Spinodal decomposition and nucleation in the presence of flow

Spinodal decomposition and nucleation of critical fluids are discussed in the presence of laminar shear and turbulence on the basis of recent experiments. In such situations we can realize stationary emulsion-like domain structures due to dynamical balance between thermodynamic instability and shear-induced deformations. In the spinodal decomposition case, unique is the strong shear regime in which the shear exceeds the average relaxation rate of the order parameter. In the nucleation case shear can enhance aggregation of droplets, thus speeding up the growth. But if the shear exceeds a relatively small critical value, even critical droplets can be broken, then leading to complete suppression of the droplet formation. We also predict a considerable increase of the effective viscosity and a large non-Newtonian effect due to domains in the course of spinodal decomposition.Invited paper presented at the Tenth Symposium on Thermophysical Properties, June 20–23, 1988, Gaithersburg, Maryland, U.S.A.     

Flow-induced enhancement of concentration fluctuations in polymer mixtures

Many mixtures of high-molecular-weight polymers are partially miscible, separating into two co-existing phases in some ranges of temperature and concentration. Generally these binary blends exhibit lower critical solution temperature (LCST) behaviour, becoming phase separated as the temperature is raised. We have been undertaking a systematic study of the effect of simple shear flow on the miscibility limits of a number of high-molecular-weight binary polymer blends exhibiting lower critical-solution temperatures. Using a parallel-plate shear cell and light-scattering detection, we have observed large shifts in the cloud-point curves as blends are heated while shear is applied, and we have been able to show, using ancillary measurements of glass-transition temperatures on quenched samples, that these effects are the results of changes in the miscibility of the blends and not artefacts of the scattering techniques. Both shear-induced 'mixing' and 'demixing' have been observed-the latter in temperature ranges well below the quiescent cloud points. We have investigated the kinetics of the appearance of the two-phase structures, and this is very reminiscent of the spinodal decomposition processes observed in zero shear from these blends. Small-angle neutron scattering is very sensitive to the rather short wavelength concentration fluctuations (a few nanometres) in binary systems, both in the stable one-phase region and in the early stages of instability in the two-phase region. Small-angle neutron-scattering results on blends sheared and quenched at temperatures far below the spinodal temperature show the effects of the shear in modifying the blend's structure factors.     

Phase separation mechanism of rubber-modified epoxy

The phase separation mechanism during the cure reaction of a liquid rubber-modified epoxy resin was investigated by light scattering, light microscopy, torsional braid analysis, electron microscopy, and differential scanning calorimetry. The binary mixture of epoxy oligomer (diglycidyl ether of bisphenol A) and carboxyl-terminated butadiene-acrylonitrile copolymer (liquid rubber) exhibited the upper critical solution temperature-type phase behaviour. The mixture loaded with curing agent was a single-phase system in the early stage of curing. When the cure reaction proceeded, phase separation took place via the spinodal decomposition induced by the increase in the molecular weight of epoxy. This was supported by the characteristic change of light scattering profile with curing time. Electron microscopy revealed that, in cured resin, the spherical rubber domains are dispersed somewhat regularly in an epoxy matrix. The regular domain arrangement seems to result from a specific situation; the competitive progress of the spinodal decomposition and polymerization; i.e. the coarsening process to irregular domain structure seems to be suppressed by network formation in the epoxy phase. It was also shown that curing at higher temperatures resulted in the suppression at an earlier stage of spinodal decomposition, and hence, shorter interdomain spacing.     

Apparatus for Simultaneous Small Angle Neutron Scattering and Steady Shear Viscosity Studies of Polymer Melts and Solutions

The design and construction of an apparatus for studying the simultaneous small angle neutron scattering (SANS) and steady shear viscosity behavior of polymer melts and concentrated solutions is discussed. Successful operation of the device is demonstrated on a blend of 20 weight percent deuterated polystyrene and 80 weight percent poly(vinylmethylether). The effects of shear on the critical behavior of the blend are observed in the SANS behavior as a function of temperature and shear rate and indicate shear induced mixing behavior for the range of shear rates examined. The steady shear viscosity results alone are insufficient for detecting the transition from one to two phases. The examination of shear effects in polymer blends is important for understanding the critical behavior of binary systems. Technologically, knowledge of the phase behavior of polymer blends under shear are important for the design and improvement of commercial blend processing.     

Ellipsometry of the liquid-vapor interface close to the critical point: A theoretical analysis

It is shown that the ellipsometric coefficient for a liquid-vapor interface may be written as the sum of three contributions. The first is given by Drude's formula. The second contribution is due to capillary wave fluctuations. Finally, the third contribution is due to fluctuations of the density profile around the Fisk-Widom profile with a wavelength up to roughly the bulk correlation length and thus short compared to the capillary length. Close to the critical point the first two contributions scale as (T - T _c ) ^- . The expression for the third contribution contains an integral over the excess density correlation function over wave vectors large compared to the inverse bulk correlation length. The scaling behavior of the third contribution is probably such that this term becomes unimportant close to the critical point. The formulae given in this paper only for the liquid-vapor interface may be used for a binary fluid if one makes the usual substitutions. An experimental analysis of the ellipsometric coefficient for binary fluids close to the critical point by Schmidt [1] indicates that the sum of the first two terms predicts a value which is somewhat to large but which has the correct scaling behavior. A discussion of this difference in amplitude is given.Paper presented at the Tenth Symposium on Thermophysical Properties, June 20–23, 1988, Gaithersburg, Maryland, U.S.A.Formerly National Bureau of Standards     

Compatibility of poly(α-methyl styrene-co-acrylonitrile) with PMMA: A neutron and cloud point study

Cloud point (CP) experiments were perform-ed using blends of deuterated polymethylmethacrylate (PMMA(D)) and a statistical copolymer P(αMS – co- AN) which consists of α-methylstyrene (αMS) and acrylonitrile (AN). A lower critical solution temperature (LCST) behavior is found. The corresponding interaction parameter χ is calculated accounting for temperature and concentration dependence. In order to improve the accuracy, temperature dependent small-angle neutron scattering experiments are performed for a 50/50 blend which reveal spinodal and binodal temperatures. Additionally, bilayers of P(αMS – co- AN) and PMMA(D) are prepared and annealed. The compositions of coexisting phases and the interface widths are determined by neutron reflectometry (NR). Interaction parameters calculated from the compositions of coexisting phases are in agreement with SANS and CP results. Effects of molar mass distribution are discussed. Received: 17 October 2000 / Reviewed and accepted: 18 October 2000     

Experimental apparatus for measuring the thermal diffusivity of pure fluids at high temperatures

Dynamic light scattering represents a suitable method for measuring the thermal diffusivity of optically transparent fluids. The classic application of the method is the immediate vicinity around the critical point due to its dependence upon the intensity of scattered light and its high sensitivity to undesired light scattering. By means of subsequent modifications of the experimental setup, we have been able to expand this region of applicability over the last 12 years and could systematically investigate numerous substances and their binary mixtures within a temperature range of 280 K<T<350 K. Our planned investigation of fluids suitable for ORC-HP-technology necessitates performing measurements at higher temperatures and pressures. The experimental apparatus newly designed for this purpose is capable of sustaining a relatively high temperature constance at temperatures up to 700 K. Factors restricting the measurable range of state and their influence on the design of the sample cell are discussed.Paper presented at the Tenth Symposium on Thermophysical Properties, June 20–23, 1988, Gaithersburg, Maryland, U.S.A.     

Light Scattering by Commercial Sugar Solutions

Using a direct measure of scattered light, it was found that commercial sugar solutions scatter light predominantly in a forward direction. The scattering at angles less than 30° was as much as one hundred times that at right angles to the incident beam.It was found that the light scattering by commercial sugar solutions is inversely dependent on wavelength to a power of between 2 and 3, and that severe multiple scattering occurs when the turbidity of the solution is larger than 2×10⁻¹cm⁻¹ at 436 mµ. The scattering of commercial sugar solutions is compared with that of highly purified sucrose.A method is discussed that will enable a good approximation of the turbidity of commercial sugar solutions to be made from a single forward scattering measurement at an angle of about 20° with respect to the incident light beam. A correction for scattered light in transmission measurements of these solutions is also introduced.     

Modeling and testing strain rate-dependent compressive strength of carbon/epoxy composites

A technique for testing high modulus fiber-reinforced composites in compression at different strain rates is investigated. The rate-dependent compressive behavior of unidirectional AS4/3501-6 carbon/epoxy composite is characterized by using off-axis specimens. It is found that, in the compression test, a titanium coating applied at the contact ends of the off-axis specimen can greatly reduce contact frictions, allowing a fully developed extension–shear coupling so that a state of uniform stress in the specimen can be achieved. A rate-dependent nonlinear constitutive model and a dynamic compressive strength model (fiber microbuckling model) for the unidirectional AS4/3501-6 composite are established based on the low strain rate off-axis test data. Model predictions and experimental data including high strain rate data are in very good agreement indicating that the constitutive model and compressive strength model obtained with low strain rate data are valid for high strain rates as well. A technique is also developed to extract the longitudinal compressive strength of the composite from those of the off-axis specimens.     

Experimental studies of the rheological behavior of a demixing biopolymeric sol

Experimental data are presented concerning a large transient viscosity surge occurring in the course of spinodal demixing of agarose aqueous solutions. The study includes the effects of water perturbation by minor proportions of compatible cosolutes. Three observations are noteworthy. One concerns an upward or downward shift of the spinodal temperature, caused by cosolutes, which agrees with their expected modulation of solvent-induced forces. The second concerns the time of appearance of the viscosity surge. This is observed to follow a critical law, with an exponent independent of polymer concentration and solvent perturbation. The third concerns the inverse-power-law dependence of the viscosity peak value on shear. When the shear is scaled with an appropriate relaxation time, related to the overall interdomain structure generated by spinodal demixing, all data fall on a master curve, independent of polymer concentration, quenching depth, and solvent perturbation. This allows assigning the observed viscosity behavior to distortion and rupture of the overall interdomain structure generated by spinodal demixing.Paper presented at the Twelfth Symposium on Thermophysical Properties, June 19–24, 1994, Boulder, Colorado, U.S.A.     

钛酸钙系电流变液在直流电场下静态剪切的应力响应

研究了直流电场下钛酸钙系电流变液在静态剪切模式下的力学响应,得到了材料在静态剪切模式下的应力应变关系,讨论了材料温度、电压和剪切应变对应力的影响,以理论推导和实验数据拟合的方法得出了剪切应力与剪切应变、温度以及电场强度等参数的半经验数学关系式.理论值对比实验结果表明,剪切应力表达式与实验结果符合较好,可以用于预测材料在静态剪切模式下的剪切应变,温度和电场强度对剪切应力的影响.     

Thermal diffusivity of fluids in a broad region around the critical point

Dynamic light scattering is a suitable method for the investigation of transport properties such as the thermal diffusivity of optically transparent fluids. The main advantages of the method are its quickness, the fact of the thermodynamic state of equilibrium of the sample (gradients are not required), and the relatively simple evaluation of data without the necessity of calibration. However, an insufficient production of intensity of scattered light may be a limiting effect. For that reason the vicinity of the gas-liquid critical point represents the classical range of application. In this paper, it is shown that by means of an appropriate choice of experimental apparatus, measurements are also feasible in an extended range of states. Broad regions around critical points of three pure fluids (sulfur hexafluoride, SF₆; ethane, C₂H₆; nitrous oxide, N₂O) over temperature ranges ¦T-T _c¦ of 0.02 to 50 K and density ranges (/_c) of 0.2 to 2 were investigated. In this region the thermal diffusivity shows great variations with temperature and density and cannot be described by means of ideal-gas behavior or relations for liquids. The measurements were carried out along the coexistence curve for both phases, along the critical isochore and along some isotherms with TT _c. The measured or calculated density, pressure, and thermal diffusivity data as well as some correlations are presented.     

Theory of the universal and nonuniversal quantities of fluids at the critical point

We show that the hierarchical reference theory is an accurate global theory of fluids at least above the critical temperatureT _c. The hierarchy is truncated at the first equation, the one connecting the free energy to the pair correlation function, with an Ornstein-Zernike ansatz. In this approximation the theory can be considered as a sophisticated generalization of the optimized random phase approximation which has genuine nonclassical critical exponents and for which scaling is satisfied. We study the system of hard spheres plus the Lennard-Jones attractive well and find a good agreement with measuredPVT, specific heat, correlation length, and structure factor in rare gases. The accuracy of the theory remains very good up to freezing density.Paper presented at the Tenth Symposium on Thermophysical Properties, June 20–23, 1988, Gaithersburg, Maryland, U.S.A.     

Laser-induced thermal acoustics (LITA) signals from finite beams

Laser-induced thermal acoustics (LITA) is a four-wave mixing technique that may be employed to measure sound speeds, transport properties, velocities, and susceptibilities of fluids. It is particularly effective in high-pressure gases (>1 bar). An analytical expression for LITA signals is derived by the use of linearized equations of hydrodynamics and light scattering. This analysis, which includes full finite-beam-size effects and the optoacoustic effects of thermalization and electrostriction, predicts the amplitude and the time history of narrow-band time-resolved LITA and broadband spectrally resolved (mulitplex) LITA signals. The time behavior of the detected LITA signal depends significantly on the detection solid angle, with implications for the measurement of diffusivities by the use of LITA and the proper physical picture of LITA scattering. This and other elements of the physics of LITA that emerge from the analysis are discussed. Theoretical signals are compared with experimental LITA data.     

Simple model of a polarized bidirectional scattering cross section at 10.6 mum: application to SiO(2) sand

A model is proposed to interpret the polarized scattering behavior for natural soils. The model is based on the vector radiative transfer equation and is developed to the second order. Higher orders are modeled with a simple expression. The particles are assumed to have a large dimension with respect to the wavelength, allowing for the light to be locally specularly reflected. Apart from the complex refractive index, the model has only one extra parameter directly related to the compactness of the medium. Predicted values are compared with carefully calibrated measurements of the polarized bidirectional scattering cross section obtained with coarse SiO(2) sand. The model parameters retrieved from the fit are quite realistic. Good agreement is obtained between model-computed and experimental data for the angular behavior and the amplitude, without further adjustment. Comparison between model-computed total unpolarized bidirectional scattering cross section, Hapke's nonpolarized model, and measurements also shows good agreement.     

Thermophysical Properties of Fluids from Dynamic Light Scattering

In a continuous development for more than three decades, dynamic light scattering (DLS) has evolved into a versatile and powerful technique for the determination of transport and other thermophysical properties of fluids. The success is founded on its application in a macroscopic thermodynamic equilibrium, i.e., without the need for employing external gradients, to determine a large variety of properties, which can be derived, in some instances even simultaneously, by an appropriate experimental approach and a corresponding signal analysis. The principles, essential features, and variants of the technique are reviewed, and a survey on the determination of various desired transport and thermophysical properties is given, both for the application of light scattering from bulk fluids and for the variant of surface light scattering (SLS). The stage of development and the corresponding uncertainties are discussed for the measurement of the individual quantities, and the performance of the method is demonstrated by representative experimental results for relevant fluids.     

Self-consistent approach to the solution of the light transfer problem for irradiances in marine waters with arbitrary turbidity, depth, and surface illumination. I. Case of absorption and elastic scattering

A self-consistent variant of the two-flow approximation that takes into account strong anisotropy of light scattering in seawater of finite depth and arbitrary turbidity is presented. To achieve an appropriate accuracy, this approach uses experimental dependencies between downward and total mean cosines. It calculates irradiances, diffuse attenuation coefficients, and diffuse reflectances in waters with arbitrary values of scattering, backscattering, and attenuation coefficients. It also takes into account arbitrary conditions of illumination and reflection from the bottom with the Lambertian albedo. This theory can be used for the calculation of apparent optical properties in both open and coastal oceanic waters, lakes, and rivers. It can also be applied to other types of absorbing and scattering medium such as paints, photographic emulsions, and biological tissues.     

Effects of shear flow and viscosity difference on phase separation

We discuss some salient features recently found in phase-separating fluids under shear. They are highly elongated, bicontinuous domain structures (string phase), hysteresis in the droplet distribution in the off-critical case. existence of the spinodal due to suppression of droplet formation in shear. and critical rheology. We also examine the condition of bicontinuity and the effective viscosity when the two phases have different viscosities.Paper presented at the Twelfth Symposium on Thennophysical Properties, June 19–24, 1994 Boulder Colorado U.S.A.     

Thermodynamic and transport properties of fluids and fluid mixtures in the extended critical region

A practical representation of the thermodynamic properties and the transport coefficients related to diffusion, heat conduction, and their cross-processes in pure fluids and binary mixtures near the liquid-vapor critical line is developed. Crossover equations for the critical enhancement of those coefficients incorporate the scaling laws near the critical point and are transformed to the regular background far away from the critical point. The crossover behavior of the thermal conductivity and the thermal diffusion ratio in binary mixtures is also discussed. A comparison is made with thermal-conductivity data for pure carbon dioxide, pure ethane, and carbon dioxide add ethane mixtures.     

Dynamics of phase-separated fluids under external fields

Phase separation in external fields has attracted much attention recently. The reason is twofold. Since kinetics of phase separation and morphology of growing domains can be controlled by external fields, it is of technological importance. The other is that existence of mesoscale domains causes curious dynamical properties in fields, which provides us with a fundamental statistical dynamic problem. One example is a phase separation of binary fluids under shear flow. Phase-separated domains are deformed under the field, which causes burst, fusion, and reconnection of domains so that extra energy dissipation occurs in these processes. Because of this large deformation of domains, the system exhibits quite unusual rheological behavior. The kinetics of phase separation of binary fluids is also influenced by an external electric field when the new phases have different dielectric constants. Deformation and interaction of domains in an electric field are investigated by means of an interfacial approach.Paper presented at the Twelfth Symposium on Thermophysical Properties, June 19–24, 1994, Boulder, Colorado, U.S.A.