NUMERICAL SIMULATION OF MORPHOLOGY OF POLYMER CHAIN COILS IN COMPLEX FLOWS

A new coupled finite element formulation is proposed to calculate a conformation tensor model in two complex flows： a planar contraction flow and a planar flow around a symmetrically placed cylinder. The components of conformation tensor are first computed together with the velocity and pressure to describe the change of morphology of polymer chain coils in flow fields. Macroscopic quantities of viscoelastic flow are then calculated based on the conformation tensor. Comparisons between the numerical simulations and experiments for stress patterns and velocity profiles are carried out to prove the validity of the method.     

Computer simulation of dilute polymer solutions in transient elongational flows

The behaviour of polymer molecules in solution flowing through a succession of contraction‐expansion zones was simulated using the Brownian dynamics method. The velocity profile of the flow field calculated previously, assuming that the flow modification in dilute polymer solution is negligible, was used. In the vicinity of the cell symmetry axis the flow can be described as an oscillatory elongational planar flow. The dumbbell with conformation‐dependent friction and elastic coefficients was chosen as a model for the polymer chain. When the initial state of the polymer chain entering the first contraction zone had corresponded to a gaussian coil the initial increase in the polymer deformation along the flow direction was observed. After some time independent of the flow rate, the amplitude of deformation gradually decreased to the stationary value further in the cell where the polymer deformation followed the flow oscillations. The amplitude of the deformation oscillations showed the critical behaviour: they increased for flow rates less than a critical value and did not change with further increase in the flow rate.     

拉格朗日-欧拉方法模拟高分子复杂流体平面收缩流动

为验证拉格朗日 欧拉方法的准确性 ,对高分子溶液的 4∶1平面收缩流动问题进行了数值模拟 ,采用单松弛时间的PhanThien Tanner本构方程 ,得到PIB/C1 4溶液在De =3 0的收缩流动的计算结果 ,同Quinzani等所做的收缩流动实验中的稳态流场物理量的测量结果进行了比较 ,在定量上取得较好的一致性 .证明拉格朗日 欧拉方法能够在定性上乃至在定量上准确地预报高分子复杂流体的流动行为 ,在描述真实的物理过程时是合理、准确的 .     

微通道中高分子运动的耗散粒子动力学模拟

对不同长度及不同数量的高分子链在微直通道及微缩通道中的流动进行了模拟与分析.研究表明,高分子链的伸展状态与微通道的形状密切相关,微直通道中高分子链能较充分地伸展,方形微缩通道中高分子链未能充分伸展,而斜坡微缩通道中高分子链的伸展状态介于微直通道与方形微缩通道之间.高分子的存在对微通道系统的温度没有明显影响,对密度与水平流动速度有较明显的影响.高分子链的运动直接影响到周围的简单流体粒子,降低其周围流体粒子的流动速度,对密度与速度产生局部扰动,形成"拖曳"现象.高分子链分布越密集,长度越长,高分子链的拖曳现象越明显.     

Planar electrochromatography

Recent developments in planar electrochromatography (PEC) in both the normal-phase and the reversed-phase modes, and at both atmospheric and elevated pressure, are reviewed. Other forced-flow techniques in planar chromatography are also briefly covered. Mobile phase migration in PEC is primarily due to electroosmotic flow, which is controlled by the applied electric field. Capillary mediated flow is an important secondary contributor to migration, and occurs because the layer is unsaturated as a consequence of liquid evaporating from the layer due to Joule heating. The magnitude of the electric field and the concentration of ions in solution are important variables that control both electroosmotic flow and Joule heating. Separations are faster and more efficient than those obtained by conventional planar chromatography, provided appropriate experimental conditions are selected. With inappropriate conditions, either mobile phase accumulates on the surface of the sorbent layer, or Joule heating causes excessive evaporation. The former results in poor spot shape, and the latter can cause the layer to dry. Good separations are obtained when there is a balance between these two effects. The problems associated with mobile phase accumulating on the surface of the sorbent layer, and with excessive evaporation of mobile phase, do not occur with pressurized planar electrochromatography. This technique is performed at high pressure, under conditions that allow heat to be removed form the sorbent layer. This allows the use of a substantially higher electric field than in PEC, and results in a high mobile phase flow rate.     

Conformation dependence of DNA electrophoretic mobility in a converging channel

The electrophoresis of λ‐DNA is observed in a microscale converging channel where the center‐of‐masses trajectories of DNA molecules are tracked to measure instantaneous electrophoretic (EP) mobilities of DNA molecules of various stretch lengths and conformations. Contrary to the usual assumption that DNA mobility is a constant, independent of field and DNA length in free solution, we find DNA EP mobility varies along the axis in the contracting geometry. We correlate this mobility variation with the local stretch and conformational changes of the DNA, which are induced by the electric field gradient produced by the contraction. A “shish‐kebab” model of a rigid polymer segment is developed, which consists of aligned spheres acting as charge and drag centers. The EP mobility of the shish‐kebab is obtained by determining the electrohydrodynamic interactions of aligned spheres driven by the electric field. Multiple shish‐kebabs are then connected end‐to‐end to form a freely jointed chain model for a flexible DNA chain. DNA EP mobility is finally obtained as an ensemble average over the shish‐kebab orientations that are biased to match the overall stretch of the DNA chain. Using physically reasonable parameters, the model agrees well with experimental results for the dependence of EP mobility on stretch and conformation. We find that the magnitude of the EP mobility increases with DNA stretch, and that this increase is more pronounced for folded conformations.     

A 2D electrohydrodynamic model for electrorotation of fluid drops

A theoretical analysis of spontaneous electrorotation of deformable fluid drops in a DC electric field is presented with a 2D electrohydrodynamic model. The fluids in the system are assumed to be leaky dielectric and Newtonian. If the rotating flow is dominant over the cellular convection type of electrohydrodynamic flow, closed-form solutions for drops of small deformations can be obtained. Because the governing equations are in general nonlinear even when drop deformations are ignored, the general solution for even undeformed drop takes a form of infinite series and can only be evaluated by numerical means. Both closed-form solutions for special cases and numerical solutions for more general cases are obtained here to describe steady-state field variables and first-order drop deformations. In a DC electric field of strength beyond the threshold value, spontaneous electrorotation of a drop is shown to occur when charge relaxation in the surrounding fluid is faster than the fluid inside the drop. With increasing the strength of the applied electric field from the threshold for onset of electrorotation, the axis of drop contraction deviates from from that of the applied electric field in the direction of the rotating flow with an angle increasing with the field strength.     

The effect of gas slip on pressure drop and deposition of submicron particles in fibrous filters

The effect of gas slip at fibers on the drag to a flow and the deposition of submicron particles in model filters with a tree-dimensional flow field has been considered. The average values of the drag force and the efficiency of diffusion collection of particles with finite sizes in a double hexagonal three-dimensional model filter taken as a standard uniform filter have been calculated as depending on the packing density of fibers and the Knudsen number. It has been shown that, in the region of the sizes of the most penetrating particles, under preset conditions, and at specified filter parameters, the obtained collection efficiency values agree with the results of calculations performed by empirical formulas for a model fan filter. Moreover, formulas derived for a planar flow taking into account the slip effect are applicable to highly porous filters.     

Effect of molecular topology on the transport properties of dendrimers in dilute solution at Theta temperature: a Brownian dynamics study

Structure and transport properties of dendrimers in dilute solution are studied with the aid of Brownian dynamics simulations. To investigate the effect of molecular topology on the properties, linear chain, star, and dendrimer molecules of comparable molecular weights are studied. A bead-spring chain model with finitely extensible springs and fluctuating hydrodynamic interactions is used to represent polymer molecules under Theta conditions. Structural properties as well as the diffusivity and zero-shear-rate intrinsic viscosity of polymers with varied degrees of branching are analyzed. Results for the free-draining case are compared to and found in very good agreement with the Rouse model predictions. Translational diffusivity is evaluated and the difference between the short-time and long-time behavior due to dynamic correlations is observed. Incorporation of hydrodynamic interactions is found to be sufficient to reproduce the maximum in the intrinsic viscosity versus molecular weight observed experimentally for dendrimers. Results of the nonequilibrium Brownian dynamics simulations of dendrimers and linear chain polymers subjected to a planar shear flow in a wide range of strain rates are also reported. The flow-induced molecular deformation of molecules is found to decrease hydrodynamic interactions and lead to the appearance of shear thickening. Further, branching is found to suppress flow-induced molecular alignment and deformation.     

Interfacial forces and Marangoni flow on a nematic drop retracting in an isotropic fluid

Nematic-isotropic interfaces exhibit novel dynamics due to anchoring of the liquid crystal molecules on the interface. The objective of this study is to demonstrate the consequences of such dynamics in the flow field created by an elongated nematic drop retracting in an isotropic matrix. This is accomplished by two-dimensional flow simulations using a diffuse-interface model. By exploring the coupling among bulk liquid crystal orientation, surface anchoring and the flow field, we show that the anchoring energy plays a fundamental role in the interfacial dynamics of nematic liquids. In particular, it gives rise to a dynamic interfacial tension that depends on the bulk orientation. Tangential gradient of the interfacial tension drives a Marangoni flow near the nematic-isotropic interface. Besides, the anchoring energy produces an additional normal force on the interface that, together with the interfacial tension, determines the movement of the interface. Consequently, a nematic drop with planar anchoring retracts more slowly than a Newtonian drop, while one with homeotropic anchoring retracts faster than a Newtonian drop. The numerical results are consistent with prior theories for interfacial rheology and experimental observations.     

Anisotropic and enhanced self-diffusion of a macromolecular chain under simple shear flow as revealed by Monte Carlo simulation on lattices

Two-dimensional simple shear flow of a self-avoiding macromolecular chain is simulated by a lattice Monte Carlo (MC) method with a pseudo-potential describing the flow field. The simulated velocity profile satisfies the requirements of simple shear flow unless the shear rate is unreasonably high. Some diffusion problems for a free-draining bead-spring chain with excluded volume interaction are then investigated at low and relatively high shear rates. Three diffusion coefficients are defined and examined in this paper: the conventional self-diffusivity in zero field, D_self, the apparent self-diffusivity in flow field, D_app, and the flow diffusivity in simulation, D_flow reflecting actually the transport coefficient. It is found that these three diffusivities for a flexible chain are different from each other. What is more important is that self-diffusion exhibits a high anisotropy in the flow field. The apparent self-diffusion along the flow direction is enhanced to a large extent. It is increased monotonically with the increase of shear time or shear strain, whereas the chain configuration can achieve a stationary anisotropic distribution following an interesting overshoot of the coil shape and size. Besides a single self-avoiding chain, an isolated Brownian bead and a group of self-avoiding beads with a quasi-Gaussian spatial distribution are also simulated. According to the comparison, the effects of the connectivity of the chain on the diffusion behavior are revealed. Some scaling relations of D_app versus t are consistent with the theoretical analyses in the pertinent literature.     

Numerical simulation of three‐dimensional polymer extrusion flow with differential viscoelastic model

The numerical simulation of viscoelastic flow problems is nowadays an effective way of investigating the complex flow mechanism related to practical engineering problems, such as plastic injection, blow molding and extrusion. The mathematical model of a three‐dimensional (3D) viscoelastic flow in a typical contraction die for polymer extrusion is established and a stable solving method is investigated. The penalty finite element method (FEM) is performed to simulate the viscoelastic melts flow in the channel with a differential constitutive model. The discrete elastic‐viscous split stress (DEVSS) formulation and the streamline‐upwind Petrov–Galerkin (SUPG) technology are employed to improve the computation stability. Both the implementation of the numerical scheme and its application in the practical process analysis are investigated. The effects of various calculation control parameters and different material parameters upon the numerical results are discussed. The 3D flow patterns in the extrusion die with different contraction angles are further investigated based on the above discussions. Copyright © 2007 John Wiley & Sons, Ltd.     

Performance improvement of air-breathing proton exchange membrane fuel cell (PEMFC) with a condensing-tower-like curved flow field

Air-breathing proton exchange membrane fuel cells (PEMFCs) are very promising portable energy with many advantages. However, its power density is low and many additional supporting parts affect its specific power. In this paper, we aim to improve the air diffusion and fuel cell performance by employing a novel condensing-tower-like curved flow field rather than an additional fan, making the fuel cell more compact and has less internal power consumption. Polarization curve test and galvanostatic discharge test are carried out and proved that curved flow field can strengthen the air diffusion into the PEMFC and improve its performance. With appropriate curved flow field, the fuel cell peak power can be 55.2% higher than that of planar flow field in our study. A four-layer stack with curved cathode flow field is fabricated and has a peak power of 2.35 W (120 W/kg).     

Modeling and simulation of IEF in 2-D microgeometries

A 2-D finite-volume model is developed to simulate nonlinear IEF in complex microgeometries. This mathematical model is formulated based on the mass conservation and ionic dissociation relations of amphoteric macromolecules, charge conservation, and the electroneutrality condition. Based on the 2-D model, three different separation cases are studied: an IPG in a planar channel, an ampholyte-based pH gradient in a planar channel, and an ampholyte-based pH gradient in a contraction-expansion channel. In the IPG case, cacodylic acid (pK(1) = 6.21) and Tris (pK(1) = 8.3) are used as the acid and base, respectively, to validate the 2-D IEF model. In the ampholyte-based pH gradient cases, IEF is performed in the pH range, 6.21-8.3 using 10 ampholytes in the planar channel and 20 ampholytes in the contraction-expansion channel. The numerical results reveal different focusing efficiencies and resolution in the narrow and wide sections of the contraction-expansion channel. To explain this, the expressions for separation resolution and peak concentrations of separands in the contraction-expansion channel are presented in terms of the channel shape factor. In a 2-D planar channel, a focused band remains straight all the time. However, in a contraction-expansion channel, initially straight bands take on a crescent profile as they pass through the trapezoidal sections joining the contraction and expansion sections.     

Viscosity of confined inhomogeneous nonequilibrium fluids

We use the nonlocal linear hydrodynamic constitutive model, proposed by Evans and Morriss [Statistical Mechanics of Nonequilibrium Liquids (Academic, London, 1990)], for computing an effective spatially dependent shear viscosity of inhomogeneous nonequilibrium fluids. The model is applied to a simple atomic fluid undergoing planar Poiseuille flow in a confined channel of several atomic diameters width. We compare the spatially dependent viscosity with a local generalization of Newton's law of viscosity and the Navier-Stokes viscosity, both of which are known to suffer extreme inaccuracies for highly inhomogeneous systems. The nonlocal constitutive model calculates effective position dependent viscosities that are free from the notorious singularities experienced by applying the commonly used local constitutive model. It is simple, general, and has widespread applicability in nanofluidics where experimental measurement of position dependent transport coefficients is currently inaccessible. In principle the method can be used to predict approximate flow profiles of any arbitrary inhomogeneous system. We demonstrate this by predicting the flow profile for a simple fluid undergoing planar Couette flow in a confined channel of several atomic diameters width.     

Phase transitions in polymer brushes

Liquid crystalline ordering in planar polymer brushes is investigated theoretically by numerical calculations within a self-consistent field approximation. The brushes are formed by macromolecules with mesogenic groups in main chain and immersed in a solvent. Existence of a microphase segregated brush (MSB) regime with a collapsed orientationally ordered intrinsic sublayer and a swollen external sublayer is shown. At small grafting density, the transition from a conventional brush state to the microphase segregated state is a jump-wise first order phase transition for a finite chain length (N). The magnitudes of the jumps in the average characteristics of the brush tend to zero in the limit N → ∞ since this transition occurs only in a vanishingly small part (∝ N^−1/2) of the brush. High compressibility of MSB brush is demonstrated. The origin of phase transition in planar brushes is discussed.     

A new algorithm for extended nonequilibrium molecular dynamics simulations of mixed flow

In this work, we develop a new algorithm for nonequilibrium molecular dynamics of fluids under planar mixed flow, a linear combination of planar elongational flow and planar Couette flow. To date, the only way of simulating mixed flow using nonequilibrium molecular dynamics techniques was to impose onto the simulation box irreversible transformations. This would bring the simulation to an end as soon as the minimum lattice space requirements were violated. In practical terms, this meant repeating the short simulations to improve statistics and extending the box dimensions to increase the total simulation time. Our method, similar to what has already been done for pure elongational flow, allows a cuboid box to deform in time following the streamlines of the mixed flow and, after a period of time determined by the elongational field, to be mapped back and recover its initial shape. No discontinuity in physical properties is present during the mapping and the simulation can, in this way, be extended indefinitely. We also show that the most general form of mixed flow, in which the angle between the expanding (or contracting) direction and the velocity gradient axis varies, can be cast in a so-called canonical form, in which the angle assumes values that are multiples of π (when a mixed flow exists), by an appropriate choice of the field parameters.     

Theory of Liquid-crystalline Ordering in Polymer Brushes

Summary: We present a review of the works devoted to investigation of LC ordering in polymer brushes. This series has been carried out by the group of T. M. Birshtein and covers the following aspects of the problem: thermotropic LC phase transition in LCP brushes, microphase segregation, homeotropic and planar LC phases, LC polymer in LC solvent, lyotropic LCP brushes, LC transitions under normal or lateral force (shear flow). Analytical theory is developed for simplified model of polymer brush with accounting for thermotropic attraction in Mayer-Saupe approximation and lyotropic repulsion in DiMarzio formalism; numerical calculations are fulfilled in self-consistent field approximation (method of Scheutjens and Fleer). Brownian dynamics simulations are applied for modeling polymer brush in a shear flow.     

Stretching of a semiflexible chain composed of elastic bonds

We study the extension of semiflexible (persistent) polymer chains composed of elastic bonds under the action of forces applied to their ends. For a given discrete model of a chain, the effective potential energy includes three components: the energy of bonds in the external dipole field, the energy of elastic deformation of bonds, and the energy of bending, which depends on the angles between neighboring bonds. The extension/contraction modulus of bonds is high but finite. To calculate the relative extension and its variance, the variational method for finding the maximum eigenvalue of the transfer operator in the space of orientations of bonds is used. For chains composed of more than ten bonds, the results appear to approach the data of simulation of chain extension by the collisional molecular dynamics method. Two proposed extensionforce dependences are compared with the computer experiment, and this comparison makes it possible to define the limits of their applicability.     

Combustion waves in a model with chain branching reaction

In this paper the steady planar travelling waves in the adiabatic model with two-step chain branching reaction mechanism are investigated numerically. The properties of these solutions are demonstrated to have similarities with the properties of non-adiabatic combustion waves that is, there is a residual amount of fuel left behind the travelling waves and the solutions can exhibit extinction. It is also shown that the model possesses a new type multiple travelling wave solutions (which we call wave trains) with complex structure of the profiles and varying speeds