A study of low shear viscosity of polymer melts

An inexpensive, accurate falling coaxial cylinder viscometer is described. Viscosities can be measured at shear stresses at least as low as 10³ dynes per cm² and flow curves can be obtained with shear thinning fluids. Data for a polystyrene and a polyethylene polymer coincide with those from other techniques and with corresponding literature values. The lower Newtonian viscosities pf both polymers were experimentally accessible, and it is shown that estimation of η_o by extrapolation from viscosities in the non-Newtonian region may be subject to errors of uncertain magnitude. Shear history of the sample affects the Newtonian and low shear viscosities of high molecular weight polymer melts.     

Upgrading the melt flow index to rheogram approach in the low shear rate region

The unified viscosity function curves proposed earlier by the authors have an inherent limitation in the low shear rate region. This limitation is the effect of using the melt flow index as a normalizing factor to obtain the coalesced curves, which itself is insensitive to molecular parameters such as molecular weight distribution. A single integral constitutive equation of the BKZ type is used to derive the viscosity function which would be useful in generating unified curves based on the melt flow index but devoid of the limitation of molecular weight distribution effects in the low shear rate region.     

Effect of viscoelasticity in the film‐blowing process

Numerical simulations have been undertaken for the film‐blowing process of viscoelastic fluids under different operating conditions. Viscoelasticity is described by an integral constitutive equation of the K‐BKZ type with a spectrum of relaxation times, which can fit the experimental data well for the shear and extensional viscosities and the normal stresses measured in shear flow. Nonisothermal conditions are considered by applying the Morland–Lee hypothesis, which incorporates the appropriate shift factor and pseudotime into the constitutive equation. The momentum and energy equations are expressed in the machine direction only by using a quasi‐one‐dimensional approach introduced earlier by Pearson and Petrie. The resulting system of differential equations is solved using the finite element method and the Newton‐Raphson iterative scheme. The method of solution was first checked against the Newtonian and Maxwell results for various film characteristics given earlier. The simulations are compared with available experimental data and previous simulations in terms of film shape, velocity, stresses, and temperature. The present results show that the existing modeling of force balances is inadequate for quantitative agreement with the experimental studies. © 2007 Wiley Periodicals, Inc. J Appl Polym Sci, 2007     

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.     

Flow through porous media of a shear-thinning liquid with yield stress

Darcy's law for the laminar flow of Newtonian fluids through porous media has been modified to a more general form which will describe the flow through porous media of fluids whose flow behavior can be characterized by the Herschel-Bulkley model. The model covers the flow of homogeneous fluids with a yield value and a power law flow behavior. Experiments in packed beds of sand were carried out with solutions of paraffin wax in two oils and with a crude oil from the Peace River area of Canada. The model fitted the data well. A sensitivity analysis of the fitting parameters showed that the model fit was very sensitive to errors in the flow behavior index, n , of the Herschel-Bulkley model. A comparison of the “n” values calculated from viscometer measurements and from flow measurements agreed well. A more general Reynolds number for flow through porous media, which includes a fluid yield value, was developed. The data were fitted to a Kozeny-Carman type equation using this Reynolds number. The constant in the Kozeny-Carman equation was determined for the two packed beds studied using Newtonian oils. The data could all be represented, within the experimental error, by the relationship f^* = 150/Re^*. Since the mean volume to surface diameter of the packing was determined by the measurement of its permeability to a Newtonian oil, assuming C' = 150, the new definition of the Reynolds number allows the direct use of the Kozeny-Carman equation with Herschel-Bulkley type fluids.     

Three‐Dimensional Simulation of Bubble Formation Through a Microchannel T‐Junction

Three‐dimensional simulations of bubble formation in Newtonian and non‐Newtonian fluids through a microchannel T‐junction are conducted by the volume‐of‐fluid method. For Newtonian fluids, the critical capillary number Ca for the transition of the bubble breakup mechanism is dependent on the velocity ratio between the two phases and the microchannel dimension. For the power law fluid, the bubble diameter decreases and the generation frequency increases with higher viscosity parameter K and power law index n. For a Bingham fluid, the viscous force plays a more important role in microbubble formation. Due to the yield stress τ_y, a high‐viscous region is developed in the central area of the channel and bubbles deform to a flat ellipsoid shape in this region. The bubble diameter and generation frequency are almost independent of K.     

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.     

Lower Newtonian viscosities of polystyrene

A falling coaxial cylinder viscometer was used to measure the melt flow behaviour of a commercial polystyrene with Mw 260,000. The shear stress region extended down to 0.6 × 10⁴ dynes/cm² and shear rates were as low as 3 × 10^?2 sec^?1 at 186°C. The shear rate-shear stress plots were linear at low shear stresses with slopes (differential viscosities) of 3.3 × 10⁵ poises at total shear less than 120 units and decreasing differential viscosity with higher total shear. The flow curves at relatively low total shear were initially dilatant and became pseudoplastic with increasing shear stress. The inflection point represents a Newtonian apparent viscosity, which agrees fairly well with literature values for polystyrenes of the same Mw. Newtonian apparent viscosity is characteristic of a point value of shear stress and shear rate and is not necessarily a plateau region. Observation of a Newtonian region with decreasing shear stress or shear rate does not prove that this flow regime persists unchanged to zero values of the experimental parameter. The existence and magnitude of the Newtonian apparent viscosity reflects shear history of the polymer as well as its constitution and molecular weight distribution.     

A Survey of Rheological Properties of One-Component Epoxy Adhesives

Flow characteristics of seven commercially available one-component epoxy adhesive pastes were measured using a controlled shear stress rheometer and a controlled shear rate rheometer over a temperature range from 5°C to 60°C. Combining data obtained from both controlled rate and controlled stress experiments over a wide range of shear rates, we observed Newtonian flow (shear stress proportional to shear rate) at very low shear rates, a plateau “shear thinning” region at intermediate shear rates, and a second region of linear dependence of shear stress on shear rate at high shear rates. The adhesive pastes exhibited a very broad range of rheological behavior. Two flow parameters important to adhesive application technology, the plastic viscosity and the apparent yield stress, were measured for each adhesive. The plastic viscosity ranged from 11.6 to 329.5 Pa. s; the apparent yield stress ranged from 56.2 to 413 Pa. The temperature dependence of the rheological parameters of the epoxy adhesive pastes was also determined. The results are reported as the activation energies, E_η and E_σ , of plastic viscosity and apparent yield stress, respectively. The apparent yield stress of each adhesive paste was much less sensitive to changes in temperature than was the plastic viscosity. This suggests that the processing characteristics are likely to show qualitative as well as quantitative changes with temperature.     

Interaction of nonhomogeneous shear,nonlinear viscoelasticity,and yield of a solid polymer

A constitutive equation for small strain viscoelastic response is considered in which stress relaxation. occurs faster as strain increases. The constitutive equation is of single integral type and has a psuedo- or material time function which is calculated from a strain dependent shift function. First, it is shown that such a constitutive equation can account for yield as observed in polymers for a number of different stress and strain histories. Next, the constitutive equation is used in the analysis of the problem in which a hollow cylinder is fixed at its inner surface and a moment history is applied to its outer surface. This causes the cylindrical surfaces to rotate about the central axis, thereby inducing a radial shear strain distribution. It is shown that there is a time when the material near the inner support begins to yield and a layer of large shear strain gradient begins to grow rapidly. It is also shown that the stress or strain history at a material element will generally not be one of the standard histories used to study yield.     

Energy Dissipation Rates of Newtonian and Non‐Newtonian Fluids in a Stirred Vessel

Energy dissipation rates of water and glycerol as Newtonian fluids and carboxyl methyl carbonate solution as non‐Newtonian fluid in a stirred vessel are investigated by 2D particle image velocimetry and compared. Mean velocity profiles reflect the Reynolds (Re) number similarity of two flow fields with different rheological properties, but the root mean square velocity profiles differ in rheology at the same Re‐number. Energy dissipation rates are estimated by direct calculation of fluctuating velocity gradients. The varying energy dissipation rates of Newtonian and non‐Newtonian fluids result from the difference in fluid rheology and apparent viscosity distribution which decides largely the flow pattern, circulation intensity, and rate of turbulence generation.     

低气速条件下CO_2在牛顿及非牛顿流体中气含率

实验测定了低气速下CO2气泡群在牛顿流体、剪切变稀流体及黏弹性流体中的气含率。讨论了流体的流变性、质量分数及表观气速对气含率的影响。结果表明:在3种不同性质的流体中,气含率均随表观气速的增大而增大。同时发现流体性质对气含率具有不同的影响:对于牛顿流体,表观气速较低时,质量分数对气含率影响可忽略;对于非牛顿流体,气含率随着流动指数n的减小而减小,即剪切变稀效应对气含率有负作用,而黏弹性对气含率的影响可忽略。气含率是气液传质过程设计中最重要的参数,因此研究结果为进一步研究CO2气泡群在非牛顿流体中的传质奠定了一定基础。     

流体流变性对错位六弯叶桨流场特性的影响

利用计算流体力学(CFD)的方法,以高黏牛顿流体和假塑性非牛顿流体为研究对象,对错位六弯叶桨在层流域的搅拌流场特性进行了研究。结果表明:数值计算得到的功率值与实验测量值吻合较好,搅拌雷诺数对假塑性流体搅拌流场的量纲一速度和切应变速率影响较大,因此提高转速对改变流场的速度及切应变速率分布是一个有效的办法;而流体的流变性只对假塑性流体的量纲一速度有明显影响,对切应变速率影响较小,当流变指数n<0.3时与n基本无关。当流动由层流向过渡流转变时,搅拌桨的流量准数及泵送效率有显著提高;假塑性流体的流变指数降低时,其泵送效率显著下降。研究进一步认识了错位桨在不同流体中的搅拌流场特点,为高黏假塑性流体搅拌桨的设计、应用以及开发新型搅拌桨提供了参考。     

Some qualitative and quantitative features of die swell

Upper and lower bounds for the die swell ratio are derived for all simple fluids in the presence of surface tension and under the assumptions that the flow remains viscometric up to a finite distance from the exit and that bounds on the shear stress distribution in this length exist. Both circular and plane jets are considered and the bounds so derived depend on the normal stress on the wall in the viscometric region. For Newtonian and power law fluids, this stress can be determined, a priori, from existing theories. However, for viscoelastic liquids, it is an open question at present.     

带有内外组合桨的搅拌设备内流场的数值研究

利用滑移网格法计算了以一定转速比反向旋转的内外组合桨搅拌的搅拌设备内的流场,工作介质分别选取98％甘油和1．5％(wt)CMC水溶液。通过对单桨与内外组合桨产生的流场进行对比,研究了搅拌设备内不同高度处速度、速度变化率、表观粘度及剪切速率的分布特点。结果表明：采用内外组合桨,介质为中粘牛顿流体时,在罐内主体区远离罐壁区域径向速度受到一定削弱,但在某些局部区域被增强,而对于假塑性流体径向速度总体上得到增强。采用内外组合桨可以加强轴向循环,改善搅拌设备近壁区的流动状况,且对假塑性流体流动状况的改善要优于中粘牛顿流体,另外还可以显著地提高搅拌设备内的剪切速率,同时使剪切速率的分布比较均匀。     

纤维粘弹性流体悬浮液流变性质研究

描述了纤维Oldroyd-B流体半浓悬浮液的本构方程,计算了定常剪切流动突然开始后的纤维取向和应力的发展过程,并将计算结果与其它本构方程的计算结果和实验结果进行比较,结果表明,本文的本构方程能合理地描述应力的发展过程,尤其能刻划出应力峰值后的弹性增长,这是其它本构方程所不能描述的。     

The effect of shear‐thickening on the stability of slot‐die coating

Slot‐die coating is an economical roll‐to‐roll processing technique with potential to revolutionize the fabrication of nano‐patterned thin films at high throughput. In this study, the impact of shear‐thickening of the coating fluid on the stability of slot‐die coating was investigated. For the coating fluid, a model system fumed silica nanoparticles dispersed in polypropylene glycol was chosen. These dispersions exhibit shear and extensional thickening characterized through steady shear and capillary break‐up measurements. The critical web velocity for the onset of coating defect for different flow rates was measured, while the type of coating defect was visualized using a high speed camera. For the shear thickening particle dispersions, the coating failed through the onset of a ribbing instability. The critical web velocity for the onset of coating defect was found to decrease with increasing particle concentration and increasing fluid viscosity. The minimum wet thickness was studied as a function of capillary number for the particle dispersions and compared with a series of Newtonian fluids with similar viscosities. In all cases, shear‐thickening behavior was found to stabilize coating by reducing the minimum wet coating thickness when compared against a Newtonian fluid with similar viscosity at the same capillary number. Conversely, the shear‐thinning fluids tested destabilized the coating by increasing the minimum wet thickness when compared against a Newtonian at the same capillary number. The impact of shear‐thickening on slot‐die coating was further studied by quantifying the evolution of the ribbing instability with increasing web speed and by conducting tests over a wide range of coating gaps. © 2016 American Institute of Chemical Engineers AIChE J, 62: 4536–4547, 2016     

Effects of viscosity and relaxation time on the hydrodynamics of gas–liquid systems

Effects of liquid properties on the hydrodynamics of gas–liquid systems were investigated in lab-scale bubble column (BC) and internal loop airlift (ILA). Alginate solutions, a glycerol solution and a Boger fluid were adopted to separately address the effects of viscosity and of surface tension for Newtonian fluids, and the effects of relaxation time for non-Newtonian fluid characterized by approximately constant viscosity (low shear thinning). Hydrodynamic regimes were characterized in terms of overall gas holdup, gas–liquid mass transfer coefficient, drift-flux and liquid circulation velocity. The superficial gas velocities at the transition between hydrodynamic regimes (homogenous regime–vortical-spiral regime–heterogeneous regime) as a function the liquid viscosity was characterized by a maximum. The same behavior was observed for the maximum stable gas holdup and gas–liquid mass transfer coefficient in BC. Viscosity enhances homogeneous regime stability for μ<4.25 mPa s, in BC, and μ<7.68 mPa s, in ILA. For non-Newtonian fluids the transition velocity increases with liquid elasticity. The stabilization mechanism related to the relaxation time of Boger fluids has been discussed.     

A SIMPLIFIED APPROACH TO THE PREDICTION OF PRIMARY NORMAL STRESS DIFFERENCES IN POLYMER MELTS

A relationship between the unified primary normal stress difference function and the unified viscosity function curves proposed earlier by the authors is sought based on a strain dependent single integral constitutive equation of the BKZ-type. The predictions of the equation are checked for best fit of the unified primary normal stress difference curves of low density polyethylene, high density polyethylene, polypropylene and nylon. The approach is then extended to give theoretical predictions of the unified primary normal stress difference curves for a number of other polymers whose unified viscosity curves are known. The approach provides a method to estimate the normal stress difference versus shear rate curves at any temperature through the unified curves merely from the knowledge of the melt flow index.     

Pressure drop in a split‐and‐recombine caterpillar micromixer in case of newtonian and non‐newtonian fluids

Microreactors are very promising tools for the design of future chemical processes. For example, emulsions of very narrow size distribution are obtained at much lower energy consumption than the one spent with usual processes. Micromixers play thereby an eminent role. The goal of this study is to better understand the hydrodynamic properties of a split‐and‐recombine Caterpillar micromixer (CPMM) specially with regard to handling viscoelastic fluids, a topic hardly addressed so far in the context of micromixers in general, although industrial fluids like detergent, cosmetic, or food emulsions are non‐Newtonian. Friction factor was measured in a CPMM for both Newtonian and non‐Newtonian fluids. For Newtonian fluids, the friction factor in the laminar regime is f/2 = 24/Re. The laminar regime exists up to Reynolds numbers of 15. For shear‐thinning fluids like Carbopol 940 or viscoelastic fluids like Poly Acryl Amide (PAAm) aqueous solutions, the friction factor scales identically within statistical errors up to a generalized Reynolds number of 10 and 0.01, respectively. Above that limit, there is an excess pressure drop for the viscoelastic PAAm solution. This excess pressure drop multiplies the friction factor by more than a decade over a decade of Reynolds numbers. The origin of this excess pressure drop is the high elongational flow present in the Caterpillar static mixer applied to a highly viscoelastic fluid. This result can be extended to almost all static mixers, because their flows are generally highly elongational. © 2013 American Institute of Chemical Engineers AIChE J, 59: 2679–2685, 2013