Wall slip of concentrated suspension melts in capillary flows

The effects of wall slip of concentrated suspension melts in capillary flows were investigated at elevated temperature. The modeled material is a mixture of polymer EVA (Ethylene Vinyl Acetate) and non-colloidal spherical powder (glass microspheres) with mean particle size within 53∼63 μm. The effect of particle concentration on wall slip was studied experimentally in a capillary rheometer. For suspensions with different particle loadings (35%, 40%, and 45% by volume), the slip velocity V_s increased with an increase of particle concentration at the same testing temperature. A master slip curve can be obtained by plotting slip velocity versus the product of wall shear stress and square root of particle concentration. As such, a new particle concentration-dependent slip model is proposed. A theoretical approach coupled with the new slip model and flow equation is employed to characterize the flow behavior of concentrated suspension in a capillary rheometer, with reasonable agreement obtained with experimental observations.     

Slip velocity and slip layer thickness in flow of concentrated suspensions

The rheological characterization of highly filled suspensions consisting of a Newtonian matrix (hydroxyl-terminated polybutadiene), mixed with two different sizes of aluminum powder (30% and above by volume) and two different sizes of glass beads (50% and above by volume), was performed using a parallel disk rheometer with emphasis on the wall slip phenomenon. The effects of the solid content, particle size, type of solid particle material, and temperature on slip velocity and slip layer thickness were investigated. Suspensions of small particles of aluminum (mean diameter of 5.03 μm) did not show slip at any concentration up to the maximum packing fraction. However, suspensions of the other particles exhibited slip at the wall, at concentrations close to their maximum packing fraction. In these suspensions, the slip velocity increased linearly with the shear stress, and at constant shear stress, the slip velocity increased with increasing temperature. The slip layer thickness increased proportionally with increasing size of the particles for the glass beads. Up to a certain value of (filler content/maximum packing fraction), ϕ/ϕ_m, the slip layer thickness divided by the particle diameter, δ/D_P, was 0, but it suddenly increased and reached a value that was independent of ϕ/ϕ_m and the temperature. On average, the ratio of δ/D_P was 0.071 for aluminum and 0.037 for glass beads. © 1998 John Wiley & Sons, Inc. J. Appl. Polym. Sci. 70: 515–522, 1998     

Effect of volume fraction and particle size on wall slip in flow of polymeric suspensions

For especially highly concentrated suspensions, slip at the wall is the controlling phenomenon of their rheological behavior. Upon correction for slip at the wall, concentrated suspensions were observed to have non‐Newtonian behavior. In this study, to determine the true rheological behavior of model concentrated suspensions, “multiple gap separation method” was applied using a parallel‐disk rheometer. The model suspensions studied were polymethyl methacrylate particles having average particle sizes, in the range of 37–231 μm, in hydroxyl terminated polybutadiene. The effects of particle size and solid particle volume fraction on the wall slip and the true viscosity of model concentrated suspensions were investigated. It is observed that, as the volume fraction of particles increased, the wall slip velocity and the viscosity corrected for slip effects also increased. In addition, for model suspensions in which the solid volume fraction was ≥81% of the maximum packing fraction, non‐Newtonian behavior was observed upon wall slip correction. On the other hand, as the particle size increased, the wall slip velocity was observed to increase and the true viscosity was observed to decrease. © 2005 Wiley Periodicals, Inc. J Appl Polym Sci 98: 439–448, 2005     

压力驱动微流道内流动电势及壁面滑移效应

This study investigated the streaming potential and wall slip effects on pressure-driven liquid flow in hydrophobic microchannels.The Poisson-Boltzmann equation for the electrical double layer(EDL)and Navier-Stokes equation for incompressible viscous fluid were established.For those microchannels with high wall zeta potential, the traditional Debye-H點kel linear approximation for solving the potential distributions of EDL would produce big error, therefore, analytical expression for potential distributions and Navier slip boundary condition were introduced to solve the N-S equation analytically, then analytical solution of streaming potential could be obtained by using the electrical current balancing condition.The influences of electrokinetic parameter(K), wall zeta potential and slip coefficient on streaming potential and velocity distributions were discussed in detail.The results showed that streaming potential decreased with increasing electrokinetic parameter, while increased significantly with increasing slip coefficient.It also tended to reach a maximum value at a certain zeta potential and then decreased rapidly with increasing zeta potential.Streaming potential and wall slip both affected fluid flow in microchannels, the former retained the development of liquid flow, but the latter accelerated flow velocity.Wall slip effect played a major role at lower zeta potentials, that is, flow velocity increased at lower zeta potentials when the combined effects of streaming potential and hydrodynamic slippage appeared in microchannels.Wall slip velocity gradually reduced to zero at higher zeta potential, then wall slip effect on pressure-driven flow in microchannels could be ignored.     

Effect of the surface roughness and construction material on wall slip in the flow of concentrated suspensions

Recent studies on polyethylene, elastomers, and thermoplastics have revealed that the construction material and surface roughness are two important factors affecting wall slip. In this study, to determine the true rheological behavior of model concentrated suspensions, a multiple‐gap separation method was used in a parallel disk rheometer. The model suspensions studied were poly (methyl methacrylate) particles with an average particle size of 121.2 μm in hydroxyl‐terminated polybutadiene. The aim of this study was to investigate the effect of disk R_a in the range of 0.49–1.51 μm and disk construction material on the wall slip and the true viscosity of the model concentrated suspensions. The wall slip velocity and the viscosity were found to be independent of R_a for particle size‐to‐disk R_a ratios of 80–247. Also, the true viscosity was found not to be affected by the rheometer surface construction material. Glass surfaces resulted in the highest slip velocity, whereas aluminum surfaces resulted in the lowest slip velocity. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 103: 3341–3347, 2007     

Experimental investigation of particle migration in suspension flow through bifurcating microchannels

Experimental measurements of velocity and concentration profiles were carried out to study transport of non‐colloidal suspension in bifurcating micro channels for both diverging and converging flow conditions using a combination of mirco‐particle image velocimetry and particle tracking velocimetry techniques. Migration of particles across the streamline was observed and symmetric velocity and concentration profile in the inlet branch becomes asymmetric in the daughter branches. Further migration of particles toward the center of the channel in the outlet branch make the profiles again symmetric. The evolution of velocity and concentration profiles was observed to be different in the symmetric and asymmetric bifurcation channels. The comparison of the streamlines for the fluid and the particles showed significant deviation near the bifurcation region. This may explain why there is unequal flow and particle partitioning during flow of suspension in asymmetric bifurcating channels as reported in many previous studies. © 2018 American Institute of Chemical Engineers AIChE J, 64: 2293–2307, 2018     

Determination of pressure drop for concentrated suspension in a capillary flow

The rheological behavior of concentrated suspension melts in a capillary die is investigated. Particle migration and wall slip are two major factors affecting the flow behavior. A numerical model is proposed to describe the coupling effect of particle migration and wall slip in a capillary tube flow, incorporating a power‐law model for binder viscosity and a concentrated suspension viscosity model proposed by Krieger. Wall slip of a non‐Newtonian concentrated suspension is characterized by a modified Mooney method for which the conventional Mooney method is not applicable. We characterized the flow behavior of a concentrated suspension of a non‐Newtonian binder, EVA 460 (ethylene vinyl acetate), mixed with spherical glass beads of 40% by volume. Predicted results were compared with experimental observations, with good agreement. POLYM. COMPOS., 2010. © 2009 Society of Plastics Engineers     

温度和固相粒径与浓度对水煤浆管内流动壁面滑移的影响

通过改变管径、温度、煤粉粒度和浓度,在中试规模的输送装置上研究水煤浆直管内的滑移流动规律,联合采用Mooney滑移修正方法和Tikhonov正则化方法确定浆体壁面滑移特性。结果表明,随温度和固相粒径的增大,临界剪切应力降低,壁面滑移速度显著增加;浓度越高,临界剪切应力及产生相同滑移速度所需的壁面剪切应力越大,温度升高对临界剪切应力和屈服应力的降低越显著;低壁面剪切应力下的滑移贡献率主要取决于临界剪切应力及屈服应力的相对大小,高壁面应力下主要取决于壁面滑移速度和浆体真实流变特性。     

Wall slip velocity measurement of molten polypropylene in capillary flow based on length‐corrected Mooney technique

In this study, to measure wall slip velocity of molten polypropylene (PP) by using different length‐to‐diameter (L/D) ratios of capillary dies with fixed diameter, a length‐corrected Mooney technique was proposed. Moreover, the effects of pressure, temperature, and L/D ratio were considered to better represent wall slip mechanism. To verify the feasibility of the length‐corrected Mooney technique, a series of capillary rheological experiments for molten PP were carried out. Meanwhile, the power‐law quantitative equations of slip velocity were established by shear stress. Moreover, the effects of L/D ratio and temperature on rheological properties of PP were investigated. In addition, numerical simulations for slip velocity and rheological properties of PP were performed. Numerical results validated that the length‐corrected Mooney technique, and the power‐law quantitative equations of slip velocity were available. Results showed that wall slip velocity of molten PP decreased with the capillary die's L/D ratio, but increased with the temperature and shear rate. © 2016 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2017 , 134, 44589.     

Experimental test of a model for laminar slurry flow with sedimentation

The ability of a flow-sedimentation model to simulate the flow of a slowly-settling suspension being transported in the laminar regime through a pipeline with a constant overall pressure drop imposed on it was assessed using experimental scaled-down pipeline data. Comparison of predicted volumetric flow rate versus time profiles to those observed suggested that the blockage process took place in two steps. Initially, a sediment grew on the lower pipe wall and the flow gradually lessened, as was modelled. As the flow slowed down, ultimately a plug, which enclosed the full cross-section of the pipe, formed and lead to the rapid blockage of the pipe. It was envisioned that the granular properties of the concentrated suspension became dominant during the final blockage process. A deposit velocity criterion was also developed from the flow-sedimentation model and was used to generate a deposit velocity versus pipe diameter plot. Results from the plot indicate that the laminar pipeline flow of a slowly-settling suspension is possible in small diameter pipes.     

Turbulence structure for plane Poiseuille–Couette flow and implications for drag reduction over surfaces with slip

Direct numerical simulations were used to simulate plane channel and plane Poiseuille–Couette flows. For Poiseuille–Couette flow, the walls of the channel were moving with a specified velocity. This is equivalent to forcing a slip velocity at the wall of the channel, and such flow behaviour can be viewed as the effect due to an ultra‐hydrophobic wall. It was found that the location of the zero Reynolds stress value shifted towards the wall moving in the streamwise direction. The near‐wall eddies were found to be longer and weaker than for the plane‐Poiseuille channel flow. It appears that such an eddy structure can lead to turbulence drag reduction.     

滑移效应下纤维绕流场及过滤阻力的数值计算与分析

考虑实际纳米/微米纤维表面的流体滑移效应,采用数值方法求解滑移流动机理下纳米/微米纤维绕流场及过滤阻力,分析讨论了Knudsen数Knf和填充率C对纤维近壁面速度分布及纤维过滤阻力的影响规律.结果表明,对纳米/亚微米纤维过滤情形,纤维表面流体的滑移效应导致纤维绕流场与非滑移条件下情形有显著差异,尤其在高填充率下,纤维表...     

The surface renewal model of wall turbulence for boundary layer flow with transpiration

The object of this paper is to develop and evaluate the basic surface renewal modeling approach for transpired turbulent boundary layer flows. Using a simple form of the surface renewal model in conjunction with the standard mixing length representation of the turbulent core, calculations are established for the dimensionless burst frequency s⁺, and distributions in velocity u⁺ within the inner region as a function of transpiration rate v⁺ and pressure gradient P⁺.     

Shear viscosity,extensional viscosity,and die swell of polypropylene in capillary flow with pressure dependency

The shear and extensional viscosities of a polypropylene resin were studied using a capillary rheometer and capillary dies of 1‐mm diameter and length of 10, 20, and 30 mm. Melt temperatures at 190, 205, and 220°C and shear rates between 100 and 5000 s^?1 were used. At the highest shear rate a visible melt fracture was observed. An equation relating the pressure drop and die length was derived with consideration of pressure effects on melt viscosities and the end effect. After the correction for pressure effects the true wall shear stress and end effect at zero pressure were calculated. The end effect showed a critical stress of melt fracture around 10⁵ Pa, and increased rapidly when shear stress increased above the critical stress. From shear stress the shear viscosity was calculated, and a power law behavior was observed. Extensional viscosity was calculated from the end effect and showed a decreasing trend when strain rate increased. After time–temperature superposition shift shear viscosity data correlated well, but an upward trend was observed in extensional viscosity when melt fracture occurred. Die swell ratio at different temperatures can be plotted as a function of wall shear stress and was higher for shorter dies. © 2002 Wiley Perioodicals, Inc. J Appl Polym Sci 84: 1269–1276, 2002; DOI 10.1002/app.10466     

借助变阱宽方阱链流体状态方程模拟非电解质体系表面张力和粘度(英文)

The equation of state(EOS)for square-well chain fluid with variable range(SWCF-VR) developed in our previous work based on statistical mechanical theory for chemical association is employed for the correlations of surface tension and viscosity of common fluids and ionic liquids(ILs).A model of surface tension for multi-component mixtures is presented by combining the SWCF-VR EOS and the scaled particle theory and used to produce the surface tension of binary and ternary mixtures.The predicted surface tensions are in excellent agreement with the experimental data with an overall average absolute relative deviation(AAD)of 0.36%.A method for the calculation of dynamic viscosity of common fluids and ILs at high pressure is presented by combining Eyring’s rate theory of viscosity and the SWCF-VR EOS.The calculated viscosities are in good agreement with the experimental data with the overall AAD of 1.44% for 14 fluids in 84 cases.The salient feature is that the molecular parameters used in these models are self-consistent and can be applied to calculate different thermodynamic properties such as pVT,vapor-liquid equilibrium,caloric properties,surface tension,and viscosity.     

Gas hold‐up in bubble columns: Operation with concentrated slurries versus high viscosity liquid

The hydrodynamics of bubble columns with concentrated slurries of paraffin oil (density, ρ_L = 790 kg/m³; viscosity, μ_L = 0.0029 Pa·s; surface tension, σ = 0.028 N·m¹) containing silica particles (mean particle diameter d_p = 38 μm) has been studied in columns of three different diameters, 0.1, 0.19 and 0.38 m. With increasing particle concentration, the total gas hold‐up decreases significantly. This decrease is primarily caused by the destruction of the small bubble population. The hold‐up of large bubbles is practically independent of the slurry concentration. The measured gas hold‐up with the 36% v paraffin oil slurry shows remarkable agreement with the corresponding data obtained with Tellus oil (ρ_L = 862 kg/m³; μ_L = 0.075 Pa·s; σ = 0.028 N·m^?1) as the liquid phase. Dynamic gas disengagement experiments confirm that the gas dispersion in Tellus oil also consists predominantly of large bubbles. The large bubble hold‐up is found to decrease significantly with increasing column diameter. A model is developed for estimation of the large bubble gas hold‐up by introduction of an wake‐acceleration factor into the Davies‐Taylor‐Collins relation (Collins, 1967), describing the influence of the column diameter on the rise velocity of an isolated spherical cap bubble.     

Shear dispersion in combined pressure‐driven and electro‐osmotic flows in a capillary tube with a porous wall

An analytical expression is derived for the shear dispersion during transport of a neutral nonreacting solute within a coupled system comprised of a capillary tube and a porous medium under the combined effects of pressure‐driven and electro‐osmotic flows. We use the Reynolds decomposition technique to obtain a dispersion coefficient by considering a sufficiently low wall or zeta potential that accounts for the combined flows. The coupled dispersion coefficient depends on the Debye–Hückel parameter, Poiseuille contribution fraction, and Péclet number. The developed model also provides a shear dispersion coefficient for an impervious capillary tube (noncoupled system). The ratio of the coupled (porous wall) and noncoupled (impervious) dispersion coefficients reveals that it is essential to include the transport of chemical species from the tube to the porous medium in several important physical situations. These findings have implications for design of chemical species transport in porous microfluidic networks and separation of emulsions in microchannel‐membrane systems. © 2015 American Institute of Chemical Engineers AIChE J, 61: 3981–3995, 2015     

中等过冷度下含不凝性气体蒸汽冷凝传热特性

通过对竖直圆管外表面含不凝性气体蒸汽在中等壁面过冷度条件下的冷凝传热实验研究,分析了混合气体压力0.4～0.6 MPa、空气含量0.07～0.52以及壁面过冷度13～25℃时,蒸汽的冷凝换热特性,给出了冷凝传热过程中的经验关联式,并对氦气的存在及其对换热过程的影响进行了初步分析。结果表明：在混合气体压力及不凝性气体含量不变的条件下,壁面过冷度的降低利于冷凝传热系数的增长;所得到的经验关联式在低过冷度条件下能较好地对换热过程进行预测,且其与实验值的误差在±15%以内;实验条件下未发生氦气分层现象,相同不凝性气体质量分数条件下,氦气的存在会使冷凝传热系数降低约20%。     

外加电场对静电流化床中颗粒运动与床层粘壁的调控机制

对流化床反应器中的颗粒运动行为进行调控可达到强化反应器性能的目的。通过冷模实验研究了直流/交流电场对静电流化床中颗粒运动的影响规律与影响机制,建立了通过外加电场调控静电流化床中床层粘壁的方法。结果表明,在低场强条件下,库仑力主导外加直流电场对颗粒运动的影响,由床层壁面指向床层中心的外加直流电场使得颗粒运动强度和轴向颗粒运动分率降低,而由床层中心指向床层壁面的外加直流电场则作用相反;在高场强条件下,极化力主导外加直流电场对颗粒运动的影响,使得颗粒运动强度减弱。在外加交流电场中,无库仑力存在时,极化力仍在高电场强度下使得颗粒运动强度减弱,但当库仑力存在时,电场强度和方向的周期性改变使得颗粒发生周期性摆动,颗粒运动强度增强。在本文的实验条件下,外加交流电场是一种控制床层粘壁的良好方法。2.5 kV/cm、50 Hz的正弦交流电场使得床层粘壁下降76%。研究结果可为聚烯烃流化床反应器的安全运行和过程强化提供指导。     

Dispersed plug flow model for steady-state laminar flow in a tube with a first order sink at the wall

Steady state, laminar flow transport in a tube with a first order sink at the wall involves two dimensions—radial and axial. In this paper, a novel iterative technique has been proposed for reducing such a two-dimensional model to an equivalent one-dimensional dispersed plug flow model. The latter yields an analytical expression for the equivalent axial dispersion and a simple, closed form, but approximate, analytical solution of the original two-dimensional problem. The operating range in which this analytical solution is useful has been investigated for a system with mass transfer at the wall.