The Hard Rod Fluid in a Uniform Gravitational Field

Abstract

The system of hard rods in an external, uniform gravitational field is studied and exact expressions obtained for the partition functions, and the one- and two-particle distributions. In principle all higher order distributions can be exactly expressed as finite sums and the Laplace transforms of the one-particle density and pressure for a semi-infinite system are reducible to single integrals. Limiting cases of weak field and small rod diameters are examined. In the former case, these results agree with Percus and Lebowitz's local density expansion. In the latter case, corrections to the barometric pressure and density laws are obtained. Finally some mathematical difficulties involved in the calculation of the virial expansion and distribution of roots of the grand partition function are mentioned.     

毛细管探针法测定液体表面张力系数的进一步研究

采用较大直径的毛细管对探针法测量液体表面张力系数做了进一步研究.文中引用了Prokhorov提出的改进的瑞利公式,介绍了表面张力系数α的各相关公式的适用范围.实验中利用毛细管探针法测量了几个不同温度下蒸馏水在一直径为5.744.nm的毛细管中的上升高度,用Prokhorov公式计算α.实验测得的蒸馏水的表面张力系数与公认值的百分误差约小于0.13%.最后对实验结果的误差原因进行了分析.     

An Equilibrium Lattice Model of Wetting on Rough Substrates

We consider a semi-infinite 3-dimensional Ising system with a rough wall to describe the effect of the roughness r of the substrate on wetting. We show that the difference of wall free energies (r)= _AW(r)– _BW(r) of the two phases behaves like (r)r(1), where r=1 characterizes a purely flat surface, confirming at low enough temperature and small roughness the validity of Wenzel's law, cos (r)r cos (1), which relates the contact angle of a sessile droplet to the roughness of the substrate     

Surface tension of random copolymer melts

A mean-field theory is presented to describe the surface tension and interfacial profile of random A-B multiblock copolymer melts in contact with air or a solid substrate. The copolymer model accounts for variations in average composition and block sequence distribution, and reduces to a model for statistical copolymers as the block size approaches that of a monomer. Ideal copolymers lacking chemical correlations between successive segments are predicted to have a larger surface tension than “blocky” copolymers with a tendency for repeated segments of A or B. © 1992 John Wiley & Sons, Inc.     

Enrichment of surfactant from its aqueous solution using ultrasonic atomization

Dilute aqueous solutions of dodecyl-benzenesulfonic acid sodium salt (DBS-Na) and polyoxyethylenenonylphenyl ethers (PONPEs) were ultrasonically atomized. The surfactants were concentrated in collected mist droplets. The enrichment ratio increased with decreasing surfactant concentration. Depending on the surfactant’s molecular weight and affinity to water, different enrichment ratio was observed in the range of low feed concentrations. For anionic surfactant, DBS-Na, the enrichment ratio was significantly improved by KCl addition and a peak appeared on the plot of the ratio against KCl concentration. Addition of NaCl or CaCl₂ · 2H₂O to the surfactant solution also enhanced the enrichment ratio; however, the effect was relatively small. Such behaviors of the ratio were interpreted as enhanced interfacial adsorption of the surfactant and a lack of supply of surfactant monomers from liquid bulk because of slow breaking of surfactant micelles. Time required for collecting an amount of mist was also observed. Among the three salt systems, the time for KCl system was twice as long as others. This fact suggested that the formation of smaller droplets in KCl system.     

Cassie's Law and Concavity of Wall Tension with Respect to Disorder

For the semiinfinite Ising model with quenched boundary disorder, we prove concavity inequalities for the difference of wall tensions associated with the minus and plus phases. These inequalities generalize phenomenological equalitiesknown as Cassie's law.     

The water-silicas interfacial interaction energies

The water-silicas interfacial interaction energies were calculated for samples of quartz, silicas and silicas outgassed at high temperatures using own and published data of the spreading pressure of water, its surface tension, its contact angle and using formulas obtained by the combination of the Young equation with a general equation of pair interaction. The values obtained for 18 different samples were in the range 7.80-6.92 kJ mol⁻¹. Lower values of energies are for samples that contain relatively less amounts of water at P/P₀ = 0.25 and are characterized also by relatively low values of surface pressures.     

Study of molecular interactions between lipids and proteins using dynamic surface tension measurements: a review

Molecular interactions between small molecules and proteins, such as binding of lipids to proteins, are of fundamental importance in various biological processes. A recently-developed method based on dynamic surface tension measurement is efficient and versatile in detecting such molecular interactions: Axisymmetric Drop Shape Analysis (ADSA) provides a tool for measuring the surface tension (γ) response to surface area changes. Through the analysis of the γ response pattern, surface competitive adsorption between small organic molecules and protein molecules can be detected. Surface squeeze-out of small molecules by proteins can also be observed. Molecular binding of lipids to proteins manifests itself in a modification of the γ response which is not compatible with a simple superposition of the two individual patterns. The specific binding can be studied in terms of dose effects and specificity.     

On surface tension modelling using the level set method

The paper describes and compares the performance of two options for numerically representing the surface tension force in combination with the level set interface‐tracking method. In both models, the surface tension is represented as a body force, concentrated near the interface, but the technical implementation is different: the first model is based on a traditional level set approach in which the force is distributed in a band around the interface using a regularized delta function, whereas in the second, the force is partly distributed in a band around the interface and partly localized to the actual computational cells containing the interface. A comparative study, involving analysis of several two‐phase flows with moving interfaces, shows that in general the two surface tension models produce results of similar accuracy. However, in the particular case of merging and pinching‐off of interfaces, the traditional level set model of surface tension produces an error that results in non‐converging solutions for film‐like interfaces (i.e. ones involving large contact areas). In contrast, the second model, based on the localized representation of the surface tension force, displays consistent first‐order convergence. Copyright © 2008 John Wiley & Sons, Ltd.     

Density, ultrasonic velocity, surface tension, excess volume and viscosity of quaternary fluid solutions

Density, ultrasonic velocity, surface tension, excess volume and viscosity of quaternary non-electrolyte solution n-pentane+tolune+n-heptane+cyclohexane has been experimentally determined at 25 °C over a wide range of composition. Assuming a quaternary fluid solution to be made of six binaries, a statistical approach of Prigogine–Flory–Patterson (PFP) theory has been extended to develop the expressions for dynamic viscosity, surface tension excess volume and ultrasonic velocity of quaternary fluid system. A reasonable agreement has been achieved between theory and experiment. An attempt has also bee made to explain the nature of molecular interactions involved in the light of excess thermodynamic functions whose sign and magnitude depend upon the chain length and size of the component fluids and also studied the role of order breakers (toluene and cyclohexane) on these properties.