Blending Law Research Articles

Burning velocity and Markstein length blending laws for methane/air and hydrogen/air blends

Because of the contrasting chemical kinetics of methane and hydrogen combustion, the development of blending laws for laminar burning velocity, ul, and Markstein length for constituent mixtures of CH4/air and H2/air presents a formidable challenge. Guidance is sought through a study of analytical expressions for laminar burning velocity. For the prediction of burning velocities of blends, six blending laws were scrutinised. The predictions were compared with the measured burning velocities made by Hu et al. under atmospheric conditions [1]. These covered equivalence ratios ranging from 0.6 to 1.3, and the full fuel range for H2 addition to CH4. This enabled assessments to be made of the predictive accuracy of the six laws. The most successful law is one developed in the course of the present study, involving the mass fraction weighting of the product of ul, density, heat of reaction and specific heat, divided by the thermal conductivity of the mixture. There was less success from attempts to obtain a comparably successful blending law for the flame speed Markstein length, Lb, despite scrutiny of several possibilities. Details are given of two possible approaches, one based on the fractional mole concentration of the deficient reactant. A satisfactory empirical law employs mass fraction weighting of the product ulLb.

The influence of n-butanol blending on the ignition delay times of gasoline and its surrogate at high pressures

The influence of blending n-butanol at 20% by volume on the ignition delay times for a reference gasoline was studied in a rapid compression machine (RCM) for stoichiometric fuel/air mixtures at 20bar and 678–858K. Delay times for the blend lay between those of stoichiometric gasoline and stoichiometric n-butanol across the temperature range studied. At lower temperatures, delays for the blend were however, much closer to those of n-butanol than gasoline despite n-butanol being only 20% of the mixture. Under these conditions n-butanol acted as an octane enhancer over and above what might be expected from a simple linear blending law. The ability of a gasoline surrogate, based on a toluene reference fuel (TRF), to capture the main trends of the gasoline/n-butanol blending behaviour was also tested within the RCM. The 3-component TRF based on a mixture of toluene, n-heptane and iso-octane was able to capture the trends well across the temperature range studied. Simulations of ignition delay times were also performed using a detailed blended n-butanol/TRF mechanism based on the adiabatic core assumption and volume histories from the experimental data. Overall, the model captured the main features of the blending behaviour, although at the lowest temperatures, predicted ignition delays for stoichiometric n-butanol were longer than those observed. A brute-force local sensitivity analysis was performed to evaluate the main chemical processes driving the ignition behaviour of the TRF, n-butanol and blended fuels. The reactions of fuel+OH dominated the sensitivities at lower temperatures, with H abstraction from n-butanol from α and γ sites being key for both the n-butanol and the blend. At higher temperatures the decomposition of H2O2 and reactions of HO2 and that of formaldehyde with OH became critical, in common with the ignition behaviour of other fuels. Remaining uncertainties in the rates of these key reactions are discussed.

A combined rheology and time domain NMR approach for determining water distributions in protein blends

We present a combined time domain NMR and rheology approach to quantify the water distribution in a phase separated protein blend. The approach forms the basis for a new tool to assess the microstructural properties of phase separated biopolymer blends, making it highly relevant for many food and non-food related applications. First, we determine the relaxation rate of absorbed water, and the viscoelastic properties of the separated phases as function of the water content. Next, the same properties are measured for the protein blends. Finally, predictions for water distribution obtained from rheological experiments are made via the polymer blending law, and compared to a more direct assessment of the water distribution with time-domain NMR relaxometry (TD-NMR). In this study, the protein blend consists of soy protein isolate (SPI) and vital wheat gluten (WG). We demonstrate that predictions for water distribution are similar for both TD-NMR and rheological measurements. It turns out that water does not distribute homogenously over the phases. Independent of the SPI and WG ratio, more water is absorbed by the SPI phase relative to the WG phase, which largely determines the resulting rheological properties of the blends.

Decomposition d'une loi de poisson ponderee en une combinaison convexe de lois duales

The probability distribution of a set of observation is most often dened as a convex combination of probability laws. To highlight this mixture of the laws, MCMC (Monte Carlo Markov Chain) which is an algorithm that generates a stationary Markov chain is often used; laws being considered as normal laws. In this paper, the observations are positive integer, so it is assumed that the mixture law is a Poisson weighted law and Blending laws are dual. The purpose of this work is to determine the dual laws by simple algebraic properties.Key words: Count Data; Exponetial Family; Weighted Poisson Distribution; Fisher Index; Overdispersion; Underdispersion; Dual Distribution; Convex Combination.

Gelation of microsphere dispersions using a thermally-responsive graft polymer

Dispersions of microspheres (MSs) that form self-supporting particle gels are fundamentally interesting from the viewpoints of gel formation and mechanical properties. Here, we investigate model mixed MS/thermally responsive polymer dispersions that exist as particle gels at 37°C. The MS comprised poly(caprolactone) (PCL) and was prepared by solvent evaporation. The thermally responsive polymer contained a cationic backbone and poly(2-(2-methoxyethoxy)ethyl methacrylate) side chains and is abbreviated as PMA. Mixed PCL/PMA dispersions formed weak gels due to depletion at 20°C. At higher temperatures they formed stronger gels due to a combination of bridging of PCL MS by PMA and reinforcement by a PMA network. A key parameter controlling the mechanical properties of the reinforced MS particle gels was the volume fraction of PMA with respect to total polymer present (ΦPMA). Self-healing behaviour was observed for the gels using dynamic rheology and this depended on ΦPMA. The MS particle gel mechanical properties were conceptually described in terms of isostress and isostrain blending laws. At ΦPMA less than or greater than 0.057 the gels were dominated by the PCL or PMA networks, respectively. The latter value is suggested to be analogous to a phase inversion point.

Segregative phase separation in agarose/whey protein systems induced by sequence-dependent trapping and change in pH

Abstract The structural properties and morphology of mixed gels made of aqueous preparations of agarose and whey protein were modified by changing thermal treatment and pH. The conformationally dissimilar polymers phase separated and this process was followed by small-deformation dynamic oscillation in shear, differential scanning calorimetry and environmental scanning electron microscopy. Experimental protocol encourages formation of a range of two-phase systems from continuous agarose matrices perforated by liquid-like whey protein inclusions to phase inverted preparations where a soft protein matrix suspends hard agarose-filler particles. These distinct morphologies have widely different mechanical moduli, which were followed by adapting a theoretical analysis (isostress–isostrain and Lewis–Nielsen blending laws) from the literature in synthetic block polymers and polyblends. Based on this framework of thought, reasonable predictions of the elastic moduli in the composite gels were made that led to patterns of solvent partition between the two polymeric networks. It was shown that proteins, in mixture with polysaccharide, exhibit favorable relative affinity (P-factor) for water molecules at a pH above their isoelectric point. This is an unexpected outcome that adds to the central finding of a single P value for the distribution of solvent between the continuous matrix and discontinuous inclusions of binary gels. It was thus proposed that phase continuity and solvent distribution in agarose/whey protein systems are under kinetic control that can be heavily governed by pH changes in the aqueous environment.

Morphology and Mechanical Properties of Bicontinuous Gels of Agarose and Gelatin and the Effect of Added Lipid Phase

This study examines the structural properties of binary and tertiary mixtures made of the cold-setting biopolymers agarose and gelatin and a lipid phase with solid or liquid-like viscoelasticity. The working protocol included the techniques of small-deformation dynamic oscillation on shear, modulated differential scanning calorimetry and scanning electron microscopy, and theoretical modeling that adapted ideas of relating the morphology to the elastic modulus of synthetic polyblends and block polymers. The experimental setting was designed to encourage extensive phase separation in the binary gel of agarose and gelatin whose mechanical properties were rationalized on the basis of a bicontinuous blending law. The presence of two continuous phases allowed the slower-gelling component (gelatin) to exhibit favorable relative affinity for the solvent with increasing concentrations of the protein in the system. This is an unexpected outcome that contradicts the central finding of a single value of the p factor observed in the distribution of solvent between the continuous matrix and discontinuous inclusions of deswelled binary gels reported earlier in the literature. The incorporation of a lipid phase of effectively zero elastic modulus or in excess of 10(8) Pa in the composite aqueous gel weakens or reinforces the matrix accordingly. The elastic moduli and morphology of the tertiary blend were related to changing the relative phase volumes of components using analytical expressions of isotropically dispersed soft or rigid filler particles in a polymeric matrix.

Rheological behavior of amylopectin and β-lactoglobulin phase-segregated aqueous system

The rheological behavior of amylopectin–β-lactoglobulin–water system in the region of incompatibility was studied by performing constant shear rate and oscillatory measurements. Phase-segregated samples were prepared at concentrations that laid over the binodal and tie-lines. The results were interpreted in terms of the isostress and isostrain blending laws. For this purpose the bases of Takayanagi model was used and a modified model considering the gradual formation of double emulsions close to the phase-inversion concentration that explain the transition was proposed. Good agreement between observed and calculated values was obtained using the isostress and isostrain models. Phase segregation and the phase-inversion control the rheological properties of the amylopectin–β-lactoglobulin mixture in aqueous media.

Co-gels of whey protein isolate with crosslinked waxy maize starch: Analysis of solvent partition and phase structure by polymer blending laws

Co-gels of whey protein isolate (WPI) and phosphate-crosslinked waxy maize starch (PCS) were formed by heating from 50 to 80 °C at 1 °C/min, holding for 30 min at 80 °C, cooling to 20 °C at 1 °C/min and holding for 30 min at 20 °C, with measurement of storage modulus ( G′) and loss modulus ( G″) at 1 rad s −1 and 0.5% strain throughout. G′ and G″ remained essentially constant on holding at 20 °C, and average values of log G′ during the holding period were used in analysis of co-gel moduli by the Takayanagi isostrain and isostress blending laws. WPI in the absence of starch and PCS in the absence of WPI were subjected to the same time–temperature regime as the mixtures, to provide calibration curves for use in the analyses. As anticipated, WPI and PCS showed independent thermal transitions in DSC heating scans, with no indication of any associative interactions between the two materials. During cooling, the mixtures showed appreciable increases in G′, similar to those observed for WPI alone, whereas slight decreases were observed for PCS, indicating a continuous WPI phase and dispersed starch phase. The magnitude of the increase in G′ observed on gelation of WPI also indicated development of a continuous protein network. Blending law analyses in which the starch phase was assumed to consist of fully swollen PCS granules dispersed individually through a WPI gel matrix were unsuccessful in matching the observed values of log G′ for the composites, irrespective of whether the swelling volume of PCS was held fixed at the value of Q≈11.9 mL/g determined experimentally by the polymer-exclusion method using blue dextran, or treated as a variable parameter, along with the modulus of individual swollen granules, which was varied in both analyses. However, an analysis in which PCS was regarded as a second gelling polymer gave a high standard of agreement ( r 2=0.994) between observed and fitted values of log G′ for all mixtures studied (18 in total, with concentrations of PCS ranging from 1 to 5 wt% and concentrations of WPI ranging from 1 to 10 wt%). The only variable in this analysis was the “solvent avidity parameter”, p, defined as the ratio of water to polymer in the (continuous) WPI phase divided by the corresponding ratio for the (dispersed) PCS phase. The best fit was obtained with p≈3.3. This high relative affinity of WPI for water implies restricted swelling of PCS except at low concentrations of either or both components of the mixtures. The changes in G′ observed on heating indicated that at high concentrations of WPI separation into a dispersed starch phase in a continuous protein matrix occurred prior to gelatinisation of PCS. At lower concentrations of WPI, however, gelatinisation of PCS was accompanied by large increases in G′, indicating formation of a starch network which was then fragmented by gelation of WPI. Fragments of starch network (on the length scale of ∼10–100 μm) embedded in a WPI gel matrix were visualised directly by light microscopy.

Multiple Neuro-Adaptive Control of Robot Manipulators Using Visual Cues

A new adaptive controller based on multiple neural networks (NNs) for an uncertain robot manipulator system is developed in this paper. The proposed multiple neuro-adaptive controller (MNAC) switches to a memorized control skill or blends multiple skills by using visual information on the given job to improve the transient response at the time of task variation like a change of manipulating object. MNAC is a type of adaptive feedback controller where system nonlinearity terms are approximated with multiple NNs. The proposed controller is effective for a job where some tasks are repeated but information on the load cannot be scheduled before the operation. During the learning phase, MNAC memorizes a control skill for each load with each NN. For a new task, most similar existing control skills may be used as a starting point of adaptation, which improves the performance of learning. Lyapunov-function-based design of MNAC guarantees the stability of the closed-loop system to be independent of switching or blending law. Simulation results on a two-link manipulator for changing the mass of the given load were illustrated to show the effectiveness of the proposed control scheme by comparison with the conventional neuro-adaptive controller.

Bridging the Divide between the High- and Low-Solid Analyses in the Gelatin/κ-Carrageenan Mixture

Over the past few years, a considerable amount of work has been done in several laboratories on the measurement of structural properties of low-solid biopolymer mixtures or high-solid materials of a single biopolymer in the presence of co-solute. The main objective of this work has been to establish a correlation between the two types of systems and extend it to a binary mixture in a high-solid environment. In doing so, it employed well-characterized kappa-carrageenan and gelatin samples in an aqueous preparation or in the presence of glucose syrup and sucrose. The phase behavior of the composite gel was ascertained using small-deformation dynamic oscillation, differential scanning calorimetry, and light microscopy. Experimental observations were built into polymer blending laws that argued for an explicit phase topology and distribution of solvent between the two networks. A working hypothesis was formulated and applied to high-solid mixtures thus identifying phase or state transitions in the time/temperature function. This led to the development of a mechanical glass transition temperature as the threshold of two distinct molecular processes governing the "rubber-to-glass" transformation. A stage was reached at which the predictions of the hypothesis were found to be in good agreement with the experimental development of viscoelasticity in the high-solid kappa-carrageenan/gelatin mixture ranging from the rubbery plateau and the transition region to the glassy state.

RHEOLOGICAL PROPERTIES OF HOT-MELT PRESSURE-SENSITIVE ADHESIVE (HMPSAs) BASED ON STYRENE–ISOPRENE COPOLYMERS. PART 2: INNOVATIVE MOLECULAR DESIGN FROM PREDICTIVE FORMUlATION

This article is the second in a series that deals with the viscoelastic properties of Hot-melt pressure-sensitive adhesives (HMPSAs) based on formulations of block copolymers and tackifying resins. The viscoelastic properties of HMPSAs govern, to a large extent, their adhesion, processing, and end-use properties. In the first part of this article, we present a brief description of the rheological behavior of styrene isoprene styrene–styrene isoprene [SIS–SI] copolymer blends at room temperature. We then present an original approach that may lead to the design of new block copolymers (tetrablock and radial copolymers) that mimic the rheological behavior at room temperature of optimized SIS–SI blends used in adhesive formulations. We describe the concept and calculations that lead to the design of the characteristics of these new molecules. In the third part of this article, we discuss in detail the rheological behavior of these new block copolymers compared with the observed behavior of equivalent SIS–SI. In the last part we also demonstrate how the molecular model of the rheological behavior developed in the first article of this series can be applied to these new molecules. We propose, in particular, to apply the blending law (presented in the first article) on the complex shear modulus instead of the relaxation modulus, which simplifies calculations and even leads to a better agreement with experimental data. As a conclusion, we show how this original approach can bring really innovative solutions for the formulation of adhesives with specific properties by using molecular concepts of viscoelasticity.

Composition Dependencies of the Rheological Properties of Rice Starch Blends

ABSTRACTThe gelatinization, pasting, and dynamic rheological parameters of rice starch dispersions from Kaoshiung Sen 7 (KSS7), Taichung Waxy 70 (TCW70), and their blends were examined in relation to total starch concentration (Ct) and the property of starch components. Mixing the rice starches, especially at equivalent ratios, resulted in decreasing onset temperature for gelatinization or developing viscosity and in cold‐paste viscosity, accompanied by a synergistically increased peak viscosity. The logarithmic of storage moduli, G′, for all starch dispersions except the retrograded systems of Ct = 20–30 wt%, showed two linear dependencies on the weight‐average amylose content (AC) of the blends separating at a critical AC of 20 wt% (i.e., TCW70 = 25 wt%). Interestingly, the temperatures at which G′ started to increase drastically maximized on heating, and the exponent n of G′ ∝ Ctn also maximized at the same TCW70 starch concentration Generally, the elasticity of the systems after complete gelatinization and retrogradation followed the isostress models of Takayanagi's blending laws at Ct = 10 wt%, but changed to the intermediates of isostress and isostrain at Ct = 20–30 wt%. The changes in these parameters can be explained by competitive swelling behavior, the strengthening effect of swollen granules, and shear disintegration.

Gelling property of soy protein–gum mixtures

Gelling properties of soy protein–gum mixtures were determined by small deformation oscillation measurement and the experimental data were analyzed with blending laws of polymers. Gel strength of soy protein–carrageenan mixture was found to follow either upper or lower bounds depending on the concentration of the constituents, suggesting the occurring of phase shift. G′ of soy protein–xanthan mixed gel always followed the upper bound, indicating that soy protein was the continuous phase regardless variations of the gum concentration. Combination of soy protein with propylene glycol alginate (PGA) produced a mixed gel with high gel strength and stayed above the upper bound at all gum concentrations examined. Covalent bonds between PGA and soy protein was suggested to contribute to the rigidity. Storage modulus of the mixture of soy protein–locust bean gum (LBG) was below the lower bound at low gum concentrations due to the limited demixing process of LBG. G′ values of the mixture of soy protein and LBG–xanthan followed the lower bound but approached upper bound on reducing protein concentration, suggesting that the presence of soy protein might inhibit LBG–xanthan mixture from forming continuous networks.

Rheological Characterization of Styrene Methyl Methacrylate Copolymers

The influence of copolymer composition on the rheological properties of random copolymers of styrene with methyl methacrylate (SMMA) obtained by radical polymerization in bulk was investigated. Differential scanning calorimetry (DSC) analysis shows that the glass-transition temperature of the copolymers increases with the methyl methacrylate (MMA) content. The knowledge of the glass transition is used to compare the different copolymers in an iso-free volume condition for melt rheology. Time temperature superposition was used to get a large frequency window ranging from the terminal zone up to the glassy plateau. The mechanical spectroscopy especially, was used to estimate the rubbery plateau modulus and the Newtonian viscosity. It has been possible to estimate the rubbery plateau modulus of SMMA copolymers from the experimental values of the corresponding homopolymers. For this particular system, the molecular weight between entanglement was shown to follow a simple blending law.

Ca 2+-induced gelation of low-methoxy pectin in the presence of oxidised starch. Part 2. Quantitative analysis of moduli

The observed moduli ( G′; 10 rad s −1; 0.5% strain; 5°C) of the co-gels formed by mixtures of calcium pectinate (DE 34.2; stoichiometric Ca 2+) and oxidised starch (0–40 wt%) have been matched with good precision by an analysis based on the following postulates. (i) Thermodynamic incompatibility between the two polymers causes partial precipitation of pectin chains into aggregated bundles within a supporting calcium pectinate network. (ii) The extent of precipitation is controlled by a solubility product ( K), defined as the starch concentration multiplied by the square of the concentration of unprecipitated pectin. (iii) The volume occupied by the precipitated pectin fraction is directly proportional to the amount precipitated (constant of proportionality, k). The system was regarded as comprising a continuous phase of oxidised starch and unprecipitated pectin surrounding a dispersed phase of precipitated pectin, and overall moduli were calculated using the Takayanagi isostress blending law. The root-mean-square difference between observed and calculated values of log G′ was minimised by varying the two adjustable parameters, k and K (which determine phase volumes and partition of pectin between the phases). The moduli of the individual components at their effective concentration within the appropriate phase were determined from standard calibration curves for calcium pectinate and oxidised starch alone. The overall modulus of the continuous phase was estimated by simple addition of the separate contributions from unprecipitated pectin and oxidised starch. The modulus of the dispersed particles of precipitated pectin was effectively infinite in comparison with that of the continuous phase, allowing a simplified form of the isostress equation to be used. Best agreement was obtained with K=0.83 (for concentrations in wt%) and with a value of k corresponding to a pectin concentration of ∼16.4 wt% within the precipitated bundles (∼5 g water per 1 g of pectin). Discrepancies between observed and fitted values of log G′ were not significantly beyond experimental error, suggesting that the concept of partial precipitation of calcium pectinate in response to segregative interactions with oxidised starch is a realistic interpretation of the reductions in co-gel moduli reported in the preceding paper.

Co-gelation of calcium pectinate with potato maltodextrin. Part 2. Analysis of co-gel moduli

The experimental moduli reported in the preceding paper for co-gels of calcium pectinate (DE 31.1; stoichiometric Ca 2+) with potato maltodextrin have been analysed using the procedures and assumptions developed for mixtures of calcium pectinate with oxidised starch. In outline, part of the calcium pectinate was assumed to be “precipitated” into a dispersed phase in response to segregative interactions between the two polymers, with the residual concentration of unprecipitated (“free”) pectin being controlled by a solubility product K, defined as the maltodextrin concentration multiplied by the square of the concentration of free pectin, and with the phase volume of dispersed particles being directly proportional to the amount precipitated (constant of proportionality, k). The modulus of the continuous matrix was estimated by simple addition of the individual contributions from maltodextrin and free pectin, derived from standard calibration curves, and calculated values of co-gel moduli were obtained using the Takayanagi isostress blending law in the limiting form for an infinitely hard filler. Best-fitting values of K=2.8 and k=0.059 were identified by least-squares minimisation of the overall difference between observed and calculated values of log G′ at 5°C for mixtures incorporating 2.0 wt% calcium pectinate prepared by two different procedures and measured 100 and 400 min after the start of cooling from 90°C at 1°C/min, with maltodextrin concentrations in the range 0–25 wt% (100 min values) or 0–17.5 wt% (400 min), and for 20 wt% maltodextrin with 0–3.0 wt% calcium pectinate (100 min values for one method of preparation). The fits to all five data sets were virtually within experimental error. The best-fitting value of k is almost identical to the value obtained for mixtures of calcium pectinate with oxidised starch (0.059 in comparison with 0.061), consistent with collapse of calcium pectinate network structure to a fixed concentration of ∼17 wt% in both systems.

Bulk polymerization of ε-caprolactone: Rheological predictive laws

The rheological behavior during bulk polymerization of e-caprolactone with titanium tetrapropoxide as the initiator was studied in connection with the kinetics of the reaction (conversion rate and molecular weight variations). The viscoelastic properties of the melt polycaprolactone performed by this reactive system was predicted reasonably well using phenomenological models such as the Yasuda–Carreau or relaxation spectrum models and a molecular dynamic model based on a blending law of the relaxation function. The evolution of these viscoelastic properties during bulk polymerization was calculated by combining these viscoelastic models with the kinetic laws of the system. By taking into account the dilution effect caused by the presence of a monomer, a global rheological predictive model was then achieved. It was shown to give a reasonably good depiction of the viscoelastic properties [‖η*(t)‖, G′(t) and G″(t)] whatever the processing conditions (temperature, frequency, initiator concentration, etc.) are.

Predictions of linear viscoelastic properties for polydisperse entangled polymers

Different blending laws have been proposed in the literature to describe the polydispersity effect on the rheological behavior of polymer melts. In this paper predictions of linear viscoelastic properties of entangled polydisperse polymers have been derived from the double reptation mixing rule. The results in terms of the relaxation modulus, the zero shear-rate viscosity, η0, and the steady-state compliance, Je0, have been obtained using three different relaxation functions for the monodisperse fractions, namely the Tuminello step function, the single exponential function and the BSW function. Both discrete and continuous molecular weight distributions (MWDs) have been investigated. The Generalized Exponential Function (GEX) has been considered in the continuous case.

The application of blending law on linear viscoelastic properties of linear–star and star–star polymer blends

A quadratic binary blending law of the terminal relaxation spectra is used to predict the viscoelastic properties of star–star and linear–star polymer blends. The results are compared with the experimental data reported by Struglinski et al. Star polymers with long arms are assumed to dominate the relaxation behavior of the star–star polymer blends. In the linear–star polymer blends, star polymers are assumed to dominate the relaxation behavior. The ‘iso-relaxation time’ approach is proposed to represent the linear chain by an equivalent star chain for the linear–star polymer blends. The predicted viscoelastic properties agrees with the experimental observation very well. Also, the well known relation, J e o b ∝1/v 2 ( v 2 is the volume fraction of long-arm star chains), can be deduced from the binary blending law for the concentrated long-arm star chains entangled with much shorter chains. Furthermore, it also predicts that it would systematically depart from the relation, J e o b ∝1/v 2 , when the molecular weight of shorter chain becomes closer to the molecular weight of long-arm chain. In the limit, M 1/ M 2=1, the relation is switched to J e o b ∝v 2 .