Binary Mixture Model Research Articles

Emergence of microstructural patterns in skin cancer: a phase separation analysis in a binary mixture

Clinical diagnosis of skin cancers is based on several morphological criteria, among which is the presence of microstructures (e.g. dots and nests) sparsely distributed within the tumour lesion. In this study, we demonstrate that these patterns might originate from a phase separation process. In the absence of cellular proliferation, in fact, a binary mixture model, which is used to represent the mechanical behaviour of skin cancers, contains a cell–cell adhesion parameter that leads to a governing equation of the Cahn–Hilliard type. Taking into account a reaction–diffusion coupling between nutrient consumption and cellular proliferation, we show, with both analytical and numerical investigations, that two-phase models may undergo a spinodal decomposition even when considering mass exchanges between the phases. The cell–nutrient interaction defines a typical diffusive length in the problem, which is found to control the saturation of a growing separated domain, thus stabilizing the microstructural pattern. The distribution and evolution of such emerging cluster morphologies, as predicted by our model, are successfully compared to the clinical observation of microstructural patterns in tumour lesions.

Well-posedness of an isothermal diffusive model for binary mixtures of incompressible fluids

We consider a model describing the behaviour of a mixture of two incompressible fluids with the same density under isothermal conditions. The model consists of three balance equations: a continuity equation, a Navier–Stokes equation for the mean velocity of the mixture and a diffusion equation (Cahn–Hilliard equation). We assume that the chemical potential depends on the velocity of the mixture in such a way that an increase in the velocity improves the miscibility of the mixture. We examine the thermodynamic consistence of the model which leads to the introduction of an additional constitutive force in the motion equation. Then, we prove the existence and uniqueness of the solution of the resulting differential problem.

Minimal Experimental Data Set Required for Estimating PCP-SAFT Parameters

The pure-component parameters of the Perturbed Chain Polar-Statistical Associating Fluid Theory (PCP-SAFT) equation of state are usually fitted to experimental data over broad temperature ranges. Against a background of limited experimental data, this article examines the amount and type of experimental data that are minimally required for safe parameter estimation. For nonassociating components, a minimal data set containing three data points is sufficient. For associating components, five data points are sufficient. The influence of vapor-pressure data on parameter estimation and the modeling results is larger than that of liquid-volume data. The temperature ranges of the experimental data can be chosen to be as small as 5 K for all of the data, except for the vapor pressures of associating components. These data require a range of at least 20 K. Application of the parameters fitted to the minimal experimental data set led to convincing results for the modeling of pure-component properties and binary mixtures.

Generalized Superconducting Gap in an Anisotropic Boson–Fermion Mixture with a Uniform Coulomb Field

A boson–fermion (BF) quantum-statistical binary gas mixture model of high- T c superconductors (HTSCs) recently introduced consists of resonant bosonic Cooper electron pairs (CPs) in chemical and thermal equilibrium with single unpaired electrons. Here, this model is refined and extended to include: i) the anisotropy of the original BF vertex interaction causing boson formation/disintegration and ii) momentum-independent Coulomb repulsions between electron charge carriers. It is shown that pair breakings due to Coulomb repulsion depend on the separation between boson and fermion spectra. Specifically, as such a separation shrinks, the pair-breaking ability of the Coulomb interaction weakens and disappears altogether at the Bose–Einstein condensation (BEC) T c , i.e., at the temperature at which a complete softening of bosons occurs due to boson self-energy renormalization. Simultaneous inclusion of both effects produces “islands” in momentum space of incoherent CPs above the Fermi sea as temperature is lowered. These islands grow upon further cooling and merge together just before T c is reached. The BF model thusly extended now predicts a pseudogap phase in 2D HTSCs with lines of points on the Fermi surface along which the pseudogap vanishes, hence explaining the origin of the temperature-dependent “Fermi arcs” observed in experiments.

Structural investigations and swelling behavior of 6FDA copolyimide thin films

AbstractThe effects of swelling on chain distance, free volume size and orientation of functional groups of copolyimides containing carboxyl groups were examined using wide‐angle X‐ray diffraction (WAXD), positron annihilation lifetime spectroscopy (PALS) and Fourier transform infrared (FTIR) spectroscopy. A 2,3‐dimethylbenzothiophene/n‐dodecane mixture (0.3 wt%/99.7 wt%) was used as a swelling agent, as it is a binary model mixture to investigate membrane‐based desulfurization of kerosene. Thin film samples were prepared from copolyimide structures which had been synthesized via a polycondensation reaction of 4,4′‐hexafluoroisopropylidene di(phthalic anhydride), 3,5‐diaminobenzoic acid, 2,3,5,6‐tetramethyl‐1,4‐phenylenediamine and 2,4,6‐trimethyl‐1,3‐phenylenediamine. A relationship between a lower amount of 3,5‐diaminobenzoic acid present in the copolyimide backbone and a higher amount of solvent sorption in the film was found. This was attributed to the fact that the carboxyl groups on the polymer backbone can form hydrogen bonds, reducing sorption and swelling phenomena. PALS measurements for the different structures showed significantly smaller hole sizes for the free volume sites of the copolyimide containing fewer carboxyl groups. Although WAXD of film samples after time‐dependent swelling indicated that the chain distance initially decreased slightly, FTIR experiments using polarized light did not show any significant orientation changes in the polymer chains. Copyright © 2011 Society of Chemical Industry

Evolution of glassy gratings with variable aspect ratios under surface diffusion

The structural evolution of surface gratings on a glassy material is investigated by means of molecular simulations. The gratings provide a means to probe surface diffusion in the vicinity of the glass transition temperature. A theory by Mullins [J. Appl. Phys. 30, 77 (1959)] is used to extract qu-antitative measures of surface diffusivity that rely on calculation of grating amplitude as a function of time. The simulations are implemented in the context of a model binary glass mixture [S. S. Ashwin and S. Sastry, J. Phys.: Condens. Matter 15, S1253 (2003)]. We find that surface diffusion is faster than bulk diffusion by several orders of magnitude, consistent with recent experimental data for an organic glass former. The diffusivities extracted by the grating-decay approach are consistent with those estimated on the basis of mean-squared particle displacements. The grating-decay approach, however, is more efficient than traditional techniques based on Einstein's diffusion equation. Grating decay is also more versatile and is shown to be applicable in a variety of sample geometries.

Influence of Tangent Pinch Points on the Energy Demand of Batch Distillations: Development of a Conceptual Model for Binary Mixtures

This contribution explores the influence of tangent pinch points on the performance of batch distillations of highly nonideal binary mixtures and its incorporation into a conceptual modeling framework under the assumption of a rectifier with an infinite number of stages. First of all, the y−x diagram is divided into three regions taking into account both the inflection point (IP) in the phase diagram and the slope of the equilibrium curve at xD = 1. After that, limiting values for the reflux ratio and distillate composition; namely, r* and xD*, are calculated for the instantaneous still composition xB with the aid of region-dependent algorithms, which incorporate the tangency condition in different ways. Finally, the instantaneous column performance is estimated taking into account the selected operation mode; i.e., constant reflux ratio or constant distillate composition. Applied to the mixture acetone−water, results for complete simulations are presented in terms of both rectification advance and operat...

Derivation of a new equation for prediction of the thin layer depth of the extended-Langmuir model for dilute binary mixtures

Extended Langmuir model is a model which correlates the surface tension data with bulk composition. One of main objectives of this model is considering the surface as a thin layer of finite depth. In the present work by combination of the Gibbs equation with extended Langmuir model and making some assumptions a new and simple equation was derived for estimating the depth of surface thin layer of dilute binary liquid mixtures. It was shown that the depth of surface layer decreases in a linear form with increasing of solute concentration in the dilute region.

Age-related Toxoplasma gondii seroprevalence in Dutch wild boar inconsistent with lifelong persistence of antibodies.

Toxoplasma gondii is an important zoonotic pathogen that is best known as a cause of abortion or abnormalities in the newborn after primary infection during pregnancy. Our aim was to determine the prevalence of T. gondii in wild boar to investigate the possible role of their meat in human infection and to get an indication of the environmental contamination with T. gondii. The presence of anti-T. gondii antibodies was determined by in-house ELISA in 509 wild boar shot in 2002/2003 and 464 wild boar shot in 2007. Most of the boar originated from the “Roerstreek” (n = 673) or the “Veluwe” (n = 241). A binormal mixture model was fitted to the log-transformed optical density values for wild boar up to 20 months old to estimate the optimal cut-off value (−0.685) and accompanying sensitivity (90.6%) and specificity (93.6%). The overall seroprevalence was estimated at 24.4% (95% CI: 21.1–27.7%). The prevalence did not show variation between sampling years or regions, indicating a stable and homogeneous infection pressure from the environment. The relation between age and seroprevalence was studied in two stages. Firstly, seroprevalence by age group was determined by fitting the binary mixture model to 200 animals per age category. The prevalence showed a steep increase until approximately 10 months of age but stabilized at approximately 35% thereafter. Secondly, we fitted the age-dependent seroprevalence data to several SIR-type models, with seropositives as infected (I) and seronegatives as either susceptible (S) or resistant (R). A model with a recovery rate (SIS) was superior to a model without a recovery rate (SI). This finding is not consistent with the traditional view of lifelong persistence of T. gondii infections. The high seroprevalence suggests that eating undercooked wild boar meat may pose a risk of infection with T. gondii.

A new one parameter viscosity model for binary mixtures

AbstractThe Grunberg & Nissian equation with one parameter is widely recommended in the viscosity calculation. However, it is demonstrated that this equation fails to generate satisfactory results for size‐asymmetric mixtures containing large and small molecules. In this work, a new one parameter viscosity model for binary mixtures has been developed on the basis of Eyring's absolute reaction rate theory and the Flory‐Huggins equation. The concept of molecular surface fraction is introduced for modeling liquid mixture viscosities. The viscosity calculations of the new equation are compared with the Grunberg & Nissian equation for a broad range of chemical mixtures including 527 binary systems (containing 63 binary ionic liquid cosolvent systems) and total 17,268 viscosity points. The new equation was found to have an improved performance over the frequently employed Grunberg & Nissian equation, especially for size‐asymmetric mixtures containing large and small molecules. © 2010 American Institute of Chemical Engineers AIChE J, 57: 517–524, 2011

The Study of Phase Separation in Amorphous Freeze-Dried Systems. Part I: Raman Mapping and Computational Analysis of XRPD Data in Model Polymer Systems

Phase separation in amorphous freeze-dried mixtures is likely in many systems. However, suitable detection methodology has been lacking, as the classical technique, differential scanning calorimetry (DSC), relies upon detection of multiple glass transition temperatures (T(g)), each of which is characteristic of a given amorphous phase. The lack of a detectable glass transition temperature in protein-rich phases, limits the application of DSC. Here, we focus on evaluating new methods for detection of phase separation in amorphous freeze-dried mixtures. A novel Raman mapping technique has been evaluated using model binary polymer mixtures of PVP and dextran known to phase separate. The sensitivity of this Raman technique in detecting phase separation was comparable to DSC. Phase separation was detected in compositions of 1:9 to 3:2 (PVP 10,000/dextran 5000) and 3:7 to 4:1 (PVP 29,000/dextran 10,000) by DSC and Raman. Computational methodologies applied to X-ray powder diffraction (XRPD) data from these systems are also shown to reliably detect the presence of phase separation. However, some differences between techniques were observed in cases lying on the boundary of phase separation. Thus, Raman and XRPD show promise for detecting phase separation in systems, which do not exhibit detectable glass transitions by calorimetry.

Binary Inference for Primary User Separation in Cognitive Radio Networks

Spectrum sensing receives much attention recently in the cognitive radio (CR) network research, i.e., secondary users (SUs) constantly monitor channel condition to detect the presence of the primary users (PUs). In this paper, we go beyond spectrum sensing and introduce the PU separation problem, which concerns with the issues of distinguishing and characterizing PUs in the context of collaborative spectrum sensing and monitor selection. The observations of monitors are modeled as boolean OR mixtures of underlying binary sources for PUs. We first justify the use of the binary OR mixture model as opposed to the traditional linear mixture model through simulation studies. Then we devise a novel binary inference algorithm for PU separation. Not only PU-SU relationship are revealed, but PUs' transmission statistics and activities at each time slot can also be inferred. Simulation results show that without any prior knowledge regarding PUs' activities, the algorithm achieves high inference accuracy even in the presence of noisy measurements.

Symmetrization of excess Gibbs free energy: A simple model for binary liquid mixtures

A symmetric expression for the excess Gibbs free energy of liquid binary mixtures is obtained using an appropriate definition for the effective contact fraction. We have identified a mechanism of local segregation as the main cause of the contact fraction variation with the concentration. Starting from this mechanism we develop a simple model for describing binary liquid mixtures. In this model two parameters appear: one adjustable, and the other parameter depending on the first one. Following this procedure we reproduce the experimental data of (liquid + vapor) equilibrium with a degree of accuracy comparable to well-known more elaborated models. The way in which we take into account the effective contacts between molecules allows identifying the compound which may be considered to induce one of the following processes: segregation, anti-segregation and dispersion of the components in the liquid mixture. Finally, the simplicity of the model allows one to obtain only one resulting interaction energy parameter, which makes easier the physical interpretation of the results.

GENERALIZED SUPERCONDUCTING GAP IN A BOSON-FERMION MODEL

A quantum-statistical binary gas mixture model consisting of positive-energy resonant bosonic Cooper electron pairs in chemical and thermal equilibrium with single unpaired electrons yields, via two-time retarded Green functions, an analytic expression for a dimensionless coupling λ- and temperature T-dependent generalized energy gap Eg(λ, T) in the single-electron spectrum. The new gap gives a reasonable description of overdoped Bi2Sr2CuO6+δ(Bi2201).

Multiscale modeling of binary polymer mixtures: Scale bridging in the athermal and thermal regime

Obtaining a rigorous and reliable method for linking computer simulations of polymer blends and composites at different length scales of interest is a highly desirable goal in soft matter physics. In this paper a multiscale modeling procedure is presented for the efficient calculation of the static structural properties of binary homopolymer blends. The procedure combines computer simulations of polymer chains on two different length scales, using a united atom representation for the finer structure and a highly coarse-grained approach on the mesoscale, where chains are represented as soft colloidal particles interacting through an effective potential. A method for combining the structural information by inverse mapping is discussed, allowing for the efficient calculation of partial correlation functions, which are compared with results from full united atom simulations. The structure of several polymer mixtures is obtained in an efficient manner for several mixtures in the homogeneous region of the phase diagram. The method is then extended to incorporate thermal fluctuations through an effective χ parameter. Since the approach is analytical, it is fully transferable to numerous systems.

Modeling score distributions in information retrieval

We review the history of modeling score distributions, focusing on the mixture of normal-exponential by investigating the theoretical as well as the empirical evidence supporting its use. We discuss previously suggested conditions which valid binary mixture models should satisfy, such as the Recall-Fallout Convexity Hypothesis, and formulate two new hypotheses considering the component distributions, individually as well as in pairs, under some limiting conditions of parameter values. From all the mixtures suggested in the past, the current theoretical argument points to the two gamma as the most-likely universal model, with the normal-exponential being a usable approximation. Beyond the theoretical contribution, we provide new experimental evidence showing vector space or geometric models, and BM25, as being ‘friendly’ to the normal-exponential, and that the non-convexity problem that the mixture possesses is practically not severe. Furthermore, we review recent non-binary mixture models, speculate on graded relevance, and consider methods such as logistic regression for score calibration.

Structural modeling of carbonaceous mesophase amphotropic mixtures under uniaxial extensional flow

The extended Maier-Saupe model for binary mixtures of model carbonaceous mesophases (uniaxial discotic nematogens) under externally imposed flow, formulated in previous studies [M. Golmohammadi and A. D. Rey, Liquid Crystals 36, 75 (2009); M. Golmohammadi and A. D. Rey, Entropy 10, 183 (2008)], is used to characterize the effect of uniaxial extensional flow and concentration on phase behavior and structure of these mesogenic blends. The generic thermorheological phase diagram of the single-phase binary mixture, given in terms of temperature (T) and Deborah (De) number, shows the existence of four T-De transition lines that define regions that correspond to the following quadrupolar tensor order parameter structures: (i) oblate (perpendicular, parallel), (ii) prolate (perpendicular, parallel), (iii) scalene O(perpendicular, parallel), and (iv) scalene P(perpendicular, parallel), where the symbols (perpendicular, parallel) indicate alignment of the tensor order ellipsoid with respect to the extension axis. It is found that with increasing T the dominant component of the mixture exhibits weak deviations from the well-known pure species response to uniaxial extensional flow (uniaxial perpendicular nematic-->biaxial nematic-->uniaxial parallel paranematic). In contrast, the slaved component shows a strong deviation from the pure species response. This deviation is dictated by the asymmetric viscoelastic coupling effects emanating from the dominant component. Changes in conformation (oblate <==> prolate) and orientation (perpendicular <==> parallel) are effected through changes in pairs of eigenvalues of the quadrupolar tensor order parameter. The complexity of the structural sensitivity to temperature and extensional flow is a reflection of the dual lyotropic/thermotropic nature (amphotropic nature) of the mixture and their cooperation/competition. The analysis demonstrates that the simple structures (biaxial nematic and uniaxial paranematic) observed in pure discotic mesogens under uniaxial extensional flow are significantly enriched by the interaction of the lyotropic/thermotropic competition with the binary molecular architectures and with the quadrupolar nature of the flow.

Important aspects in the formulation of solid–fluid debris-flow models. Part II. Constitutive modelling

This article is the continuation of Part I: ‘Thermodynamic Implications’ of a article with the same title. Knowledge of the content/results of Part I, Hutter and Schneider (Continuum Mech. Thermodyn., 2009) or Schneider and Hutter (Solid–Fluid Mixtures of Frictional Materials in Geophysical and Geotechnical Context, 2009), is assumed. The intention is to see whether (i) well-known formulations of binary mixture models can be derived from the thermodynamic model, (ii) classical hypo-plasticity is deducible from the frictional evolution equation and (iii) the popular assumption of pressure equilibrium is justified. To this end, we ignore mass and volume fraction interaction rate densities, restrict considerations to isothermal processes, ignore higher order non-linearities in the constitutive relations and use the principle of phase separation. These assumptions transform the equilibrium stresses, heat flux and interaction forces to considerably simplified forms. Furthermore, the analysis shows that classical hypo-plasticity can be reconstructed with the introduction of a new objective time derivative for the stress-like variable. Non-equilibrium contributions to the stresses and interaction forces are also briefly discussed. It is, finally, shown that the assumption of pressure equilibrium precludes the application of frictional stresses in equilibrium. This unphysical assumption is, therefore, replaced by a thermodynamic closure condition that is more flexible and less restrictive. It allows for frictional stresses in thermodynamic equilibrium and, therefore, is sufficiently general for applications to mixture theories.

Superconducting Pseudogap in a Boson–Fermion Model

A boson–fermion (BF) quantum-statistical binary gas mixture model consisting of positive-energy resonant bosonic Cooper electron pairs (CPs) in chemical and thermal equilibrium with single unpaired electrons is presented. Two-time retarded Green functions are shown to conveniently cope and deal with nonzero center-of-mass momentum (CMM) CPs. They yield an analytic expression for a dimensionless-coupling (λ)- and temperature ( T )-dependent generalized energy gap E g (λ, T ) in the single-electron spectrum of a superconductor. This generalized gap vanishes above a specific (“depairing” or “pseudogap”) temperature T * > T c , where T c is the critical Bose–Einstein condensation (BEC) singularity associated with the BF binary mixture, but is nonzero for all T below T * due initially to the formation of “preformed” pairs. Within the present BF model the generalized gap E g (λ, T ) is not restricted to the underdoped high-temperature superconductors as we illustrate with BSCCO, but is also applicable in optimally-doped and even overdoped compounds for which T * and T c virtually coincide as in BCS theory where nonzero-CMM CPs are neglected.

Structure and phase transitions of carbonaceous mesophase binary mixtures under uniaxial extensional flow

The Maier–Saupe model for binary mixtures of uniaxial discotic nematogens, formulated in previous studies [1], is extended to simulate the effect of uniaxial extensional flow on the phase behavior and structure. The rotational diffusivity of each disk-like component in the mixture of a high molecular weight (Mw) and a low molecular weight species, is derived based on: (i) a power law that relates molecular size to molecular weight and (ii) the excluded volume of binary disc-like molecules. The thermo-rheological phase diagram of a 50/50 mixture, given in terms of temperature ( T) and Deborah ( De) number show the existence of four T– De regions and six solutions: oblate (⊥, ∥), prolate (⊥, ∥) and scalene (⊥, ∥), where the symbols (⊥, ∥) indicate alignment of the tensor order ellipsoid with respect to the extension axis. It is found that, with increasing T, the higher molecular weight component exhibits weak deviations from the well-known pure species response to uniaxial extensional flow (uniaxial ⊥ nematic → biaxial nematic → uniaxial ∥ paranematic). In contrast, the low molar mass component is always uniaxial and the orientation of the oblate or prolate states is dictated by the coupling effects emanating from the high molar mass component. Analysis of the coupling effects reveals that the changes in conformation ( oblate ⇄ prolate ) and orientation ( ⊥ ⇄ ∥ ) is effected through changes in pairs of eigenvalues. At high temperature, extensional flow acting on an isotropic phase produces an oblate paranematic state in the high Mw species and a prolate paranematic state in the low Mw species. Finally we show that X-ray intensity calculations are able to detect the different regions of the thermo-rheological phase diagram characterized by the presence of oblate, prolate, scalene nematic and paranematic states.