Mechanics of steady flow in coextrusion fiber spinning

The steady flow of isothermal bicomponent coextrusion fiber spinning has been investigated. A model has been chosen in which a Newtonian fluid and a Phan-Thien/Tanner (PTT) fluid were considered to be the core and the skin layer, respectively. This model was adopted to study the effect on spinline velocity of an interaction between two fluids with quite different extensional rheology. The effects of the hoop stress, gravity, inertia, and surface and interfacial tensions were disregarded. Only viscous and viscoelastic forces were considered. A uniaxial extension was also assumed as the radius variation in the axial direction is small. The Newtonian fluid has been considered prone to fluctuate during melt processing while the viscoelastic skin layer has a stabilizing effect. The velocity profile was affected by the choice of two characteristic parameters: extensional and shear-thinning parameters, as well as the viscoelastic skin flow rate ratio. Both shear-thinning and extensional parameters play important roles in melt flow. The results show that as the draw ratio increases, the system is dominated by the extensional parameters, whereas slow drawing is dominated by shearing, in spite of the thin viscoelastic skin.     

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.     

Mathematical study and simulation on stenosed carotid arteries with the help of a two-phase blood flow model

The present study is focused on a medical problem called stenosed carotid artery. The problem is formulated with the help of a two-phase blood flow model. The non-Newtonian nature of blood is considered that hold power law. Physical quantities were expressed in tensorial form. Analytical and numerical methods are used to solve equations under given boundary conditions. The effects of various parameters on blood flow like stenosis size, flow flux, resistance, haematocrit, pressure drop, etc. were studied and shown through various graphs. Parameter $k$, which ensures that the fluid is Newtonian or non-Newtonian; its impact on pressure drop; resistance to flow; and flow flux were obtained during the disease and presented through the graph. A relationship between pressure drop and haematocrit was obtained, which was helpful to predict fluctuation in blood flow during stenosis. We have also given a medical use for this model with the help of pathological data. We also analyzed steady and laminar flow in a carotid artery for different heights of stenosis. The study of various physiological parameters has been performed on the basis of blockage percentage and concentration of haematocrit. The nature of the red blood corpuscle (RBC) phase is considered liquid packets in a semi-permeable membrane, which makes this model close to reality.     

Flow pattern variations of viscoelastic fluid flows in three‐dimensional branching channel

Transport phenomena in three‐dimensional branching channel are important because of their relevance in polymer processing. In this article, an experimental study on viscoelastic flow in a three‐dimensional cylindrical branching channel is carried out to investigate variations of flow pattern. Flow visualization in representative symmetric planes is made both for the viscoelastic fluid and Newtonian flow. From the results of the present investigation, the flow field in the three‐dimensional cylindrical branching channel is clarified within the range of laminar flow. It is confirmed that corner vortex, shedding vortex, and secondary vortex flow are all obviously changed with the fluid concentration and the Reynolds number, which are much more three‐dimensional and complex than the Newtonian fluid, and the flow pattern of the viscoelastic fliud flow largely depends on the Reynolds number and fluid concentration. Even for the viscoelastic flow at the low Reynolds number, shedding vortex and secondary vortex and complex three‐dimensional flow occur in the cylinder. The flow field is not symmetric space for the viscoelastic flow and however is fairly symmetric for the Newtonian fluid. The above reasons explain why the flow deflection happens even at the low Reynolds number flow. POLYM. ENG. SCI., 2010. © 2009 Society of Plastics Engineers     

Numerical simulation of entry and exit flows in slit dies

A general-purpose finite element program has been used to simulate the flow of Newtonian, power-law, and viscoelastic fluids in the entry and exit regions of a slit die. It was found that shear-thinning increases the entrance correction while it decreases the exit correction. Shear-thinning reduces the size of the small corner vortex that forms in the entry flow of a Newtonian fluid. The swelling ratio had a value of 1.196 for Newtonian fluids and decreased as the value of the power-law index decreased. Viscoelastic calculations were performed using the Criminale-Ericksen-Filbey (CEF) constitutive equation. Convergence of the iterative scheme was unattainable for Deborah numbers above 1.0. The results showed a decrease of the entrance correction and an increase of the exit correction with elasticity. Extrudate swell first decreased slightly and further increased with the Deborah number.     

SUSPENSION MODEL FOR BLOOD FLOW THROUGH ARTERIAL CATHETERIZATION

This article is concerned with the analysis of a dusty model for the axi-symmetric flow of blood through coaxial tubes such that the outer tube with an axially nonsymmetreic but radially symmetric mild stenosis and the inner tube have a balloon (assumed that is axi-symmetric in nature). The mild stenosis approximation is used to solve the problem. To estimate the effect of the stenosis shape, a suitable geometry has been considered such that the axial shape of the stenosis can be changed easily just by varying a parameter (referred to as the shape parameter). The model is also employed to study the effect of the volume fraction density of the particles C, the maximum height attained by the balloon δ₂, the radius of the inner tube, which keeps the balloon in position κ, and the axial displacement of the balloon x _d . Flow parameters such as velocity, the resistance to flow (the resistance impedance), the wall shear stress distribution in the stenotic region and its magnitude at the maximum height of the stenosis (stenosis throat) have been computed numerically for different shape parameters n, C, δ₂, κ, and x _d . It is shown that the resistance to flow decreases with increasing values of the parameter determining the stenosis shape n and the axial displacement of the balloon x _d , while the resistance to flow increases with the volume fraction density of the particles C, the radius of the inner tube, which keeps the balloon in position κ, and the maximum height attained by the balloon δ₂. The magnitudes of the resistance to flow are higher in the case of a dusty fluid model than in the case of a Newtonian fluid model. The wall shear stress distribution in the stenotic region and its magnitude at the maximum height of the stenosis possess a character similar to the resistance to flow with respect to C, δ₂, κ, and x _d . Finally, the effect of the volume fraction density of the particles C, δ₂, and x _d on the velocity profile are discussed.     

THE NORMAL FORCE EXERTED BY A SECOND ORDER FLUID ON A SMALL SPHERE TOUCHING A PLANE

The hydrodynamic force experienced by a small solid sphere of radius a_p resting on a solid plane wall in an axisymmetric stagnation creeping flow of a viscoelastic fluid is computed at order one in Weissenberg number. The solution utilises the method of the reciprocal theorem of Lorentz and the corresponding solution of the Newtonian problem to get the normal force without the need of solving for the velocity field. The resulting expression is a volume integral which has to be solved numerically. The result obtained shows that elastic effect of the constant viscosity second order fluid causes a reduction in the normal force beyond that of a Newtonian fluid of the same viscosity.     

基于四参数流变模式的旋流分离流场特性分析

利用四参数流变模式描述钻井液的非牛顿流动特性,结合雷诺应力模型(RSM),研究钻井液非牛顿性对旋流分离流场的影响. 得到3种流体介质的速度场和压力场分布规律. 结果表明,流场模拟结果与实验结果吻合,模拟结果可靠. 虽然3种流体流场分布趋势相同,但同一位置非牛顿流体的静压力(4.02和3.77 MPa)和轴向速度(11.9和12.4 m/s)大于牛顿流体(3.22 MPa和11.7 m/s),切向速度(42.5和39.7 m/s)小于牛顿流体(47.5 m/s);四参数流体的静压力(3.77 MPa)和压力降(4.51 MPa)小于幂律流体(4.02和4.79 MPa),能量损失降低0.28 MPa,四参数流体的切向速度比幂律流体小2.8 m/s,且其零轴速包络面更靠近器壁,不利于流体介质分离.     

Blade-coating of a viscoelastic fluid

A theory is presented which describes the dynamics of blade-coating of a viscoelstic fluid onto a moving sheet. The method begins with the usual “lubrication” approximation, and develops the solution as a perturbation about the Newtonian case. Viscoelasticity is described by an empirical constitutive equation which shows non-Newtonian viscosity and finite normal stress behavior consistent with typical observations of polymeric fluids. Theoretical results indicate a small increase in coating thickness due to departure from Newtonian behavior, and a significant decrease in the magnitude of the pressure developed under the blade. Consequently, the blade loading can be reduced significantly by viscoelastic effects. The results for the loading may be an artifact of the specific constitutive model, since it can be shown that some viscoelastic fluids, specifically an “elastic Newtonian” fluid, would exhibit increased loading relative to the inelastic Newtonian case.     

Flow of a Newtonian fluid and a yield stress fluid around a plate inclined at 45° in interaction with a wall

This experimental and numerical study focuses on the determination of drag and lifts forces acting on inclined plate at 45° placed near a wall in a uniform flow of Newtonian and yield stress fluid. The inertia of the fluid is considered negligible. The influences of yield stress, shear thinning, and the distance between the plate and the wall were examined precisely. It is shown that the drag and lift coefficients decrease as the Oldroyd number increases and increase as the gap decreases. The unyielded zones around the plate were also determined. Their surfaces increase with the Oldroyd number. When the yield stress is low, the decrease of the shear thinning index n tends to decrease these unyielded zones. For the experimental part, a Carbopol gel was used as a fluid model. Experimental measurements were compared with numerical and published results, particularly in the plasticity context developed for soil mechanics. Differences are discussed in terms of the influence of elasticity and plasticity.     

A theory of roll coating of viscous and viscoelastic fluids

A theory for roll coating of a fluid onto a moving sheet is developed utilizing the usual “lubrication approximations.” The effects of fluid and operating parameters on coating thickness and pressure distribution are determined for a Newtonian fluid, and for a purely viscous non-Newtonian fluid obeying the Power Law. The results for these cases are obtained analytically, and are rather straightforward. A viscoelastic fluid is considered, of a type which shows typical non-Newtonian shear behavior observed in polymer melts and solutions and which also exhibits normal stress behavior. Analytical solutions are not possible, but a perturbation method, using a viscoelastic perturbation parameter related to a Deborah number, yields an approximate solution. Only terms to first order in the perturbation parameter are given. Subject to that degree of approximation, the following conclusions are drawn:

• 1 Non-Newtonian shear behavior reduces the pressure distribution, and increases the coating thickness.
• 1 Elasticity of the type usually observed in polymer solutions makes only a minor contribution to the roll-separating (load-carrying) force. The contribution is positive, but smaller than the corresponding negative contribution due to the non-Newtonian shear effects.
• 1 An increase in load-carrying capacity would require a different viscoelastic fluid than the type considered here—one that is essentially Newtonian in shear but, independently, capable of developing significant normal stresses.

     

特型螺带桨叶在高粘弹性和非弹性流体中的搅拌功率

本文研究了层流区域有较大叶片截面积的特型双螺带──锚桨叶在高粘弹性和非弹性流体中的搅拌功率，测定了Ｋ_ｐ和Ｋ_ｓ，采用广义二阶流体本构方程导出搅拌功率计算式参数ｆ_ｓ和Ｆ_（１ａｃ）由实验数据确定。该式适用于牛顿型流体、假塑性和粘弹性流体的功率消耗计算。     

影响连续油管摩阻系数及压降因素分析

连续油管作业技术在油田得到广泛的应用,但是钻井液在油管内的摩阻系数的研究比较复杂,尤其是在卷筒上的螺旋段。现有的经验公式有些和工程实际出入较大,有些只适用于某一情况。因此在分析前人的基础上得到了连续油管直管段,螺旋段摩阻系数和影响因素。在牛顿流体方面研究了曲率对摩阻系数的影响,另外发现在雷诺数较高情况下粗糙度对其影响不容忽略;在非牛顿流体方面研究了曲率和流性指数对摩阻系数的影响。根据摩阻计算模型研究了压降与下入深度的关系。分析结果表明,由于二次流的影响,螺旋段的摩阻系数比直管段的要大,所以,在相同的条件下,螺旋段的压降要比直管段的压降大,流性指数增大1倍,摩阻系数增大近1.5倍。     

Finite difference solution for flow from a slit die

A finite difference solution for an isothermal viscoelastic liquid flowing through a film forming die is investigated. The fluid is described by a Maxwell model in which the time derivative has been replaced by an Oldroyd's convective derivative and the numerical technique used combines features of the Solution Algorithm (SOLA), Simplified Marker and Cell method (SMAC), and SOLASMAC. The numerical scheme was tested with a Newtonian fluid and high density polyethylene (HDPE). Two slit dies with gap-to-length ratios 4 and 16 were used. In the two cases, die swell has occurred: A maximum of 4.5% swell was observed for the Newtonian fluid, while up to 77% swell was attained with HDPE. The simulated flow behavior of HDPE exhibited high amplitude oscillations at dimensionless time greater than 0.18. These oscillations are thought to be related to the nature of sheet flow, which can be unstable. This study shows that with some improvement the finite difference method can be used for studying the extrusion of polymer through slit and capillary dies.     

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。     

The application of an integral type constitutive equation to numerical flow analyses of viscoelastic fluid in unsteady flow

The applicability of the Wagner model to numerical flow analyses of the injection molding process is investigated under the following approximations: the strain and stress histories of the molten polymer before the injection is negligible, and the flow field in a mold cavity is treated as Hele‐Shaw flow. A comparison between the results for simple step‐strain‐rate flow calculated with the Wagner model and that calculated with the Leonov model suggests that the Wagner model is superior to the Leonov model for unsteady flow because of its stability and accuracy. Therefore, numerical flow analysis software of a viscoelastic fluid in the injection molding process is developed using the Wagner model. For the analysis, the velocity profile of a Newtonian fluid is used instead of that obtained through iterative calculation. The validity of the developed program is confirmed through a comparison of the results of the computation for two simple flow velocity histories with the analytical results from the Wagner model. Furthermore, the computation time of the developed software is only 1.4 times greater than that of the previous numerical flow analysis of a viscous fluid.     

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     

Thermal Instability of Oldroydian Viscoelastic Fluid with Suspended Particles in Hydromagnetics in Porous Medium

The effect of suspended particles on the thermal instability of an Oldroydian viscoelastic fluid in hydromagnetics in porous medium is considered. The magnetic field, suspended particles, viscoelasticity, and porous medium effects create oscillatory modes in the system which did not exist previously. For stationary convection, the viscoelastic fluid behaves like a Newtonian fluid and the magnetic field has a stabilizing effect, whereas medium-permeability, suspended particles have destabilizing effects on the system. The sufficient conditions for the avoidance of overstability are obtained, and these also hold good for the case of a Maxwellian viscoelastic fluid.     

FURTHER RESULTS ON HYDROMAGNETIC BOUNDARY-LAYER FLOW OF A NON-NEWTONIAN POWER-LAW FLUID OVER A CONTINUOUSLY MOVING SURFACE WITH SUCTION

The flow of a non-Newtonian, power-law conducting fluid under the effect of a constant transverse magnetic field is considered. The flow is produced by a plate moving with constant velocity in a calm fluid. The plate is porous and fluid can either be sucked or injected through it. The boundary layer equations are transformed into a nondimensional form and are solved with a finite difference method. Part of this problem has been investigated in the past but only for suction and pseudo-plastic fluids. However, all flows of the present work reach an asymptotic state and exact analytical solutions exist for Newtonian fluids. In the present work we extend the investigation to both pseudo-plastic Newtonian and dilatant fluids in both suction and injection cases.     

Stability of Newtonian-PTT coextrusion fiber spinning

Linear stability analysis has been applied to a coextrusion fiber spinning flow that consists of a Newtonian fluid as a core layer and a Phan-Thien/Tanner (PTT) fluid as a skin layer. These two chosen fluids show entirely different rheological behaviors. The stability of this coextrusion system was affected by the choice of three characteristic parameters: the skin layer fraction (f), the extensional parameter (ϵ), and the shear thinning parameter (ξ) in the Phan-Thien/Tanner model. The linear stability results indicate that the viscoelastic skin layer (PTT fluid) has a stabilizing effect that delays the onset of draw resonance. Under fixed compositions (f is fixed), the stability envelopes changed from upturned curves to flattened ones as extensional force dominated the system. The neutral stable curves closed to the horizontal line at a critical draw ratio of around 20, showing similar behavior to a Newtonian fluid where the system has a very high Deborah number or it is dominated by shear thinning effects.