Dynamics of liquid membranes. II: Adaptive finite difference methods

Two domain-adaptive finite difference methods are presented and applied to study the dynamic response of incompressible, inviscid, axisymmetric liquid membranes subject to imposed sinusoidal pressure oscillations. Both finite difference methods map the time-dependent physical domain whose downstream boundary is unknown onto a fixed computational domain. The location of the unknown time-dependent downstream boundary of the physical domain is determined from the continuity equation and results in an integrodifferential equation which is non-linearly coupled with the partial differential equations which govern the conservation of mass and linear momentum and the radius of the liquid membrane. One of the finite difference methods solves the non-conservative form of the governing equations by means of a block implicit iterative method. This method possesses the property that the Jacobian matrix of the convection fluxes has an eigenvalue of algebraic multiplicity equal to four and of geometric multiplicity equal to one. The second finite difference procedure also uses a block implicit iterative method, but the governing equations are written in conservation law form and contain an axial velocity which is the difference between the physical axial velocity and the grid speed. It is shown that these methods yield almost identical results and are more accurate than the non-adaptive techniques presented in Part I. It is also shown that the actual value of the pressure coefficient determined from linear analyses can be exceeded without affecting the stability and convergence of liquid membranes if the liquid membranes are subjected to sinusoidal pressure variations of sufficiently high frequencies.     

Improvement of the properties of polyarylate reinforced with liquid crystalline polymers

Blends of polyarylate of bisphenol A, PAr, with two commercial main chain liquid crystalline polymers, Vectra A950 and Vectra B950, are studied. From dynamic viscoelastic measurements it is deduced that both systems (PAr/Vectra A950 and PAr/Vectra B950) are immiscible and scanning electron microscopy (SEM) micrographs show the presence of spherical domains of the liquid crystalline polymer when PAr constitutes the matrix. Extrusion capillary measurements reveal that, under conditions of temperature and shear rate similar to those of processing, the viscosity is reduced to approximately 10% of its value when the content of liquid crystalline polymer is only 20%. This great improvement of the rheological properties is observed in both PAr/Vectra A950 and PAr/Vectra B950 blends. The effect of draw ratio on Young's modulus for different compositions is also analyzed, pointing out the reinforcing action of both liquid crystalline polymers on polyarylate: for instance, 20% of Vectra B950 in the blend gives rise to a 700% increase of the modulus of fibres prepared at a draw ratio of 50. SEM of the extrudates reveals that the spherical domains are elongated at the entrance of the capillary giving rise to a microfibrillar morphology which is related to the excellent rheological and mechanical properties of the blends.     

Use of a long-spacer-side-chain liquid crystalline polysiloxane containing a crown ether as a stationary phase for capillary gas chromatography

A new kind of side chain liquid crystalline polysiloxane containing a crown ether with a longer spacer (PSC-11) has been prepared and coated on a fused silica capillary column. The main chroma-tographic characteristics including efficiency, polarity, and selectivity have been examined. The phase exhibits the retention properties of both liquid crystal and crown ether stationary phases and possesses higher efficiency and better selectivity than PSC-3, which has a shorter spacer between the main polysiloxane chain and liquid crystalline side chain.     

Anomalous behavior of conductivity of the confined Q1D electron system over liquid helium

Conductivity of electrons in a quasi-one-dimensional (Q1D) system over liquid helium in narrow channels with the parabolic profile of the potential well has been investigated at temperature T, from 0.4 to 1.8 K, for different driving electric fields and radius of channel curvature. The interval of linear electron densities varied from 2.18×10³ up to 1.7×10⁶ cm⁻¹.

The inverse mobility (1/μ_eff) in the electron-ripplon scattering region at the high linear densities of charges in the channel increases with temperature decreasing. This anomalous behavior of the electron transport in the low-temperature region has been explained by either the electron ordering or the polaronic effects in confined conducting channels. The nonlinear behavior of the electron velocity as a function of a driving electric field is supposed to be due to Breg–Cherenkov radiation of the ripplons. The radiation occurred if the velocity of electrons in the channel approaches to the critical value.     

Recognition of Monohydrogen Anions of Geometrical and Positional Isomers of Dicarboxylic Acids Based on Polymeric Liquid Membranes Incorporating Polyamine Host

Macrocyclic lipophilic polyamines were applied as the sensory elements of polymeric liquid membrane electrodes. These hosts gain the anion receptor functionality upon protons uptake from the aqueous solutions. The electrodes studied were able to distinguish potentiometricaly isomers of monocharged and doublecharged forms of ethylene and benzene dicarboxylic acids. The selectivity of interaction between protonated hosts and anionic guests relays not only on the electrostatic interactions, but on hydrogen bounds formations as well. The influence of lipophilicity of protonated hosts on the potential response generation was discussed.     

An estimation of the measurement uncertainty for an optical emission spectrometric method

 A validation procedure based on the ISO/IEC 17025 standard was used to demonstrate the long-term stability of a calibration process and to assess the measurement uncertainty of a standard test method for optical emission vacuum spectrometric analysis of carbon and low-alloy steel (ASTM E 415–99a). The validation was used to provide documented evidence that the selected method fulfils the requirements and that the method is ”fit for purpose”. A test for drift was applied to determine statistically whether the analytical results vary systematically with time. The accuracy and traceability of the optimised method were tested by an analysis of closely matched matrix certified reference materials (CRMs). The measurement uncertainty estimations took account of the precision study, the bias and its uncertainty, and the qualification of uncertainties not considered in the overall performance studies. Received: 2 November 2002 Accepted: 2 January 2003 Acknowledgement The author expresses gratitude to Dr. Aleš Fajgelj for helpful discussions during the 3rd Central European Conference on Reference Materials and Measurements. Presented at CERMM-3, Central European Reference Materials and Measurements Conference: The function of reference materials in the measurement process, May 30–June 1, 2002, Rogaška Slatina, Slovenia Correspondence to T. Drglin     

Kinetic theories and mesoscopic models for solutions of nonhomogeneous liquid crystal polymers

We present a systematic derivation of hydrodynamic theories for nonhomogeneous nematic liquid crystal polymers (LCPs) by approximating the molecules as rigid ellipsoids, which can be either uniaxial molecules (spheroids) or biaxial ones. The short range interaction is assumed to be dominated by the excluded volume effect. Additional molecular properties with ellipsoidal molecules, e.g., a dipole–dipole interaction in extended nematics and chiral molecular structure in cholesterics, are accounted for through additional intermolecular potentials. Long-range molecular interaction is implemented through an averaged mean-field potential characterized by interaction functions. The extra elastic stress tensor is calculated using an extended virtual work principle consistent with conservation of angular momentum on the material volume, whereas the extra viscous stress is obtained by Batchelor’s volume averaging method. In the isothermal case, the theories are shown to satisfy the second law of thermodynamics, i.e., they admit positive production of entropy or energy dissipation. In the case of cholesterics, the kinetic theory reduces to the Leslie–Ericksen theory in the limit of weak translational diffusion, weak long range interaction, and weak flow.     

ICF靶丸中液氢层厚度的确定

 利用靶丸内部的质量守恒，提出了计算惯性约束聚变靶丸内液氢层厚度的函数关系式，从而得到了求解惯性约束聚变靶丸内液氢层厚度的一般模型，并在此基础上对影响液氢层厚度的各类因素如温度、充气密度等进行了讨论。该模型的分析方法同样适用于惯性约束聚变中的燃料气体氘、氚或者氘氚混合物。