Notes on the theory of high polymer solutions

We have noted some correspondences in the theories of high polymer solutions. This article is divided in two independent sections: (I) Osmotic pressure. The second virial coefficients for polymers of the pearl-necklace type are given and discussed in two limiting cases—the dumbbell and the infinitely polymerized molecule having a definite length. The variation of the coefficients against the polymerization is predictable from these limiting cases (Fig. 1). Attention must be paid to the manner of taking the (abscissa). The case of infinite polymerization can be considered as corresponding to polymers of a compact single-body type such as globular proteins. Thus, an interesting correspondence in the second virial coefficients can be judged for the pearl-necklace and the compact single-body type of polymers. The general feature of the coefficient is also discussed. (II) Intrinsic viscosity. The relation between the two methods (Kirkwood-Riseman and Debye-Bueche) for intrinsic viscosity of high polymer solutions is discussed. Because the respective fundamental equations are equivalent to each other, we may choose whichever of these two methods we like.     

Capillary hydrodynamics of oligomer binders

In this work, we consider wetting and flow of oligomer binders for tissue fibers made of carbon and organic fibers. A correlation between the specific surface of fibers and strength of the boundary layers is established. The effect of fibers on structure formation of binders in the boundary layers is explained via the surface density of reticulation of fiber. The fibers with minimum surface reticulation exert a pronounced influence on the structure of binders, forming thicker and strong boundary layers.     

流体动力学逆流色谱分离柱研究进展

近年来,以流体动力学为基础的逆流色谱仪在天然产物与生化药物分离中得到了广泛应用。柱设计是色谱体系的核心环节,分离柱管子的几何形状、安装方式,分离柱的位置、体积等因素都会对色谱行为和分离效率产生不同的影响。本文对基于流体动力学的现代逆流色谱分离柱的研制进展与应用情况进行综述,并对未来逆流色谱的改进进行了展望。     

Electrophoresis: When hydrodynamics matter

The combination of hydrodynamic and electrostatic interactions leads to non-trivial effects that can be observed in various electrophoretic and electro-osmosis systems. In this article, we focus our attention on problems involving polyelectrolytes. First, we examine the free-draining behavior of polyelectrolytes such as DNA, a remarkable phenomenon that makes it impossible to use free-solution electrophoresis to fractionate nucleic acids. We show that the common assumption that hydrodynamic interactions are screened and therefore irrelevant in this system is wrong, and that one must be very careful when dealing with electro-hydrodynamics, especially when mechanical forces are also present. In the limit of small forces, one can superimpose the mechanical and hydrodynamic flow fields and make predictions that are often in excellent agreement with experiments. For DNA, the full electro- and hydrodynamics can then be reduced to the conformationally dependent superposition of a polymer sedimenting through a fluid and a polyelectrolyte being electrophoresed. This superposition or Electro-hydrodynamic Equivalence Principle has been used to explain a variety of problems and to propose methods that can allow the electrophoretic separation of DNA.     

A microscopic theory of interfacial hydrodynamics

The exact evolution equations for the conserved densities of a one-component two-phase fluid are reduced, in each bulk phase to the corresponding linearized hydrodynamic equations and at the interface, to boundary conditions, relating the jump in the stress tensor and heat current to surface excess thermodynamic and surface transport properties.     

Influence of biomass on hydrodynamics of an internal loop airlift reactor

The effect of the biomass presence on the overall circulation velocity, the linear velocities both in the riser and the downcomer and the overall gas hold-up was studied in a three-phase internal loop airlift reactor (ILALR). The measured data were compared with those obtained using a two-phase system (air—water). All experiments were carried out in a 40 dm³ ILALR at six different biomass concentrations (ranging from 0 g dm⁻³ to 7.5 g dm⁻³), at a temperature of 30°C, under atmospheric pressure. Air and water were used as the gas and liquid model media, respectively. Pellets of Aspergillus niger produced during the fermentation of glucose to gluconic acid in the ILALR were considered solid phase. In addition, liquid velocities were measured during the fermentation of glucose to gluconic acid using Aspergillus niger. All measurements were performed in a bubble circulation regime. At given experimental conditions the effect of the biomass on the circulation velocities in the ILALR was negligible. However, increasing of the biomass concentration led to lower values of the total gas hold-up. Presented at the 33rd International Conference of the Slovak Society of Chemical Engineering, Tatranské Matliare, 22–26 May 2006.     

The influence of polymer morphology on polymer film electrochemistry

The electrochemical behavior of functionalized polystyrene-coated electrodes shows a marked dependence on the nature of the electrolyte ions. Scanning electron microscope and surface profile measurements are presented which show that changes in polymer film volume and morphology accompany electrochemical oxidation. Changing polymer morphology by doping the films with soluble monomers during preparation is shown to produce large changes in electrochemical response. Diffusion coefficients were determined for a neutral organic dye dopant in each of the polymer films investigated, and these correlate very well with the oxidation overpotentials observed electrochemically. The nature of polymer film/solvent interactions and the mechanism by which counter ions penetrate the polymer phase is discussed and is related to other physical properties of amorphous polymers in terms of free volume concepts.     

Time-dependent wave packet propagation using quantum hydrodynamics

A new approach for propagating time-dependent quantum wave packets is presented based on the direct numerical solution of the quantum hydrodynamic equations of motion associated with the de Broglie–Bohm formulation of quantum mechanics. A generalized iterative finite difference method (IFDM) is used to solve the resulting set of non-linear coupled equations. The IFDM is 2nd-order accurate in both space and time and exhibits exponential convergence with respect to the iteration count. The stability and computational efficiency of the IFDM is significantly improved by using a “smart” Eulerian grid which has the same computational advantages as a Lagrangian or Arbitrary Lagrangian Eulerian (ALE) grid. The IFDM is generalized to treat higher-dimensional problems and anharmonic potentials. The method is applied to a one-dimensional Gaussian wave packet scattering from an Eckart barrier, a one-dimensional Morse oscillator, and a two-dimensional (2D) model collinear reaction using an anharmonic potential energy surface. The 2D scattering results represent the first successful application of an accurate direct numerical solution of the quantum hydrodynamic equations to an anharmonic potential energy surface.     

Sandwich structure containing liquid crystal polymer grafted on polymer support

Graft post-polymerization of mesogenic monomers onto fluorine-containing polymer support was initiated by the simultaneous action of vacuum ultraviolet radiation and atomic oxygen. The resultant two-layer structure possesses the combined physical–mechanical properties of the polymer-supporting film and the optical characteristics of the anisotropic liquid crystal layer.     

Influence of the hydrodynamics on the biofilm formation by mass transport analysis

Biofilm are formed wherever there is some water in our environment: pipes, pipelines, tap water systems, air conditioning systems... Furthermore, the ecological and economical consequences are very important: energy losses, bacterial contamination, material deterioration. The aim of this work is to develop a new method to detect and monitor the biofilm formation. This method can also determine some mechanical properties of the biofilm. An application of this method is a realization of a biofilm sensor. Biofilm is considered as an inert porous layer with respect to mass transport. In our experiment, the biofilm is grown on a gold electrode in natural seawater. Its thickness is determined by considering the oxygen diffusion limiting current measured for different rotation speeds on this electrode. Two different incubators are used during the biofilm development: one, with a laminar flow, permits the rotation of the electrode during the biofilm formation, and for the second, a tube is used under turbulent conditions during the biofilm formation. This experiment allows us to characterize the mechanical behavior (thickness, elasticity, rigidity) of the biofilm in function of different conditions of development.     

Notes on polynomial perturbation problems

The convergence behaviour of Rayleigh-Schrodinger perturbation theory for polynomial perturbation problems is discussed with some specific examples. It is emphasized that the choice of the perturbation parameter becomes crucial in this issue, in the light of certain seemingly contradictory conclusions drawn recently.     

Quantum hydrodynamics: capturing a reactive scattering resonance

The hydrodynamic equations of motion associated with the de Broglie-Bohm formulation of quantum mechanics are solved using a meshless method based upon a moving least-squares approach. An arbitrary Lagrangian-Eulerian frame of reference and a regridding algorithm which adds and deletes computational points are used to maintain a uniform and nearly constant interparticle spacing. The methodology also uses averaged fields to maintain unitary time evolution. The numerical instabilities associated with the formation of nodes in the reflected portion of the wave packet are avoided by adding artificial viscosity to the equations of motion. A new and more robust artificial viscosity algorithm is presented which gives accurate scattering results and is capable of capturing quantum resonances. The methodology is applied to a one-dimensional model chemical reaction that is known to exhibit a quantum resonance. The correlation function approach is used to compute the reactive scattering matrix, reaction probability, and time delay as a function of energy. Excellent agreement is obtained between the scattering results based upon the quantum hydrodynamic approach and those based upon standard quantum mechanics. This is the first clear demonstration of the ability of moving grid approaches to accurately and robustly reproduce resonance structures in a scattering system.     

Quantum hydrodynamics: application to N-dimensional reactive scattering

The quantum hydrodynamic equations associated with the de Broglie-Bohm formulation of quantum mechanics are solved using a new methodology which gives an accurate, unitary, and stable propagation of a time dependent quantum wave packet [B. K. Kendrick, J. Chem. Phys. 119, 5805 (2003)]. The methodology is applied to an N-dimensional model chemical reaction with an activation barrier. A parallel version of the methodology is presented which is designed to run on massively parallel supercomputers. The computational scaling properties of the parallel code are investigated both as a function of the number of processors and the dimension N. A decoupling scheme is introduced which decouples the multidimensional quantum hydrodynamic equations into a set of uncoupled one-dimensional problems. The decoupling scheme dramatically reduces the computation time and is highly parallelizable. Furthermore, the computation time is shown to scale linearly with respect to the dimension N=2,...,100.