Characterization of viscoelastic fluid flow in a periodically driven cavity: Flow structure,frequency response,and phase lag

Transport phenomena in periodically driven cavities are important because of their relevance in polymer processing and microfluidics. The transient periodic flow of viscoelastic fluids in a cuboidal cavity, with periodic motion of top plate, was studied in this work. Flow with a characteristic time scale was achieved through the simple harmonic motion of the top plate. The flow in the cavity was characterized by measuring planar velocity fields using particle image velocimetry (PIV). Temporal variation of velocity except at central vertical plane showed predominance of the plate frequency. The temporal point variations, though seemingly similar to those for Newtonian and purely viscous non‐Newtonian fluids, led to rich varieties of spatial flow structures in case of the viscoelastic fluids. The overall flow behavior was characterized using spatial variations, phase trajectories, and streamline patterns. The transition from low Reynolds number steady‐lid driven type flow to complex vortical patterned flow was observed during a cycle of periodic motion of viscoelastic fluids. The effects of elasticity and inertia on the flow fields were analyzed. Computational fluid dynamics simulations with purely viscous shear thinning fluid (power law) and Newtonian fluid showed significant differences with experimental measurements on viscoelastic fluids. POLYM. ENG. SCI., 2008. © 2008 Society of Plastics Engineers     

Flow of a viscoelastic shear-thinning fluid between two concentric rotating spheres

The flow of a viscoelastic fluid, which is simulated by a Criminale-Ericksen-Filbey model, between two concentric rotating spheres is analyzed theoretically. This problem has wide applications in practice. The assessment of the performance of a polymerization reactor, for example, requires knowledge about the rheological properties of the reacting fluids and flow patterns around agitators. We show that the shear-thinning effects of both the viscosity and the elasticity of a fluid may lead to double-vortex flows. The origin of these vortices are discussed, and the effect of the relative sizes of the inner and the outer spheres on the vortex flows is investigated. The influence of the elasticity on the torque required to rotate the spheres is also evaluated.     

Mixing of viscoelastic fluids with helical-ribbon agitators. I — Mixing time and flow patterns

Batch mixing of viscous fluids with helical-ribbon agitators in 2.4 liter and 13 liter vessels has been studied for agitator speeds up to 200 RPM. Seven different agitators of different dimensions were employed in this work. Mixing times were measured using a decoloration technique and circulation times were determined by the tracer bead method. In addition, velocity profiles were obtained from streak photographs using selective illumination of the vessel and PVC powder as tracer particles. It was found that the mixing times of Newtonian fluids, which agreed with previously published data, were considerably (3 to 7 times) shorter than those of the viscoelastic fluids. The mixing time was strongly affected by the fluids' elasticity; increasing as the fluid elasticity increased. The velocity profiles were qualitatively similar for all the fluids but showed decreased axial circulation and increased circumferential flow as fluid elasticity increased. However, mixing is not only a function of the axial circulation (impeller pumping rate) but also is a function of the perturbations superimposed on the main flow. A simple, first approximation model based on the impeller geometry and flow patterns is proposed to correlate the circulation capacity and mixing time data for the various geometries studied.     

聚合物溶解槽内双搅拌器流场特性的数值模拟

搅拌设备是目前海上油田实施聚合物驱油的配注系统的关键设备之一。利用计算流体力学方法对聚合物溶解过程采用翼型上推式搅拌器KCXU和锚式搅拌器MS的内外3种组合槽内流场进行了数值模拟,获得了搅拌器槽内的流场特性、循环流量及搅拌器的功率消耗。结果表明:在第1种混合状态时,KCXU搅拌器与转动的MS搅拌器组合时的流场变得更为复杂、无序。在第2,3种混合状态时,KCXU搅拌器与正转的MS搅拌器的组合形成的流场速度较大,加强了KCXU搅拌器的流动范围,并,且形成了最大的循环流量,其功率居中。     

Power consumption scale-up in agitating non-newtonian fluids

A method for the determination of power consumption of industrial agitators in non-Newtonian fluids on the basis of measurements on a model device is presented. The applicability of this method for purely viscous, time dependent and viscoelastic fluids is discussed. The method was tested experimentally using agitators of two different sizes and results of measurements confirmed the applicability of the present method for engineering calculations.     

Mixing in the transition flow regime with helical ribbon agitators

The effects of the non-Newtonian properties on the effective deformation rate, mixing and circulation times and flow behaviour have been investigated in the transition flow regime of mixing systems. Based on the equivalent Couette flow, three models are proposed and are shown to predict similar and drastic increases of the effective deformation rate with the impeller rotational speed in the transition regime. The predictions are shown to fit very well data obtained for various non-Newtonian fluids mixed with helical ribbon agitators, and with literature data for anchor, blade turbine and flat disc agitators. The elasticity along with shear-thinning properties appear to have slight effects on the dimensionless mixing and circulation times in the transition regime, whereas their effects in the laminar regime are quite drastic, as reported by others.     

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.     

A new expression of the Ks factor for helical ribbon agitators

The purpose of this note is to present a new model that is able to predict an effective shear rate in a vessel equipped with helical ribbon agitators, when mixing shear‐thinning fluids. This model is based on well established results obtained for non‐Newtonian flow in cylindrical ducts.     

Elongational,hysteresis, and oscillatory flows of complex fluids

The simple model proposed earlier to describe te rheological properties of complex fluids is used to calculate (a) the extensional viscosity, (b) the hysteresis loops, and (c) the complex viscosity. It has been found that the rheological properties predicted by the model agree with experimental observations. It is shown that for some viscoelastic fluids the extensional viscosity is always finite and for some other fluids the extensional viscosity tends t infinity at finite extensional rate. In the latter case, steady flow is not attainable. The shape of the hysteresis loops depends on the maximum shear-rate. It also depends on the material properties. In a small amplitude oscillatory flow, our model reduces t a linear viscoelastic fluid.     

非牛顿流体搅拌流场的数值模拟研究进展

对非牛顿流体搅拌流场数值模拟过程中的控制方程、旋转桨叶的处理以及数值计算方法三个方面进行了综合论述。阐述了广义牛顿流体模型形式简单、计算量低,在非牛顿流体搅拌流场数值模拟过程中应用广泛;黏弹性流体本构方程具有高度的非线性,采用计算流体力学(CFD)方法对其搅拌流场进行数值模拟难度较高,目前仍处于起步阶段;通过合理简化黏弹性流体本构方程以及采用恰当的数值离散方法,有助于在黏弹性流体的搅拌流场数值模拟中取得进展。     

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。     

黏弹性表面活性剂压裂液的研究与应用进展

黏弹性表面活性剂压裂液是以黏弹性表面活性剂为主剂的清洁压裂液。黏弹性表面活性剂压裂液体系具有破胶后无残渣、携砂性好、滤失控制性能好等特点,但随着对环保问题的日益重视及钻井深度的不断增加,丰富黏弹性表面活性剂压裂液体系迫在眉睫。本文介绍了黏弹性表面活性剂压裂液的发展和应用。根据压裂液配方不同,将其分为常规黏弹性表面活性剂压裂液和非常规新型黏弹性表面活性剂压裂液,总结了不同种类的黏弹性表面活性剂压裂液的组成、耐温耐剪切等性能及应用情况。分析表明,降低成本、研制简单的配制工艺是常规黏弹性表面活性剂压裂液的主要发展方向;在油田进行大规模实际应用及得到更完善的体系是非常规新型黏弹性表面活性剂压裂液的主要发展方向。     

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     

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.     

Viscoelastic characterization of semiconducting dodecylbenzenesulfonic acid doped polyaniline electrorheological suspensions

Dodecylbenzenesulfonic acid (DBSA)‐doped polyaniline particles were synthesized via emulsion polymerization, and electrorheological (ER) fluids were prepared by dispersing the synthesized polyaniline particles in silicone oil. The viscoelastic properties of DBSA‐doped polyaniline/silicone oil ER systems were examined using a vertical oscillation rheometer (VOR), which is designed for the rheological measurement of ER fluids, with a high voltage generator. Viscoelastic data obtained from the VOR were compared with those obtained from a commercial Physica rotational rheometer. The data from VOR were quite reliable in a broad range of both strain and frequency. © 2000 John Wiley & Sons, Inc. J Appl Polym Sci 79: 108–114, 2001     

筒式搅拌器及其开发

介绍了实用新型专利——筒式搅拌器的结构和设计原理。筒式搅拌器主要有筒体和内弯叶片组成,搅拌时能同时产生强大的径向流和轴向流,具有较大的排液量和循环流量,混合效果极强。筒式搅拌叶轮的各尺寸设计取决于液体性质、混合要求、容器直径和转速等因素。     

Numerical simulation of the flow in an extensional flow mixer. Effect of fluid elasticity on the flow

We discuss the viscoelastic flow of the matrix fluid in an Extensional Flow Mixer (EFM) obtained by a numerical simulation. The effect of the fluid viscoelasticity on the flow state in an EFM was considered by the comparison of the flow states of the purely viscous fluid and the viscoelastic fluid. The mixing performance of the EFM is also considered. The Phan‐Thien Tanner model was used as the constitutive equation of the viscoelastic fluid and the Carreau model was used as that of the purely viscous fluid. Results obtained are as follows: (1) Stagnation flows occur in the converging‐diverging plates (c‐d plates) in the case of viscoelastic fluid. The size of stagnation flow region becomes large when the fluid has a strain‐thickening elongational viscosity. (2) The absolute value of the extensional strain and the pressure drop in the c‐d region increase with fluid elasticity. Meanwhile, the residence time in the c‐d region decreases with that. (3) There is no stagnation region in the c‐d plates for a purely viscous fluid. The stagnation flow has an effect on the estimation value of EFM's performance. The prediction by the purely viscous fluid is not useful for the flow in an EFM because of extremely low accuracy.     

最大叶片式桨在假塑性流体中的搅拌流场模拟

为研究最大叶片式桨在高黏假塑性流体中的搅拌流动行为,以黄原胶溶液为研究体系,采用计算流体力学方法重点研究了釜内流体的功耗特性、速率分布、剪切速率、表观黏度分布和总体流动状况。结果表明:最大叶片式桨具有与大多数径流桨相似的"双循环"流型结构,且预测的功耗特性与实验数据一致性良好。最大叶片式桨适用于高黏假塑性流体的混合,而对于高黏牛顿流体的混合则效果不佳。釜内的剪切速率分布较宽泛,且受转速影响较大。转速可作为该桨改善黄原胶体系混合效率的重要参数之一。     

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。     

Multiscale fluid transport theory for swelling biopolymers

Fluid flow through a (bio) polymeric matrix has multiscale characteristics and is affected by the relaxation of surrounding polymers. Models developed in the past were either single scale (Polymer (1982) 23 (4) 529; Chemical Engineering Science (1992) 47 (12) 3037) or were limited to systems with a short memory (Achanta, 1995; Moisture transport in shrinking gels during drying, Ph.D. thesis, Purdue University, West Lafayette, IN). To address these limitations, we use the generalized Darcy's law equations of Singh (Effect of viscoelastic relaxation on fluid and species transport in biopolymeric materials, Ph.D. thesis) and the mass balance equations of Bennethum and Cushman (International Journal of Engineering Science (1996) 34 (2) 125) to develop a multiscale fluid transport model. The effect of viscoelastic relaxation of solid polymers on the flow of vicinal (adsorbed) fluid is considered at the mesoscale. At the macroscale two bulk fluids are incorporated, one of which is identical to the vicinal fluid. The mass balance equations for the vicinal fluid and its bulk counterpart are coupled via source/sink terms. The resulting fluid transport equation includes a novel integral term related to viscoelastic properties of the biopolymeric matrix. This term incorporates viscoelastic effects with both short and long memory. The model can describe both Darcian (Fickian) and non-Darcian (non-Fickian) modes of fluid transport. The model suggests fluid transport is Darcian in the rubbery and glassy states when the biopolymers are sufficiently far from the glass transition region. In the proximity of glass transition the flow of fluids is anomalous or non-Darcian. These predictions are in agreement with the experimental observations of Kim et al. (Chemical Engineering Science (1996) 51 (21) 4827). In spite of its multiscale characteristics, the resulting transport equation is simple and can be easily solved. The experimental parameters needed to solve the equation are the effective diffusivity, a sorption or drying curve and viscoelastic properties of the material.