非牛顿流体自然收敛半角方程的实验验证

引言非牛顿流体从大截面流道进入小截面流道时形成的收敛流动，是工业过程中常见的流型，如石油输运、聚合物加工过程等．流体的自然收敛角定量地描述了流体在流道入口前区的流动形态．在先前的工作中，作者应用最小能原理，导出非牛顿流体自然收敛半角方程式中，e是Bagley校正因子，n是非牛顿指数，是与流体的粘附性能有关的系数．聚合物熔体属于典型的非牛顿流体．本工作中，拟在考察聚乙烯熔体于毛细管挤出过程中流变行为的基础上，对方程（2）作初步验证1实验1.1原材料选用高密度聚乙烯（HDPE）和低密度聚乙烯（LDPE）作为试样材料…     

Melt rheology of nanometre‐calcium‐carbonate‐filled acrylonitrile–butadiene–styrene (ABS) copolymer composites during capillary extrusion

The melt flow properties during capillary extrusion of nanometre‐calcium‐carbonate‐filled acrylonitrile–butadiene–styrene (ABS) copolymer composites were measured by using a Rosand rheometer to identify the effects of the filler content and operation conditions on the rheological behaviour of the sample melts. The experiments were conducted under the following test conditions: temperature varied from 220 to 240 °C and shear rate ranged from 10 to 10⁴ s^?1. The filler volume fractions were 0, 10, 20, 30, 40 and 50%. The results showed that the shear flow did not strictly obey the power law under the test conditions, and that the entry pressure drop (ΔP_en) and the extension stress (σ_e) in entry flow increased nonlinearly, while the melt shear viscosity (η_s) and extension viscosity (η_e) decreased with increasing the wall shear stress (τ_w) at constant test temperature. The dependence of the melt shear viscosity on the test temperature was approximately consistent with the Arrhenius expression at fixed τ_w. When τ_w was constant, η_s and η_e increased while ΔP_en and σ_e decreased with the addition of the filler volume fraction. © 2002 Society of Chemical Industry     

Stress-strain behavior of polychloroprene vulcanizates containing polymer-gel particles

The equations of stress-strain of gel-filled polymer under large deformation were derived by using a simple model i.e. a sphere in a cubic matrix. The author finds for no adhesion between the phases: In case of perfect adhesion between the phases: where σ(α) is the stress of a blend at an elongation ratio of α, σ_R(α) the stress of a rubber matrix at α, σ_G(α_G) the stress of a gel component at α_G, σ_R (α_R) the stress of a rubber matrix at α_R, ? the volume fraction of gel. The validity of Eq 1 was shown for the polychloroprene vulcanizates containing polystyrene-gel which exhibits no adhesion with the polychloroprene matrix. This result shows the value of the model proposed here. The tensile strength of polychloroprene vulcanizates filled with polychloroprene-gel at break is discussed by the use of Eqs 2–4.     

Influence of die angles on pressure drop during extrusion of rubber compound

The factors affecting pressure losses during extrusion of polymer melts are discussed in the present article. The rheological properties of an unvulcanized rubber compound were examined by using a Monsanto processability tester (MPT) under experimental conditions of temperatures varied 90 to 120°C and shear rates from 10² to 10³ s^?1. Furthermore, a set of dies with different entry angle (2α) was selected to identify the effects of die angles on pressure losses in capillary extrusion of the sample fluid. It was found that the total pressure drop (ΔP) decreased when 2α < 75 degrees, and then increased with increasing 2α. The ΔP reached the minimum value when 2α is around 75°. It suggests that the natural converging angle of the sample fluid be about 75° under the experimental conditions, according to the research results presented in previous work. © 2001 John Wiley & Sons, Inc. J Appl Polym Sci 80: 1150–1154, 2001     

Study on kinetic of natural rubber vulcanization by using vulcameter

The velocity of vulcameter torque change during the vulcanization of natural rubber consists of two increasing and decreasing stages. The vulcanization process in the stage of velocity increasing is not a simple reaction, and can be expressed in an equation of ln(M_H ? M_t) = lnA ? K₁(t ? t₀)^α, which is different from the famous equation of V_ut = ? (aK₃/K₄)ln[(K₂e^K1t ? K₁e^K2t)/(K₂ ? K₁)] deduced by Coran, the value of K₁^1/α in the former can be used as a rate constant to calculate the value of activation energy (E₁) according to the Arrhenius equation. The vulcanization process in the stage of velocity decreasing consists of two first‐order reactions, and can be expressed in a kinetic equation of ln(M_H ? M_t) = lnB ? K(t ? t_dis). The time (t_p) at which the torque change reaches to the maximum velocity (V_m) is corresponding to the time (t_dis) suggested by Coran. © 2003 Wiley Periodicals, Inc. J Appl Polym Sci 88: 680–684, 2003     

Electrodeposition from a fluidized bed electrolyte. II. Effects of bed porosity and particle size

Mass transfer from a fluidized bed electrolyte containing inert particles has been found to depend on bed porosity and particle size. The optimum porosity was found to vary from 0.52 – 0.57 with decreasing particle size but mass transport increased with particle size.A mass transfer entry length effect was observed on the cylindrical cathode but its position within the bulk of the bed was found not to be critical, thus indicating that the hydrodynamic entry length was small. The limiting current density was found to vary as (d _e/L _e)^0.15 whered _e is the annular equivalent diameter andL _e the electrode length.List of symbols Re_I modified Reynolds No. =U _o d _p /v(1–) - Re_II particle Reynolds No. =U _o d _p /v - Re_O sedimentation Reynolds No. =U _i d _p v (constant value) - Re_t terminal particle Reynolds No. =U _t d _p /v - Sc Schmidt No. =v/D - St_I modified Stanton No. =k _L /U _o - C _b bulk concentration, M cm^–3 - D diffusion coefficient, cm² s^–1 - d _t tube diameter, mm - d _e electrode equivalent diameter, mm - d _p particle diameter, mm - bed porosity - zF Faradaic equivalence - cd current density - i _L limiting current density, mA cm^–2 - i _LO limiting current density in the absence of particles - k _L mass transfer coefficient, cm s_–1 - L _e electrode length, mm - m, n constants or indices - v kinematic viscosity, cm² s^–1 - U _o superficial velocity, cm s^–1 - U _i sedimentation velocity, cm s^–1     

The development of the velocity field in polymer melts in a reservoir approaching a capillary die

Color motion pictures have been made of the flow of low-density polyethylene, polystyrene, and isotactic polypropylene at 180°C in the reservoir approach to a capillary extrusion rheometer. Detailed observations of the variation of flow patterns with extrusion rate were made. At low flow rates, essentially radial flow into the capillary entrance was observed in all polymers. With increasing flow rate, the included entrance angle α for the polyethylene and polystyrene decreased from 180°C and a “wine glass” structured velocity field was observed with stagnant circulating regions in the corners and the melt channeling in through the wine glass to the capillary entrance. The angle α was related to entrance pressure drop Δp_e and capillary wall shear stress σ_w data through the semilogarithmic equation where α is in degrees; Δp_e/σ_w is interpreted as a Weissenberg number. The breakdown of stable laminar flow of the melts in the reservoir and the distortion of extrudates was observed. These phenomena seemed to be initiated by the formation of a spiralling motion in the reservoir.     

Determination of fracture toughness of poly (ethylene terephthalate) film by essential work of fracture and J integral measurements

Abstract

The plane stress fracture toughness of a semicrystalline poly (ethylene terephthalate) (PET) film of thickness 0·125 mm has been measured as a function of specimen size, specimen geometry, loading rate, and temperature using the essential work of fracture (EWF) approach. It was found that the specific essential work of fracture w _e was independent of specimen width, specimen gauge length, and loading rate, but was dependent upon specimen geometry and test temperature. Below the glass transition temperature (93°C), w _e for double edge notched tension (DENT) type specimens was temperature insensitive, but increased with temperature for single edge notched tension (SENT) type specimens. The w _e value for SENT specimens was consistently higher than for DENT specimens. Estimation of w _e via crack opening displacement was reasonable using the relationship w _e = σ_n e _0,y; estimations made via similar type equations were either too high or too low and were generally unsatisfactory. It was found that values of J integral obtained by power law regression and linear extrapolation of the J–R curves to zero crack growth were lower than w _e. The power law regression of the J–R curves with ?a taken as half the crack opening displacement value at maximum load gave J _c values which agreed reasonably well with w _e.     

The dependence of shear and elongational viscosity on the molecular weight of poly(vinylidene fluoride)

The dependence of shear and elongational viscosity on the molecular weight of poly(vinylidene fluoride) has been studied using a capillary rheometer. The elongational viscosity was evaluated based on Cogswell's method with two types of capillaries: capillary length (L)/capillary diameter (D) = 10 mm/1 mm and L/D = 0 mm/1 mm. We used the ratio P₀/P_L that indicates the contribution of elongational flow to the total flow involving both the shear and elongational flows. P_L and P₀ are the pressure losses in the capillary and the converging flows, respectively. P₀/P_L increased with molecular weight and shear rate. This corresponds to decreasing the number of entanglements of molecular chain under a large displacement, especially high shear. Thus, we suggest using P₀/P_L as the parameter of the entanglement interaction on the molecular chain under a large displacement. © 1999 John Wiley & Sons, Inc. J Appl Polym Sci 71: 2381–2384, 1999     

Studies of three-dimensional electrodes in the FMO1-LC laboratory electrolyser

A FMO1-LC parallel plate, laboratory electrochemical reactor has been modified by the incorporation of stationary, flow-by, three-dimensional electrodes which fill an electrolyte compartment. The performance of several electrode configurations including stacked nets, stacked expanded metal grids and a metal foam (all nickel) is compared by (i) determining the limiting currents for a mass transport controlled reaction, the reduction of ferricyanide in 1 m KOH and (ii) measuring the limiting currents for a kinetically controlled reaction, the oxidation of alcohols in aqueous base. It is shown that the combination of the data may be used to estimate the mass transfer coefficient, _L, and the specific electrode area, A _e, separately. It is also confirmed that the use of three dimensional electrodes leads to an increase in cell current by a factor up to one hundred. Finally, it is also shown that the FM01-LC reactor fitted with a nickel foam anode allows a convenient laboratory conversion of alcohols to carboxylic acids; these reactions are of synthetic interest but their application has previously been restricted by the low rate of conversion at planar nickel anodes.Nomenclature A _e electrode area per unit electrode volume (m²m^–3) - c bulk concentration of reactant (mol m^–3) - E electrode potential vs SCE (V) - E _1/2 half wave potential (V) - F Faraday constant (96 485 C mol^–1) - I current (A) - IL limiting current (A) - j _L limiting current density (A m^–2) - _L mass transfer coefficient (m s^–1) - n number of electrons transferred - p empirical constant in Equation 2 - P pressure drop over reactor (Pa) - R resistance between the tip of the Luggin capillary and the electrode surface () - q velocity exponent in Equation 2 - (interstitial) linear flow rate of electrolyte (ms^–1) - V _e volume of electrode (m³)     

Reflectance spectra of Munsell standard chips and their appearance

In this article, we present the results of analysis by two different methods for representing information in reflectance spectra of Munsell standard chips that relates to their appearance. The spectrum of a chip j is denoted as r_jμ where μ represents wavelength λ from 430 to 660 nm with 1 nm intervals. The spectrum of light reflected from a chip j under D65 is r_jμ × e_μ where e_μ represents the spectral power distribution of D65 illumination. In one method, singular value decomposition is applied to a matrix of (r_jμ × e_μ). Combining results of this analysis with results of human assessment experiments, we obtain four curves ξ_0α(H) that represent principal hue components α in Munsell Hue, α = redness, yellowness, greenness, and blueness (Fig. 6). The other method is multiple regression of each (r_jμ × e_μ) to activities of three kinds of cones in the retina. From this analysis, we obtain three curves B_q(H) that represent relative involvements of q = L, M, S cone activities in determining the appearance of Munsell Hue (Fig. 10). Two sets of curves, ξ_0α(H), and B_q(H), are compared with predictions from a model of higher order color mechanism (Fig. 12) that has been proposed on the basis of experiments with light stimuli of wavelength λ. It is found that ξ_0α(H), and B_q(H) constructed from broadband spectra of Munsell chips are interpretable in terms of this model. © 2008 Wiley Periodicals, Inc. Col Res Appl, 33, 229–237, 2008     

The determination of network chain density and the chemical stress relaxation of crosslinked polymers

Both initial network chain densities n_M(0) and n_s(0) of dicumyl peroxide-cured natural rubbers were determined from the tensile stress and swelling method, respectively. The difference between n_M(0) and n_S(0) was usually constant, independent of the magnitude of network chain density. That is, it was found that the number of entanglement network chains in the crosslinked natural rubber was usually constant, independent of network chain density. The entanglement network chain density n_II(0) was 0.7 × 10^?4 mole/cc. This led to the supposition that the molecular weight between entanglement points (M_e) would be about 9000. Although this value is far from exact, it does not differ too greatly from the value found for noncrosslinked natural rubber. Next, in order to calculate the number of main-chain scission of crosslinked polymers from their chemical stress relaxation, we proposed our modification of Tobolsky's equation. Using our equation, it was found that the scission of dicumyl peroxide-cured natural rubber occurred in the main chain only. Furthermore, this value agreed with the one obtained from the oxidation of toluene solution of noncrosslinked rubber under the same conditions.     

A model for the zero shear viscosity

An empirical equation for the number of entanglements per molecule has been proposed, which applies over all the molecular weight range. On this ground a simple equation for the zero shear viscosity of monodisperse polymer melts, η₀, has been worked out that appears able to properly take into account the sharp transition of viscosity between the monomeric and the entanglement regimes. The molecular parameters appearing in the new viscosity equation are: the monomeric molecular weight m₀, the monomeric friction factor ζ₀, the molecular weight M, the average molecular weight between entanglements M_e, and the entanglement friction factor ζ_e^3.4. This last parameter was evaluated for a number of monodisperse polymers.     

Wood's metal porosimetry and its relation to mercury porosimetry

Wood's metal porosimetry permits the determination of the frequency distribution α(D, D_e) of the volume of pores having diameters in the range D → D + dD whose penetration by Wood's metal (or mercury) is controlled by pores having diameters in the range D_e → D_e + dD_e. The results obtained in sandstone samples indicate that the volume of the entry pores is very small in comparison with the volume of the much larger (up to four times) pores which are penetrated through the entry pores. The accessibility of pores of a wide diameter range is controlled by pore necks of diameters which are distributed over a narrower range. The accessibility function α(D, D_e) has been the starting point of a great deal of in-depth research of pore structure.     

Effect of 2‐mercaptobenzothiazole level on kinetics of natural rubber vulcanization

The kinetics of natural rubber vulcanization were investigated by use of a vulcameter. The vulcanization process before t_dis (the time when the accelerators and/or intermediates react to depletion) was expressed in an equation as ln(M_H ? M_t) = ln A ? k₁(t ? t₀)^α, which is different from the famous equation of Vu_t = ?[α(k₃/k₄)]ln[(k₂e ? k₁e)/(k₂ ? k₁)] deduced by Coran. It was found that the rate constants of two vulcanization processes with different reaction mechanisms before and after t_dis increase and their activation energies decreased with an increase in 2‐mercaptobenzthiazole (MBT) level. The considerable effect of MBT level on the activation energies of the vulcanization process before t_dis and the obvious temperature dependency of the reaction rate of vulcanization process after t_dis were observed. The time t_dis was shortened with an increase in MBT level, whereas the degree of vulcanization at t_dis remained unchanged. © 2004 Wiley Periodicals, Inc. J Appl Polym Sci 92: 3260–3265, 2004     

Order Distance Estimation in Porous Glasses via Transformed Correlation Function of Small-Angle Scattering

A mesoporous two-phase system, consisting of colloidal silica in the cavities of the main silica frame work of a macroporous glass, was investigated by use of Small-Angle X-ray scattering. The transformed correlation function _T(r) was determined for this material for distances r<40 nm. The application of the intrinsic properties of _T(r) yields estimations for two fundamental order distances L ₁=11 nm and L ₂=120 nm of the~porous glass possessing a clear geometric interpretation: L ₁, a short-order-range, is the mean chord length of the mesopores plus the mean chord length in the secondary particles. L ₂, a long-order-range, is an estimation of the mean diameter of a macropore plus the mean free distance in the silica framework which separates two nearly parallel segments of two adjacent macropores.     

Study of ion solvation and ion association in polymer gel electrolyte with polyethylene oxide-co-polypropylene oxide as a plasticizer

Using a molal conductance method, ion solvation and ion association in polytriethylene glycol dimethacrylate (PTREGD)–LiClO₄ gel electrolytes with amorphous ethylene oxide-co-propylene oxide (EO-co-PO, M̄_n = 1750) as the plasticizer were investigated. It was found that the fraction of solute existing as single ions (α_i) and ion pairs (α_p) decreases, while that of triple ions (α_t) increases linearly with increasing salt concentration. The dependence of these fractions on molecular weight of plasticizer was also examined. It was shown that α_i and α_t increase and α_p decreases with increasing molecular weight. The result of temperature dependence of these fractions was very interesting: when the temperature is lower than 55°C, α_i increases while α_p and α_t decrease with increasing temperature; however, when the temperature is higher than 55°C, the reverse is true.     

Behaviour of the spin-spin relaxation time for natural rubber vulcanizates under large deformation

The spin-spin relaxation time, T₂, for DCP-cured natural rubber with various crosslink densities, v_e, has been measured under various deformation. T₂ is separated into two components: one is the long T₂ component, T_2L, for the mobility of amorphous network chains, the other is the short one, T_2S, for that of the strain-induced crystalline chains. T_2L decreased exponentially with increasing extension ratio,α, and the decreasing rate was more remarkable with increasing v_e. The α and v_e dependence of T_2L has been quantitatively explained by the equation experimentally derived by Nishi et al.T_2L under various extension increased and became almost constant with increasing temperature, while the corrected fraction of T_2S, T_2S (%), gradually decreased. The apparent melting point, T_m, at which the corrected T_2S (%) was zero under various deformation was determined. The α dependence of T_m, has been discussed by using Flory's equation.     

聚合物流体入口收敛流动的数值模拟

聚合物流体从大截面流道进入小截面流道时产生的入口收敛流动,是工业中常见的流型之一。基于聚合物流体入口收敛边界流线方程,应用MATLAB对入口收敛流动进行了数值模拟,讨论了Bagley校正因子(e)、非牛顿指数(n)、流道收缩比(λ)等因素对入口收敛流线和入口自然收敛半角(α0)的影响。结果表明:在一定的条件下,入口收敛边界流线的半径r随着e的增加而增大,但随着n的增加而减小,而λ对入口流型的影响不明显;另外α0随着e的增加而减小,但随着n的增加而增大,α0与λ之间呈非线性关系。模拟结果与实验观测较为接近。