用激光多普勒测速计（LDA）分析粘弹性对Metzner和Otto系数的影响

The Metzner and Otto correlation is the single practical method for incorporating non-Newtonian effects in the mixing process. In this article, the Metzner and Otto' s idea, the role of viscoelasticity on the Metzner and Otto coefficient, ks, effects of flow regime on ks and the determination of ks for Rushton turbine impeller have been studied using the direct method of the laser Doppler anemometry (LDA) velocity measurement for the case of viscoelastic liquids. The normalized mean tangential velocity profiles are independent of Rushton turbine impeller speeds. Contrary to literature findings, it is shown that the variation of local shear rate against the impeller speed is better correlated by the power equation, i.e. γ= ks' · Nb' , in the transition region, i. e. ～ 30 < Re <～ 2000. Also, a correlation between improved coefficient, ks', and the elasticity number of viscoelastic liquids is given which is very helpful in designing of the mixing of both viscoelastic and inelastic non-Newtonian fluids t     

THE LOCAL VOLUME-AVERAGED EQUATIONS OF MOTION FOR A SUSPENSION OF NON-NEUTRALLY BUOYANT SPHERES

The local volume averages of the equations of motion as well as the appropriate boundary conditions are developed for a flowing suspension of non-neutrally buoyant, uniform spheres in an incompressible Newtonian fluid under conditions such that inertial effects can be neglected. These equations do not represent an asymptotic theory with respect to the volume fraction of solids. Higher order terms have been retained everywhere, except where it has been necessary to estimate the velocity distribution within the immediate neighborhood of each sphere by neglecting the effects of the other spheres present. The resulting local volume-averaged equations of motion and boundary conditions involve no free or undetermined parameters.

For the special case of a very dilute suspension of neutrally buoyant spheres, the total local volume average of Cauchy's first law reduces to the form of the Navier-Stokes equation with the effective viscosity computed by Einstein (1906, 1956).

In two succeeding papers, we demonstrate for several flows [in vertical tubes, in a cone-plate viscometer, between rotating concentric cylinders (Couette flow), and between rotating parallel plates] that our general theory describes more concentrated neutrally buoyant suspensions than does its limiting case of very dilute suspensions.     

黏弹性表面活性剂溶液中颗粒沉降特性研究

黏弹性表面活性剂溶液悬浮颗粒流广泛存在于自然界和工业生产中,黏弹性表面活性剂溶液的非线性流变性质及应力松弛效应对其中颗粒沉降有着显著影响。采用FENE-P和Giesekus黏弹性本构模型对表面活性剂溶液中颗粒沉降特性进行研究,发现两种本构模型不仅表现出剪切稀化,而且出现拉伸硬化。颗粒在沉降初期的不稳定性主要是由溶液自身的弹性效应引起,弹性效应越强,颗粒沉降速度不稳定性越强,而剪切稀化效应会减弱颗粒沉降速度的不稳定。颗粒沉降过程中在其尾部形成一个“负尾迹”,随着剪切稀化和拉伸硬化效应增强,负尾迹区增大,弹性效应增加,负尾迹增强,负尾迹区流体内部反向速度分布导致的表面活性剂溶液中微观胶束的拉伸断裂和重构可能是引起颗粒沉降速度持续波动的原因。     

锚式搅拌槽中高粘弹性流体的流速分布及其功率消耗

用照相法测定了锚式搅拌槽中高粘弹性流体的流型和流速分布,另测定了搅拌功率消耗,结果发现:1.与牛顿流体相比,在低Re数下,粘弹性流体的切向速度较大,而径向速度则较小.2.转速相同时,在高剪切率区域,粘弹性流体的剪切率大于牛顿流体.由CEF方程导出功率计算式N_pRe_af_s~(1-n)=k_pf_vf_s~2[1+F_1avf_s~(m-n-3)Wi/K_s~2]用实验数据确定f_(?)和F_(1av),得到可适用于牛顿流体、假塑性流体和粘弹性流体的普适功率计算式,计算结果与实验值比较接近.     

Experimental study of film thickness and free surface velocity around a rotating roll for non-newtonian fluids

Measurements are performed on film thickness and free surface velocity around a rotating roll for Newtonian, non-Newtonian inelastic, and viscoelastic fluids by using noncontact methods of a capacitance probe and a laser Doppler velocimeter probe. The film thickness decreases with increasing inspection angle for Newtonian fluids. For non-Newtonian fluids, it retains an approximately constant value, owing to shear-thinning of viscosity, except for a meniscus region development, which is dependent on fluid elasticity. Comparison of current results with the film thickness from a previous work is also made. With the increment of inspection angle, the free surface velocity increases rapidly in the meniscus region and maintains a constant value almost equal to a roll speed in the other region for viscoelastic fluids, while it increases linearly for Newtonian fluids. The shear rate at a roll surface is presented assuming that the velocity distribution in the liquid film is a polynomial equation. It is found that viscoelastic fluids exhibit different behavior from that of Newtonian and non-Newtonian inelastic fluids. Evaluation of the force acting on the liquid film for Newtonian fluids implies that the velocity gradient at a roll surface in an ascending region may be steeper than the parabolic form assumed in this study.     

TURBULENT FLOW OF MILDLY VISCOELASTIC LIQUIDS IN CURVED TUBES

The turbulent flow of mildly viscoelastic liquids in curved lubes is analyzed using boundary layer approximations. The momentum integral approach is used and the governing equations are solved numerically by the Runge-Kutta-Merson technique. The influence of Deborah number on the velocity distribution and the boundary layer thickness has been studied for the first time. The theoretically developed expression for frictional losses was checked with available experimental data and sound agreement was found. The results of this analysis are likely to find application in the biomedical fluid mechanics and in the analysis of the flow with so-called “drag reducing” additives.     

TURBULENT FLOW OF MILDLY VISCOELASTIC LIQUIDS IN CURVED TUBES

The turbulent flow of mildly viscoelastic liquids in curved lubes is analyzed using boundary layer approximations. The momentum integral approach is used and the governing equations are solved numerically by the Runge-Kutta-Merson technique. The influence of Deborah number on the velocity distribution and the boundary layer thickness has been studied for the first time. The theoretically developed expression for frictional losses was checked with available experimental data and sound agreement was found. The results of this analysis are likely to find application in the biomedical fluid mechanics and in the analysis of the flow with so-called “drag reducing” additives.     

Viscosity of organic liquids at elevated temperatures and the corresponding vapour pressures

This work involved the measurement of the viscosities of pure organic liquids at temperatures ranging from 353.15 K to 463.15 K and at the corresponding vapour pressures. A rolling ball viscometer was used where considerable emphasis was given to achieve simplicity and rapidity in obtaining results, without sacrificing the accuracy. Considering the forces affecting the motion of the ball inside the viscometer tube, an equation for the calibration of the viscometer at the same working temperature was derived. The constants of this equation were determined using benzene as the reference liquid, and the dependency of the constants on the temperature was also established. Comparing the derived equation with published ones demonstrated its adequacy in both the streamline and transition flow conditions. The liquids studied were toluene, methanol and n-hexane. In some cases, the results compared reasonably well with published data while in others, deviations of up to 15% were found. Nine equations were tested with the experimental results for the prediction of the viscosity of these liquids. It was found that the 3-constant Agrawal and Thodos empirical equation gave the least average deviation.     

Rheology and flow of phosphate slurries (mine tailings) in pipes

An experimental study of the flow of phosphate mine tailings was carried out in order to characterize these suspensions of fine particles for pipeline transport. Rheological measurements with a rotating cylinder viscometer indicate a viscoplastic behaviour which can be represented by a Herschell-Bulkley or by a Casson model. The variation of the parameters of these models with solids concentration reveals a change in the behaviour at a concentration of 10 to 15%. The pressure drops were measured during flow in capillary tubes, in both laminar and turbulent regimes. The variation of the pressure drop coefficient (Fanning friction factor) as a function of the generalized Reynolds number confirms the validity of the employed rheological models. The results are in good agreement with measurements made in pipes of industrial size. The velocity profiles measured with a novel ultrasonic velocimeter demonstrate the influence of the rheological behaviour on the yield and wall stresses.     

VISCOSITY OF GLYCEROL AND ITS AQUEOUS SOLUTIONS MEASURED BY A TANK-TUBE VISCOMETER

In this paper we demonstrate several series of experiments for the measurement of viscosity of neat glycerol and its aqueous solutions using a tank-tube viscometer. Measuring viscosity of highly viscous liquids with the tank-tube viscometer is easier than other types of viscometers. This inexpensive viscometer continuously generates numerous reproducible viscosity data of highly viscous neat glycerol and its aqueous solutions under given experimental conditions such as a desired temperature and a desired concentration of water in aqueous glycerol solutions.

Fabricating the tank-tube viscometer is inexpensive, since this viscometer does not need sophisticated accessories such as a high-pressure liquid pump, a sensitive pressure sensor, and an accurate flow meter. The tank-tube viscometer consists of a large-diameter reservoir and a long, small-diameter, vertical tube.

The viscosity equation was developed under the following assumptions. Both the quasi steady state approach and the negligible friction loss due to a sudden contraction between the reservoir tank and the tube are valid. The kinetic energy of the emerging stream from the bottom end of the vertical tube of the tank-tube viscometer also is assumed to be negligible. Very viscous glycerol and its aqueous solutions were used to test the viscometer by comparing viscosity values from the viscometer with those from literatures.

The main objective of this study is to demonstrate effects of water as well as temperature on viscosity of aqueous glycerol solutions, applying experimental data of accumulated amounts of aqueous glycerol solutions at various drain durations to the newly-developed viscosity equation for the fabricated tank-tube viscometer.     

Mass transfer from spheres submerged in Newtonian and non-Newtonian fluids

Mass transfer from spheres immersed in Newtonian and power-law fluid flows in the high Reynolds number region is discussed using a modified penetration model. By defining appropriate characteristic velocity and length, the proposed model in which a velocity gradient at the transfer surface is taken account of can be used to evaluate the rate of mass transfer from a sphere in complicated practical flow situations. The proposed model compares reasonably well with previously reported experimental data and correlations for mass transfer from a sphere in a fluid flowing at uniform approach velocity, in a fixed or fluidised bed, and in a stirred tank. Futhermore, good agreement is found between the model and the available experimental data and correlation for mass transfer from a rotating sphere.     

Rheological phenomena during the polymerization of styrene in a stirred tank

An experimental study of the bulk polymerization of styrene has been carried out. The rate of polymerization, molecular weight, and flow patterns around agitators as a function of conversion have been observed. The rate data are interpreted in terms of free-radical polymerization kinetics. Duerksen and Hamielec's modified termination rate constant and initiator efficiency relations are generally consistent with our data. The flow patterns were interpreted in terms of the mechanics of viscoelastic liquids and observations for nonreacting systems. Specifically, at low conversions for spheres and similar agitators, the flow patterns are dominated by centrifugal forces with fluid drawn in at the poles and expelled at the equator for spherical agitators. At higher conversions, normal stresses interact with the centrifugal forces causing segregated secondary flow regions adjacent to the sphere. At very high concentrations, normal stresses dominate, yielding Weissenberg effects.     

Drag on non-spherical particles in non-newtonian fluids

Extensive experimental results on the free fall of a range of non-spherical particles such as square bars, cylinders, spheres and crushed rock chips in Newtonian, inelastic, viscoelastic and Boger fluids are presented. It is demonstrated that the use of a volume equivalent sphere diameter in addition to a shape factor provides an adequate approximation for the non-sphericity of particles used in this study. The applicability of two rheological models, namely, the power-law and the Carreau viscosity model has been examined in representing the drag coefficient results. Appropriate predictive expressions of the drag coefficient as a function of the particle Reynolds number and the Deborah number, encompassing wide ranges of rheological and kinematic conditions, are presented.     

Hydrodynamic method for cleaning inner surfaces of pipes

A new method for cleaning inner surfaces of pipes was studied both theoretically and experimentally. The method is based on the phenomenon of a sphere rotating in a pipe (levitation), when the translational movement of the sphere is restricted and the sphere is subjected to fluid flow in the pipe. The high rotation velocity causes a vibration process, which may be exploited for cleaning sediments or rust from the inner surfaces of pipes. A simplified theoretical model for the determination of the relationships among the dimensionless parameters governing the rotation phenomenon was developed. The model was validated with experimental data and found to be appropriate for engineering design of the system. Application of the cleaning method was demonstrated by cleaning the sediments and rust off the inner surface of a one-inch nominal diameter pipe.     

Kinematic Simulation and Experimental Study on Rotating Air Flow for Drying Alfalfa

An auxiliary device for rotating alfalfa in air flow with waste air recycling was designed in this study. The motion characteristics of rotating alfalfa in air flow and the new crafts of herbage drying for drying homogeneity were studied. An aerodynamic model of alfalfa segments was established based on the result of the experiment on alfalfa rotation in air flow. The movement of alfalfa segments was analyzed using kinematic simulation. The movement trail and the behavior of alfalfa rotation in air flow were tested and verified. Experimental results revealed that the effect of alfalfa rotation in air flow depends on the air flow parameters and the mechanism of the new device. The influence of drying air flow velocity, initial velocity, and air flow angle were analyzed using a nonlinear regression orthogonal design and rotating alfalfa in air flow and building mathematical models of rotating alfalfa parameters on experimental criteria to optimize the parameters of alfalfa drying homogeneity. MATLAB was used for single-target optimization and experimental verification. Optimized drying parameters were ascertained (i.e., air flow velocity, 2.82 m/s; initial velocity, 0.05 m/s; air flow angle, 5.0° to 5.5°) based on the simulation of the alfalfa drying study and experimental result.     

Low-Reynolds-number motion of a heavy sphere between two parallel plane walls

A novel boundary-integral algorithm [Staben, M.E., Zinchenko, A.Z., Davis, R.H., 2003. Motion of a particle between two parallel plane walls in low-Reynolds-number Poiseuille flow. Physics of Fluids 15, 1711-1733; Erratum: Phys. Fluids 16, 4206] is used to obtain O(1)-nonsingular terms that are combined with two-wall lubrication asymptotic terms to give resistance coefficients for near-contact or contact motion of a heavy sphere translating and rotating between two parallel plane walls in a Poiseuille flow. These resistance coefficients are used to describe the sphere's motion for two cases: a heavy sphere driven by a Poiseuille flow in a horizontal channel and a heavy sphere settling due to gravity through a quiescent fluid in an inclined channel. When the heavy sphere contacts a wall in either system, which occurs when the gap between the sphere and the wall becomes equal to the surface roughness of the sphere (or plane), a contact-force model using the two-wall resistance coefficients is employed. For a heavy sphere in a Poiseuille flow, experiments were performed using polystyrene particles with diameters 10%-60% of the channel depth, driven through a glass microchannel using a syringe pump. The measured translational velocities for these particles show good agreement with theoretical results. The predicted translational velocity increases for increasing particle diameter, as the spheres extend further into the Poiseuille flow, except for particles that are so large (diameters of 80%-85% of the channel depth) that the upper wall has a dominant influence on the particle velocity. For a heavy sphere settling in a quiescent fluid in an inclined channel, the transition from the no-slip regime to slipping motion occurs for a larger inclination angle of the channel with respect to the horizontal for an increase in particle diameter, since the larger particles are more slowed by the second wall. Limited experiments were performed for Teflon spheres with diameters 64%-95% of the channel depth settling in a very viscous fluid along the lower wall of an inclined acrylic channel. The measured translational velocities, which are only about 15%-25% of the tangential component of the undisturbed Stokes settling velocity, are in close agreement with theory using physical parameters obtained from similar experiments with a single wall [Galvin, K.P., Zhao, Y., Davis, R.H., 2001. Time-averaged hydrodynamic roughness of a noncolloidal sphere in low Reynolds number motion down an inclined plane. Physics of Fluids 13, 3108-3119].     

Polymer characterization by thermal field flow fractionation with a continuous viscosity detector

A sensitive flow viscometer detector has been successfully used with time-delay, exponential-decay thermal field flow fractionation (TDE-TFFF) to produce unique information on polymers. TFFF with a concentration-dependent detector (e.g., refractometer) and a differential capillary viscometer is unable to produce a universal calibration plot that eliminates the necessity of polymer standards for accurate molecular-weight calibration. However, this system directly provides valuable information on the inherent (or intrinsic) viscosity distribution of polymers. Absolute intrinsic viscosity values are measured by TFFF without the need of calibration. Detailed TFFF/inherent-viscosity distribution profiles uniquely describe individual sample differences and are not affected by the experimental conditions used in TFFF separations. These viscosity distributions should be very useful in polymer characterization, since they are closely correlated with polymer end-use and solution properties, as well as to polymer molecule weight.     

旋转喷头喷射外流场计算流体力学仿真分析

介绍了计算流体力学(CFD)仿真的原理、方法和步骤;通过CFD仿真软件Fluent对旋转喷头射流喷射外流场进行仿真分析,得到了旋转喷头射流外流场的射流形态、速度与气液两相分布等微观信息,从而获得旋转喷头打击分布规律,为进一步开展旋转喷头喷射性能的试验研究提供了参考数据.     

SLOW NON-NEWTONIAN FLOW PAST AN ASSEMBLAGE OF RIGID SPHERES

Previous work on slow flow of non-Newtonian fluids past particles assemblages has been reviewed. Using a combination of Happel's free surface model and variational principles, bounds on the drag have been obtained for the creeping flow of a Carreau Model fluid past an assemblage of rigid spheres. The bounds are related to friction factor for flow through fixed beds of spherical particles. Numerical results covering a wide range of model parameters and bed voidages are presented.

Theoretical predictions are validated by comparing with experimental results reported in the literature that involve viscoelastic fluids. Arithmetic averages of the two bounds compare well for 182 data points with an average error of 12%. It is demonstrated that the present analysis, though based on a purely viscous model, can predict creeping flow behaviour in rigid particles assemblage for both inelastic and viscoelastic fluids.     

A STUDY OF SPINLINE DYNAMICS USING ORTHOGONAL COLLOCATION

Previous work on slow flow of non-Newtonian fluids past particles assemblages has been reviewed. Using a combination of Happel's free surface model and variational principles, bounds on the drag have been obtained for the creeping flow of a Carreau Model fluid past an assemblage of rigid spheres. The bounds are related to friction factor for flow through fixed beds of spherical particles. Numerical results covering a wide range of model parameters and bed voidages are presented.

Theoretical predictions are validated by comparing with experimental results reported in the literature that involve viscoelastic fluids. Arithmetic averages of the two bounds compare well for 182 data points with an average error of 12%. It is demonstrated that the present analysis, though based on a purely viscous model, can predict creeping flow behaviour in rigid particles assemblage for both inelastic and viscoelastic fluids.