, E, which is one of the key parameters of the model. In particular, E accounts for the intrinsic rigidity of polyelectrolyte molecules and can be used to explain the impact of solvent salinity on polyelectrolyte rheology. With two preaveraging approximations, the constitutive equations of the resulting fluid model are formulated in closed form. Material functions predicted by the model for steady shear flow, steady extensional flow, small-amplitude oscillatory shear flow, and start-up and cessation of steady shear flow are obtained and investigated using a combination of analytical and numerical methods. In particular, it is shown how these material functions depend on E. The two limiting cases of the model—uncharged dumbbells (E = 0) and rigid dumbbells (E → ∞)—are included in the analysis. It is found that despite its simplicity, the model predicts most of the experimentally observed rheological features of polyelectrolyte solutions.

A statistical field theory of salt solutions of ‘hairy’ dielectric particles

In this paper, we formulate a field-theoretical model of dilute salt solutions of electrically neutral spherical colloid particles. Each colloid particle consists of a ‘central’ charge that is situated at the center and compensating peripheral charges (grafted to it) that are fixed or fluctuating relative to the central charge. In the framework of the random phase approximation, we obtain a general expression for electrostatic free energy of solution and analyze it for different limiting cases. In the limit of infinite number of peripheral charges, when they can be modelled as a continual charged cloud, we obtain an asymptotic behavior of the electrostatic potential of a point-like test charge in a salt colloid solution at long distances, demonstrating the crossover from its monotonic decrease to damped oscillations with a certain wavelength. We show that the obtained crossover is determined by certain Fisher–Widom line. For the same limiting case, we obtain an analytical expression for the electrostatic free energy of a salt-free solution. In the case of nonzero salt concentration, we obtain analytical relations for the electrostatic free energy in two limiting regimes. Namely, when the ionic concentration is much higher than the colloid concentration and the effective size of charge cloud is much bigger than the screening lengths that are attributed to the salt ions and the central charges of colloid particles. The proposed theory could be useful for theoretical description of the phase behavior of salt solutions of metal-organic complexes and polymeric stars.

Investigation of Thermodynamic Nonideality of Solid Li-ion Electrodes Using Concentrated Solution Theory

Li-Ion batteries (LIBs) is poised to dominate the energy storage market of electric vehicles (EVs) and renewable-energy-integrated grids over the next few decades. To address safety and lifetime concerns of the technology, significant efforts have been devoted to advancing online battery diagnostic tools and evolving charging/discharging protocols to enhance their stability and elongate their lifetime, and both have been found to be highly amenable to physics-based models (PBMs). With the continuous improvements and breakthroughs of computer technology, PBMs in substitute of equivalent circuit models (ECMs) have been employed to produce high-fidelity, low-computational-cost reduced-order-models (ROMs) for battery management system (BMS), despite the fact that simplifications have regularly been made. For example, in a general PBM of LIBs, Li-ion diffusion is governed by Fick’s second law of diffusion in a dilute solution (Fig. 1), which neglected the thermodynamic nonideality of a solid active material which experiences large concentration variation in electrochemical processes. Though the above fact likely indicates that such PBMs contain some battery physics to represent the key electrochemical processes, it does not exclude the possibility that important correlations could be associated with physics that have been neglected. For example, although both ks (solid/liquid interface reaction rate) and D (diffusivity of Li-ion in a solid phase) exhibited correlations with battery State-Of-Charge (SOC), especially at the end of discharge, they have been assumed to be constants over the entire range of SOC. In fact, their values reported from different researchers show variation spanning over 2 to 5 order of magnitude. With this large variation, both battery SOC and State-Of-Health (SOH) will remain unpredictable, which means that ultimately the battery management and diagnosis remains uncertain. Numerous theoretical and experimental studies support the inevitable Li-Li interactions when Li-ion deintercalation/intercalation from/into the active materials, especially with a sufficiently large concentration. This Li-Li interaction introduces thermodynamic nonideality which could not be described by the Fick’s second law of diffusion. Consequently, critical electrochemical kinetic and transport properties such as ks and D will have a strong correlation with the SOC. In this research, we will try to understand the nonideality of a solid Li-ion solution by the concentrated solution theory, as shown in Fig.1. We will use nonequilibrium thermodynamics in a concentrated solution to correlate ks/D with the activity coefficient of the solid solution γ and elaborate new governing equations for D and ks. Then, utilize the new correlations to process experimental data tested by EIS method and to regress the experimental activity coefficient γ. Furthermore, a methodology in determining the most appropriate constants for ks and D with a minimum discrepancy for a full charge/discharge cycle will be provided. Figure 1. (a) Inconsistency in KsS and D values between dilute solution model prediction and experimental results; (b) Ks and D comparison between dilute solution theory and concentrated solution theory; (c) Experimental and model prediction based on concentrated solution theory. Figure 1

A deep insight into the polystyrene chain in cyclohexane at theta temperature: molecular dynamics simulation and quantum chemical calculations.

Molecular characteristics of an atactic polystyrene (aPS) chain with different lengths in a theta solvent, cyclohexane at 307.65K, were studied via molecular dynamics (MD) simulation. The interaction energy of the aPS dilute solution models and Flory-Huggins (FH) interaction parameter were calculated to investigate the effect of the chain molecular weight on its compatibility with the solvent molecules. The simulation results illustrated that increasing the chain length increased the interactions between the chain and the solvent molecules. The chain dimensions via calculating the radius of gyration (Rg) and end-to-end distance, <r0>, were measured. Mean square displacement (MSD) and diffusivity coefficient of the chains were calculated to determine their dynamic behavior. The results exhibited that two factors of the chain movability and size were important for the diffusion in oligomeric state. Additionally, viscosity of the resultant dilute solutions was calculated via nonequilibrium molecular dynamics simulation (NEMD). Moreover, the steric hindrance of the chains was determined by radial distribution function (RDF) analysis. The calculated characteristics of the chain and solution viscosity results showed a good agreement with experimental published works. Measurement of the potential field of cyclohexane-cyclohexane and aPS-cyclohexane pairs was also based on their potential field via quantum chemical calculations to determine the special orientation of the solvent molecules to each other and to the polymer segments, respectively. Graphical abstract (a) The equilibrated dilute solution model of polystyrene in cyclohexane at theta temperature (the red and yellow balls represent carbon and hydrogen atoms, respectively. The cyclohexane molecules are illustrated in line style in the box), (b) the electrostatic potential field around an optimized structure containing two cyclohexane molecules, and (c) around the sole cyclohexane molecule and polystyrene with two repeating units (carbon and hydrogen atoms are represented in green and yellow, respectively).

Global Well-Posedness of Strong Solutions of Doi Model with Large Viscous Stress

We study models of dilute rigid rod-like polymer solutions. We establish the global well-posedness of the Doi model for large data and for arbitrarily large viscous stress parameter. The main ingredient in the proof is the fact that the viscous stress adds dissipation to high derivatives of velocity.

Small- and large-amplitude oscillatory rheometry with bead–spring dumbbells in Stokesian Dynamics to mimic viscoelasticity

In many areas of suspension mechanics, such as filled polymer fluids or household products such as toothpaste, the suspending fluid itself is inherently non-Newtonian and may exhibit viscoelastic properties. In this paper, we extend the Stokesian Dynamics formalism to incorporate a simple model of viscoelasticity by using small spheres as ‘beads’ in a bead–spring dumbbell (such as is found in the derivation of Oldroyd and FENE constitutive models for dilute polymer solutions). Various different spring laws are then tested in both small-amplitude and large-amplitude oscillatory shear, and their rheological behaviour is compared to continuum constitutive models.

Concentration and fluid flow effects on kinetics, dendrite remelting and stress accumulation upon rapid solidification of deeply undercooled alloys

Upon free solidification of a deeply undercooled melt, the solute diffusion in both the interface and the bulk liquid is far from equilibrium, and the concentration and the fluid flow may also play an important role in the solidification. Thus, under such conditions, assumptions about local equilibrium, ideal dilute solution solidification and solidification free of fluid flow can no longer be valid. In the present work, first, in order to reveal the concentration effect, we compared the results of the non-equilibrium dendrite growth models describing the solidification of dilute and non-dilute undercooled melts. It was found that under local non-equilibrium conditions, the predicted results of the non-dilute solution model and the dilute solution model are to a certain extent different from each other at the intermediate undercooling range. It was also found that the concentration effect could substantially decrease the relaxation effect. Second, we considered the effect of fluid flow on the rapid solidification of an undercooled melt. It was found that the fluid flow would affect not only the size of the dendrite tip radius, mainly at the small undercooling range, but also the dendrite growth velocity at the intermediate undercooling range. In particular, fluid flow makes the sizes of the dendrite tip radius at high undercooling close to those predicted by the dilute model. Thus, fluid flow could make the non-dilute solution exhibit dilute solution solidification behaviors. It was also found that fluid flow reduces the relaxation effect to some extent. Considering the fluid flow effect, we used an extended chemical superheating model to predict the dendrite remelting phenomenon of the non-dilute melt. The model predicted that the dendrite remelting phenomenon would abruptly disappear once the dendrite growth velocity exceeded the solute diffusion velocity in a bulk undercooled melt. Third, considering the fluid flow effect, we used the concept of equivalent undercooling and a recently developed physical model to calculate the stress accumulation during rapid solidification. The results of this new model could explain well the stress-induced dendrite breakup mechanism of grain refinement at high undercooling.

Electron paramagnetic resonance and magnetic properties of α-BiNb1−xFexO4−δ

Iron-containing ceramic materials based on BiNbO4 of orthorhombic modification were obtained by solid-phase synthesis. The solid solutions α-BiNb1-xFexO4-δ were synthesized of х ≤ 0.03. The single-phase structure of these samples was established by X-ray diffraction and SEM- analyses. In the EPR spectra of BiNb1-xFexO4-δ, a wide band with a center at g = 2.16–2.37 were observed, which had a low-intensity signal with a g-factor of ~ 4.3 on the low-field wing. Along with the broad spectrum component, a "noise-like" signal was observed in the magnetic field range of 190-400 mT, which was formed by a large number of narrow lines related to the integral signal of ferromagnetic resonance and its fine structure. The isotherms of the paramagnetic component of the magnetic susceptibility of iron atoms in BiNb1-xFexO4-δ are typical for antiferromagnets. The value of the effective magnetic moment of iron atoms increases along with the increase in temperature from 5.84 MB (90 K) to 6.43 MB (320 K). This can be explained by the presence of exchange-bound aggregates of Fe (III) atoms with the antiferro- and ferromagnetic types of exchange in the solid solutions. Magnetic behavior of BiNb1-xFexO4-δ was investigated taking into account the presence of possible types of clusters of iron atoms by theoretical calculation of the magnetic susceptibility within the framework of the model of dilute solid solutions. The best agreement between the experimental and calculated data was obtained for the dimer parameters of Jdim - 17 cm-1 and Jdim 45 cm-1, for antiferro-and ferromagnetic type of exchange.

Thickening of viscoelastic flow in a model porous medium

We study numerically two-dimensional creeping viscoelastic flow past a biperiodic square array of cylinders within the Oldroyd B, FENE-CR and FENE-P constitutive models of dilute polymer solutions. Our results capture the initial mild decrease then dramatic upturn (‘thickening’) seen experimentally in the drag coefficient as a function of increasing Weissenberg number. By systematically varying the porosity of the flow geometry, we demonstrate two qualitatively different mechanisms underpinning this thickening effect: one that operates in the highly porous case of widely spaced obstacles, and another for more densely packed obstacles, with a crossover between these two mechanisms at intermediate porosities. We also briefly consider 2D creeping viscoelastic flow past a linear array of cylinders confined to a channel, where we find that the flow is steady for all Weissenberg numbers explored.

Ab initiostudy of Cu impurity diffusion in bulk TiN

TiN is an important material used as a diffusion barrier in microelectronic devices to prevent copper from contacting silicon. There is, however, little known about the elementary atomistic processes underlying the excellent performance of TiN. In this work, we perform a density functional theory study of the copper impurity diffusion coefficient in bulk TiN. Several diffusion mechanisms are considered. For each mechanism, the temperature effect is taken into account within the quasiharmonic approximation. Moreover, the influence of the TiN stoichiometry on its diffusion properties is taken into account through the change in the concentrations of the intrinsic point defects as a function of composition. These concentrations are obtained via a thermodynamic formalism based on the dilute solution model. We find that in stoichiometric TiN the copper impurity diffusion proceeds via the vacancy mechanism on the Ti sublattice. In the off-stoichiometric ${\mathrm{TiN}}_{0.96}$, the dominant diffusion mechanism switches to the vacancy-mediated diffusion on the N sublattice. The Arrhenius equation for the diffusion coefficient is $D=3.8\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}exp(\ensuremath{-}4.5\phantom{\rule{0.28em}{0ex}}\mathrm{eV}/{k}_{B}T)\phantom{\rule{4pt}{0ex}}{\mathrm{m}}^{2}\phantom{\rule{4pt}{0ex}}{\mathrm{s}}^{\ensuremath{-}1}$ for the stoichiometric TiN and $D=6.7\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}8}exp(\ensuremath{-}2.7\phantom{\rule{0.28em}{0ex}}\mathrm{eV}/{k}_{B}T)\phantom{\rule{4pt}{0ex}}{\mathrm{m}}^{2}\phantom{\rule{4pt}{0ex}}{\mathrm{s}}^{\ensuremath{-}1}$ for the substoichiometric TiN. Our calculations provide the basis for a better interpretation of the experimental measurements.

Finite Element Modelling of the Electrical Conductivity of Fluorite-Type Oxygen Ion Conductors

Oxygen ion conductors of the fluorite structure, like acceptor doped zirconia or ceria, are the major electrolyte materials for SOFCs. However, the influence of dopant concentration, temperature, oxygen partial pressure and microstructure on these material’s electrical conductivity is still not fully understood [1]. While theory and experiments generally agree on the influence of the first three parameters, the influence of the microstructure remains controversial. Some researchers predict a higher conductivity for nanocrystalline materials [2]. Indeed, the diffusivity of charge carriers, vacancies and mobile ions, is greater along the grain boundary and the grain boundary density increases with decreasing grain size [3]. However, most experiments show the opposite trend where conductivity decreases with decreasing grain size [1], [4]. A reliable model of the material’s electrical conductivity is thus necessary to interpret the existing measurements and to predict the optimal material architecture for use as an SOFC electrolyte. Until now, modelling of the electrical conductivity of these materials relies on the analytical solution of the dilute solution model [1]. This approach yields useful insights but it also has multiple drawbacks. First of all dilute solution theory is invalid at high doping percentages, which makes it impossible to predict the conductivity trend over a large range of dopant concentrations. Moreover experiments clearly show that the electrical conductivity reaches a maximum at a certain dopant concentration and declines when the doping percentage is further increased. This phenomenon is qualitatively explained through an association mechanism between dopant ions and vacancies. We observe that the implementation of such a mechanism in the dilute solution model leads however to an asymptotic maximal conductivity and not to a distinct maximum. It is generally accepted that the grain boundary is enriched in vacancies relative to the grain interior, which leads to a potential difference between both regions. In existing models, this potential difference is imposed as a boundary condition to arrive at a closed form analytical solution. This approach is unable to treat very small grains; below a certain grain size bulk vacancy concentrations are not reached inside the bulk and thus there exists no reference level for the potential difference. The same problem arises when a bias current is applied to the sample; analytical models can only predict the electrical conductivity when the material is not conducting a net current. We propose a model based on the linear phenomenological relations for a crystal lattice [5]. This model respects the crystalline nature of the material where only a limited number of lattice sites are available to the charge carriers, and a lattice site can only accommodate one charge carrier at a time. As a result, our model predicts a distinct maximum in the electrical conductivity when a dopant-vacancy association mechanism is implemented. We show that this maximum exists because the association not only limits the amount of available charge carriers, but also the amount of available diffusion paths. The doping percentage for which maximum conductivity is reached is dependent on the operating temperature. The finite element method is used to solve our model on one-dimensional geometries. This numerical approach enables us to treat grains of arbitrarily small size and to predict electrical conductivities at any applied current density. We show that the ionic conductivity of a sample perpendicular to the grain boundary decreases with decreasing grain size. The grain boundary conductivity itself is independent of grain size, except for very small grains and small dopant concentrations. The results predicted by our model are in good agreement with the available measurements in literature over a large range of dopant concentrations and temperatures. Our model is thus a good tool to interpret measurement data and to improve our understanding of these materials. The final goal of the model is designing optimal solid electrolytes. [1] X. Guo and R. Waser, “Electrical properties of the grain boundaries of oxygen ion conductors: Acceptor-doped zirconia and ceria,” Progress in Materials Science, vol. 51, no. 2, pp. 151–210, 2006. [2] J. Maier, “Ionic conduction in space charge regions,” Progress in solid state chemistry, vol. 23, no. 3, pp. 171–263, 1995. [3] H. Mehrer, Diffusion in solids: fundamentals, methods, materials, diffusion-controlled processes, vol. 155. Springer, 2007. [4] C. Peters, A. Weber, B. Butz, D. Gerthsen, and E. Ivers-Tiffée, “Grain-Size Effects in YSZ Thin-Film Electrolytes,” Journal of the American Ceramic Society, vol. 92, no. 9, pp. 2017–2024, 2009. [5] D. Van Laethem, J. Deconinck, A. Hubin, D. Depla, “Finite element modelling of the ionic conductivity of acceptor doped ceria”, In preparation.

Culation of partial molar volume and its components for molecular dynamics models of dilute solutions

This paper is a review of our recent computational studies of volumetric characteristics using computer models of dilute solutions. Partial molar volume (PMV) and its components are calculated for simple and complex molecules in water (methane, noble gases, surfactants, polypeptides). Advantages and disadvantages of various computational methods are discussed. It is proposed to use the Voronoi-Delaunay technique to determine the reasonable boundary between a solute molecule and solvent molecules and to identify the PMV components related to the molecule, the boundary layer, and the solvent. It is noted that the observed increase in PMV with temperature for large molecules is due to an increase in the volume of voids in the boundary layer, i.e., due to the “thermal volume.” In this case, the solvent gives a negative contribution to the PMV. In contrast, for simple molecules (methane), the contribution from the solvent is positive and is the main factor in the increase in the PMV, which is associated with a specific change in water structure around a spherical hydrophobic particle outside the boundary layer. For surfactant molecules, the contribution from the solvent changes sign (from negative to positive) with increasing temperature.

A new ALS model for dilute polymer solutions in flows with strong shear components

Ghosh et al. (J Rheol 46:1057–1089, 2002) developed a new model for dilute polymer solutions in flows with strong extensional components. The model based on introducing an adaptive length scale (ALS) as an internal variable was developed to reproduce the fine-scale physics of the Kramers chain. The ALS model describes the polymer molecule as a set of identical segments in which each segment represents a fragment of the polymer that is short enough so that it can sample its entire configuration space on the time scale of an imposed deformation and therefore stretch reversibly. As the molecule unravels, the number of the segments decreases, but the maximum length of each segment increases, so that the constant maximum contour length of the molecule is preserved. Though the single-segment-based ALS model accounts for the orientability of the polymer molecules, it cannot describe the internal motions of the molecules due to the lack of internal nodes. Hence, in this work we consider the more realistic chain (multi-segments) model composed of Nseg springs connected linearly. The model presented in this work is an extension of the ALS model developed by Ghosh et al. (J Rheol 46:1057–1089, 2002). We demonstrate that the ALS varies with the flow strength. Specifically, it is found that as the flow strength increases, the ALS decreases. This implies that as the flow strength increases, the polymer molecule is required to divide into finer and finer segments such that each segment can locally equilibrate with the imposed flow. However, there is a critical number of such subdivisions beyond which further subdivision of the polymer molecule is not required to capture the polymer dynamics for a given flow strength. Both shear viscosity and first normal stress coefficient predictions from ALS model show shear thinning behavior with Weissenberg number. In weak flows, the ALS model and the finitely extensible non-linear elastic model exhibit the same behavior.

Large-amplitude oscillatory shear flow from the corotational Maxwell model

Using the single relaxation time corotational Maxwell fluid, we derive explicit analytical expressions for the first, third, and fifth harmonics of the alternating shear stress response in large-amplitude oscillatory shear (LAOS). We also derive corresponding expressions for the zeroth, second, and fourth harmonics of both the first and second normal stress differences. These harmonics are found to depend upon just two dimensionless groups: the Deborah and Weissenberg numbers, each of which causes non-Newtonian behavior. The form of the solution for the corotational Maxwell model in LAOS matches the forms of the analytical solutions for two molecular models for dilute solutions and one for concentrated solutions or melts. We also derive an analytical solution for the corotational Maxwell model after startup of LAOS. For this we find that both small and large amplitude cases approach a periodic limit cycle (alternance) at the same rate for both the shear stress response and for the normal stress differences. For molten high density polyethylene that is lightly filled with carbon black, we find good quantitative agreement with measured LAOS behavior when our analytical solution is superposed for multiple relaxation times.

Kinetic models for dilute solutions of dumbbells in non-homogeneous flows revisited

We propose a two-fluid theory to model a dilute polymer solution assuming that it consists of two phases, polymer and solvent, with two distinct macroscopic velocities. The solvent phase velocity is governed by the macroscopic Navier–Stokes equations with the addition of a force term describing the interaction between the two phases. The polymer phase is described on the mesoscopic level using a dumbbell model and its macroscopic velocity is obtained through averaging. We start by writing down the full phase-space distribution function for the dumbbells and then obtain the inertialess limits for the Fokker–Planck equation and for the averaged friction force acting between the phases from a rigorous asymptotic analysis. The resulting equations are relevant to the modelling of strongly non-homogeneous flows, while the standard kinetic model is recovered in the locally homogeneous case.

Solubility of Piperine in Supercritical and Near Critical Carbon Dioxide

Piperine is a member of the lipids family commonly found in peppercorn, ginger and other natural sources and is grouped as an alkaloid. The solubility of piperine has been determined in carbon dioxide at near critical and supercritical conditions in a dynamic extraction apparatus. The conditions studied were at pressures ranging from 10 to 20 MPa and temperatures at 293, 300, 313, 323 and 333 K. The results showed that piperine solubility increased with increasing pressure at all temperatures studied. The solubility of piperine in near critical conditions was slightly higher than that at supercritical conditions only at the low-pressure range. Two semi-empirical density dependent correlations, namely the Chrastil model and the Dilute Solution model, were also used to estimate the solubility data. Although both models showed good correlation with the solubility data, the Dilute Solution model performed better prediction than the Chrastil model.