Effect of temperature on polymer migration II: Concentration equation

Polymer migration is a generally well-known phenomenon in a flow field, and it has been verified that the sources of such phenomena are nonhomogeneity of the flow, concentration effects and hydrodynamic interactions between the polymer molecules. In addition, temperature effects were found to be another source of polymer migration. The Langevin equation for a polymer molecule was first derived from single chain dynamics using a kinetic theory for the bead-spring elastic harmonic dumbbell model, as described in part I (reference [1]). In this paper the diffusion equation and concentration profile of the polymer molecules induced by a temperature gradient are obtained from the Fokker-Planck equation. A new differential operator is also introduced to calculate the concentration profile. From the concentration equation obtained in the general flow geometry, we find that in dilute polymer solution there are significant effects on the polymer migration not only due to the nonhomogeneity of the flow field but also due to temperature gradients.     

Effect of temperature on polymer migration

In this study, we investigated the temperature gradient effect on the polymer dynamics in a flow field. To simplify our analysis, we adopted a two-bead harmonic dumbbell model, and found that there were significant effects on the polymer migration not only due to the nonhomogeneity of the flow field, but also due to the temperature difference.     

Coupled analysis of injection molding filling and fiber orientation,including in-plane velocity gradient effect

On injection molding of short fiber reinforced plastics, fiber orientation during mold filling is determined by the flow field and the interactions between the fibers. The flow field is, in turn, affected by the orientation of fibers. The Dinh and Armstrong rheological equation of state for semiconcentrated fiber suspensions was incorporated into the coupled analysis of mold filling flow and fiber orientation. The viscous shear stress and extra shear stress due to fibers dominate the momentum balance in the coupled Hele-Shaw flow approximation, but the extra in-plane stretching stress terms could be of the same order as those shear stress terms, for large in-plane stretching of suspensions of large particle number. Therefore, a new pressure equation, governing the mold filling process, was derived, including the stresses due to the in-plane velocity gradients. The mold filling simulation was then performed by solving the new pressure equation and the energy equation via a finite element/finite difference method, as well as evolution equations for the second-order orientation tensor via the fourth-order Runge-Kutta method. The effects of stresses due to the in-plane velocity gradient on pressure, velocity, and fiber orientation fields were investigated in the center-gated radial diverging flow in the cases of both an isothermal Newtonian fluid matrix and a nonisothermal polymeric matrix. In particular, the in-plane velocity gradient effect on the fiber orientation was found to be significant near the gate, and more notably for the case of a nonisothermal polymer matrix.     

微细管内电渗流动的瞬态热效应

建立微细圆管内电渗流动的非稳态数学模型,模型通过温度将电渗流的Poisson-Boltzmann方程、动量守恒和能量守恒方程耦合起来.详细讨论了在电渗流的初始阶段,焦耳效应对温度场和速度场演化的影响.同时讨论了不同冷却条件和外部电势场强度条件下,电渗流速度场及温度场变化的特点以及自热的发生过程.研究发现,由于速度场的发展主要受温度主控的电解液黏度影响,因此速度场和温度场是同步发展起来的.通过所得到的结果可以为微细管内的电渗流确定合适的冷却条件,以便同时达到有效抑制样品温度和获得较高流动速度的目的.     

Pervaporation separation of methanol/methyl tert‐butyl ether with poly(lactic acid) membranes

Poly(lactic acid), as a natural source polymer, was used to prepare pervaporation dense membranes. The performance of these membranes for the separation of the methanol (MeOH)/methyl tert‐butyl ether (MTBE) mixtures was investigated. The effects of different operating conditions, including the feed concentration of MeOH, temperature, and flow rate, were examined. Several characterization tests were performed as well. The swelling results, scanning electron microscopy images, contact angles, and mechanical strength measurements are presented. These membranes were found to be selective to MeOH, particularly for traces of MeOH in MTBE with a separation factor of more than 30. There was a small decrease in the separation factor when the feed temperature was increased; meanwhile, the total flux increased to some extent. This could be explained with respect to the thermal motions of the polymer chains and the permeating molecules. With an increase in the feed flow rate, both the selectivity and total flux increased because the concentration and temperature polarizations decreased. At higher flow rates, the feed components were homogeneously distributed over the membrane surface, whereas there may have been a concentration or temperature gradient at lower flow rates. © 2010 Wiley Periodicals, Inc. J Appl Polym Sci, 2010     

CHEMICALLY INDUCED MIGRATION OF PARTICLES ACROSS FLUID STREAMLINES

The velocity of a colloidal particle that moves because of a gradient of concentration of a molecular solute depends on the concentration field at the surface of the particle. Effects of macroscopic convection of the suspending fluid on two such transport phenomena, capillary-driven movement of fluid particles and diffusiophoresis of rigid particles, are considered here. In the case of fluid particles our results also apply to motion caused by a temperature gradient. If the particles are in a laminar flow with the solute gradient directed perpendicular to the direction of flow, as might arise in the boundary layer near a surface to which the particles are being deposited, the local solute concentration field around each particle is disturbed from that of pure diffusion of the solute. Using published results for these concentration disturbances in a simple-shear flow, we determine the effect of the imposed velocity gradient on the speed of the particles in the direction of the solute gradient. For both fluid and rigid particles, the correction due to macroscopic shear is 0(Pe^3/2:) where Pe is the Peclet number based on particle radius and fluid shear rate; this effect opposes the zero-shear particle velocity. A possible consequence of this result is that by increasing the shear rate in a laminar boundary layer in the hope of enhancing the rate of particle adsorption, one may actually be decreasing the rate.     

Measurement of thermal diffusion parameters of polystyrene using a thermal field flow fractionation method

Thermal diffustor parameters such as the thermal diffusion factor and the thermal diffusion coefficient for polystyrene in toluene are measured by using a thermal field flow fractionation (TFFF) method The dependence of these parameters upon temperature concentration and polymer molecular weight is ex-amined. The thermal diffusion coefficien is found to be independent of the molecular weight for sufficiently large polymer molecules but on the other hand the ordinary diffusion coefficient is known to be pronouncedly dependent on the molecular weight. This result indicates that the fractionation effect is primarily governed by the differences in ordinary dif-fusion coefficients.     

Effect of temperature gradient on capillary migration slag components in refractories

Conclusions On the assumption of capillary migration of particles due to the overflow of a sufficiently thin external contact layer, an equation is obtained for the velocity of droplets in immiscible liquids. In the temperature gradient field, the rate of separation of the segregating phases and the formation of the zones in the refractory is proportional to the temperature coefficient of the interphase tension, and is retarded with increase in the slag's viscosity. In contrast to previously known equations, we postulate an inverse relationship for the rate of displacement and the size of the separating droplet of segregating iron-manganese oxide melt.Translated from Ogneupory, No.5, pp. 15–19, May, 1992.     

Modified bead spring theory of dilute polymer solutions. III. Inclusion of multiple relaxation times

A previously derived constitutive equation, representing a blending of the molecular dumbbell theory and a continuum theory of anisotropic fluids, has been extended to the multidumbbell (Rouse-Zimm) case. The equation thus derived yields predictions equivalent to the Rouse-Zimm theory in small-amplitude dynamic shearing, with the exception that the introduction of an “effective molecular weight” as the concentration of polymer is increased is no longer required. In simple shearing flow, the theory predictions are far superior to those of the Rouse-Zimm model, yielding realistic non-Newtonian viscosity behavior, a positive primary normal stress difference, and a negative secondary normal stress difference. In stress relaxation following the cessation of steady shearing flow, the rate of relaxation is found to depend to the initial velocity gradient, but the effect is predicted to be too small to be observed experimentally in typical dilute polymer solutions. The effects of molecular weight, molecular weight distribution, and polymer–solvent interaction are explicitly accounted for, and in all cases the theory predictions are in excellent qualitative agreement with accepted experimental behavior.     

Simultaneous effects of chemical reaction and Ohmic heating with heat and mass transfer over a stretching surface: A numerical study

In this article,we have considered the simultaneous influence of ohmic heating and chemical reaction on heat and mass transfer over a stretching sheet.The effects of applied magnetic field are also taken into consideration while the induced magnetic field is not considered due to very small magnetics Reynolds number.The governing flow problem comprises of momentum,continuity,thermal energy and concentration equation which are transformed into highly nonlinear coupled ordinary differential equations by means of similarity transforms,which are then,solved numerically with the help of Successive Linearization method (SLM) and Chebyshev Spectral collocation method.Numerical values of skin friction coefficient,local Nusselt number,and Sherwood number are also taken into account with the help of tables.The physical influence of the involved parameters of flow velocity,temperature and concentration distribution is discussed and demonstrated graphically.The numerical comparison is also presented with the existing published results and found that the present results are in excellent agreement which also confirms the validity of the present methodology.     

Flow-induced stripe pattern formation in phase-separating fluids

We demonstrated that the introduction of a temperature gradient along the free surface induces a particular stripe pattern in phase-separating fluids. The horizontal temperature gradient drove lateral-periodic spiral liquid motion flowing from warmer to cooler places due to thermocapillarity. Properly chosen polymer compositions and initial film thicknesses in ternary solutions allowed us to promote a phase separation in the presence of spiral flow, which assembled the demixed polymer droplets along the flow-stagnation lines. The resulting assembled phases aligned in the temperature gradient direction and eventually formed periodic polymer stripes involving the same spacing as that of the flow axis. The critical condition for the stripe pattern formation was given by the ratio of two relevant film thicknesses, i.e. the thickness for the onset of the phase separation and that for the cessation of liquid motion.     

微小三角形槽道内电渗流动特性分析

提出了微小三角形槽道内电渗流动理论计算方法，通过Galerkin法计算并分析了其内部的电势及速度分布，获得了温度、槽道尺寸、外加电势的电场强度、ζ电势以及电解质浓度对微小三角形槽道内电渗流动的影响规律。计算结果表明：微小三角形槽道内液体的质量流量随ζ电势、电场强度、流体温度及电解质浓度的增加而增加，随微小三角形槽道尺寸的增加先增加后减小。     

Laser transmission welding of PMMA to alumina ceramic

In this paper, a method of laser transmission welding on ceramic surface after pulse laser microtexture pretreatment was proposed to address the problem that welding ceramics with high transparency polymers is demanded but difficult to be performed. In this method, the polymer flows into the micro-texture of the blind hole on the surface to form mechanical riveting to enhance the welding strength. The formation characteristics and welding mechanism of PMMA welded joint with micro-texture alumina ceramics were studied experimentally and simulatively. The effects of blind hole microtexture size, continuous laser power and continuous laser scanning rate on solution flow and welding strength were studied. The results showed that the air bubbles formed in the welded seam by entering the micro-texture blind hole and trapped air in the blind hole were the key factors affecting the strength of the joint. A 3D finite element model of the transient temperature field and flow field of polymer during laser welding was established. The simulation results showed that the polymer on the left side of the blind hole melted first when heated and inflowed along the wall due to the effects of self-gravity and buoyancy caused by temperature differences. The gas expanded and extruded upward to the left, forming bubbles in the polymer melt pool and pushing the polymer melt into the blind pore microtexture. Finally, a complete molten pool was formed. The flow of polymer melt, the formation of bubbles and the formation of joint were revealed.     

含聚浓度对旋流器性能影响的数值模拟与试验

以螺旋导流式旋流器为研究对象,选用幂律流体模型和离散相模型（DPM）计算了不同含聚浓度条件下的分离性能,对旋流器流场（速度场、压力场）及油滴运移特性进行了细致的分析,并采用高速摄像技术（HSV）开展了相应的分离特性试验。研究发现：聚合物浓度为0时,油滴存在明显的乳化效应,实测效率81.7%;浓度增大后,乳化效应减弱,油滴分散在旋流器内,中心油核消失,效率急剧下降,4000mg/L时旋流器基本无分离效果;浓度增大对压降影响较小,底流压降最高增幅5.6%,最大值不超过200kPa。分析表明,效率下降与切向速度衰减、径向压力梯度减小有关;浓度增大后油滴轴向向下运动的距离增加,呈现向旋流器外壁面运动的趋势,分离时间延长。     

The effect of temperature on the flow field in a continuous rotating annular electrophoresis column

The effect of a non-uniform temperature profile on the flow field in a continuous rotating annular electrophoresis column is investigated. The momentum balance equation is solved for packed as well as unpacked columns using a centered-difference finite difference technique with a known temperature profile. The packed column analysis utilizes a parallel annular channel model similar to the capillary channel model used in packed bed columns. Results indicate that the changes in density and viscosity as result of the temperature variation have a significant effect on the flow field. Effects of voltage gradient and column geometry are also discussed.     

Effects of Electrohydrodynamic Flow and Turbulent Diffusion on Collection Efficiency of an Electrostatic Precipitator with Cavity Walls

The effects of electrohydrodynamic (EHD) flow and turbulent diffusion on the collection efficiency of particles in a model ESP composed of the plates with a cavity were studied through numerical computation. Electric field and ion space charge density in the ESP were calculated by the Poisson equation of electric potential and the current continuity equation of ion space charge. The EHD flow field was solved by the continuity and momentum equations of gas phase, including the electrical body force induced by the movement of ions under the electric field. RNG k - l model was utilized to analyze turbulent flow. Particle concentration distribution was calculated from the convective diffusion equation of particle phase. As the ion space charge increased, the collection efficiency of charged particles increased because the electric potential increased over the entire domain in the ESP. The collection efficiency decreased as the EHD flow became stronger when the electrical migration velocity of charged particles was high. However, the collection efficiency could increase for the stronger EHD flow when the electrical migration velocity of charged particles was relatively lower. Also, the collection efficiency decreased as the turbulent diffusion of particles increased when the electrical migration velocity of particles was high. However, the collection efficiency could increase with the turbulent diffusion when the electrical migration velocity of particles was relatively lower.     

ON FLOW LENGTH REQUIREMENT FOR STRESS-INDUCED POLYMER MIGRATION IN FINE CAPILLARIES

The development of macromolecular concentration gradient caused by the stress induced migration phenomenon in capillary flows has been studied numerically. It is shown that for reaching a given level of flow enhancement, the capillary lengths required are considerably less than those expected from prior analyses, which have neglected the strong interdependence between the flow field and the resulting concentration profiles. The implications of the present findings in terms of detection of macromolecular migration in capillary flows and also the influence on transport rates have been discussed critically.     

Direct Numerical Simulation of Kinematics and Thermophoretic Deposition of Inhalable Particles in Turbulent Duct Flows

Three-dimensional, incompressible turbulent air-particle flows in a channel with a temperature gradient are simulated by direct numerical simulations (DNS). The calculations used the fractional projection method to directly solve the Navier-Stokes equations. For obtaining more accurate results, the Oberbeck-Boussinesq model was used for considering the convective heat transfer and applied two-way coupling between the particles and the air phase to accurately simulate flow field state. The particles motions including mutual collisions were calculated with the direct simulation Monte-Carlo method (DSMC). The particles agglomeration and deposition in the turbulent channel flow with a temperature gradient were simulated by the Dahneke model. The research focused on the effects of the Reynolds number, the temperature gradient and particle concentration which simultaneity affect particle kinematics, impacts, agglomerations, and deposition characteristics. The numerical results show that the thermophoresis dominates the particle deposition, which agrees well with the experimental data, the particle concentration determines the particle collision and agglomeration rate, the Reynolds number determines the particle distribution in the duct and the 2.5 μm particles do not obviously affect the air phase motion under comparatively low concentration referred in this research.     

VELOCITY AND TEMPERATURE DISTRIBUTIONS BETWEEN PARALLEL POROUS PLATES WITH HALL EFFECT AND VARIABLE PROPERTIES

Unsteady hydromagnetic flow and heat transfer between two parallel porous plates is studied with the Hall effect and temperature-dependent properties. The fluid is acted upon by a constant pressure gradient and an external uniform magnetic field, and uniform suction and injection are applied perpendicular to the parallel plates. A numerical solution for the governing nonlinear equations of motion and the energy equation is obtained. The effects of the Hall term and the temperature-dependent viscosity and thermal conductivity on both the velocity and temperature distributions are examined.     

气辅注射成型矩形腔中熔体流动的数值模拟

应用Hele-Shaw物理模型和改进的Ｃross流变模型对辅助射成型过程中充填区域内熔体的流动进行数值模拟,采用控制体积法对充模过程中的熔体前沿、熔体－气体边界进行跟踪,运用有限元／有限差分混合数值方法求解气体注射阶段的速度场、压力场、温度场,以图表的形式列举了不同时刻压力场的分布和充模过程中的流线图。在计算过程中,采用压力场和温度场耦合的方法。