Empirical viscosity model for polymers with power‐law flow behavior

The aim of this study is the creation of an empirical model that can be used to predict the viscosity of a semicrystalline polymer melt for polymer process control. We have developed an empirical viscosity equation from both analysis and experimentation that takes into consideration the effect of temperature on both the flow behavior and the consistency index in the power law. The analysis is based on previously published literature, whereas the experimental data have been obtained from both the literature and laboratory investigations. The coefficients of the empirical model for low‐density polyethylene and polypropylene have been obtained from the experimental data derived from capillary rheometer measurements in the laboratory. This empirical model is able to produce results matching the experimental data with remarkable accuracy. © 2003 Wiley Periodicals, Inc. J Appl Polym Sci 88: 3045–3057, 2003     

Semianalytical solution for power‐law polymer solution flow in a converging annular spinneret

A semianalytical solution for a power‐law fluid flowing through a conical annulus was derived to estimate the velocity profile in the axial direction, the shear rate and the elongation rate within a spinneret during the spinning of hollow fiber membranes. The angle coefficient was introduced as a new parameter to account for the effect of radial flow and to modify the governing equation, which initially neglected the effect of radial flow. The results estimated from this semianalytical solution agreed more closely with computational fluid dynamics simulation results than those obtained from the approximate analytical solution in our previous study. By accurately predicting the velocity profile in the axial direction and the shear and elongation rates in a conical annulus, the solution derived in this study is expected to provide a reliable criterion for spinneret design to achieve a specified membrane morphology with a desired performance. © 2015 American Institute of Chemical Engineers AIChE J, 61: 3489–3499, 2015     

The influence of power‐law rheology on flow distribution in coathanger manifolds

Coathanger dies are effective in delivering uniform flow if a polymer melt; however, when the fluid flow index varies from the design values, the flow is not uniform. Although mechanisms such as die lip adjustments have been effective tools for adjusting flow profiles, the issue of a variable flow index has not been fully addressed at the design stage. An analytical solution, based on the assumptions present in the 1‐D design equation, has been developed for the flow distribution in a coathanger manifold. This solution determines the flow distribution for a power‐law fluid with a flow index n* in a manifold designed for a separate flow index n*. From this solution, a uniformity index and a critical design angle are defined. The critical design angle is the angle at which the local derivative of the uniformity index with respect to n* approaches a maximum (for n* < n) or a minimum (for n* > n) as a function of the design angle. The critical design angle is independent of n and is presented as a function of the manifold aspect ratio.     

A simple correlation for gas bubbles rising in power‐law fluids

Recently, the author (Rodrigue, 2001 a, b) proposed a generalized correlation for the steady rise of gas bubbles in uncontaminated viscous Newtonian fluids of infinite extent. It is the purpose of this note to show that this model can be modified for inelastic non‐Newtonian power‐law fluids. Using data taken from six different studies, it is shown that the modified model can predict quite nicely the bubble velocity for these non‐Newtonian inelastic fluids.     

Unified entry length for newtonian and power–law fluids in laminar pipe flow

A numerical method based on finite differencing is used for investigating the steady–state entrance region laminar flow of incompressible Newtonian and power–law fluids in a circular pipe. The Solution method is validated by comparing the results for Newtonian fluids with those reported in the literature. For power–law fluids, the entry length results are compared with other approximate solutions in the literature. On the basis of the calculated results, a generalized entry length ξ99 = 0.056 is shown to be valid for the laminar flow at Re > 200 of both Newtonian and power–law fluids with 0.75 < n < 1.5.     

Power‐law polymer solution flow in a converging annular spinneret: Analytical approximation and numerical computation

A simplified analytical solution for the flow of power‐law liquids through a conical annulus was derived to estimate the flow profile, wall shear rate, and elongation rate in the spinneret during the spinning of hollow fiber membranes. The velocity profiles and shear and elongation rates of the power‐law fluid showed good agreement with those obtained from computational fluid dynamic simulations. Although the actual spinneret is characterized by an annulus with a converging cross section, most studies to date have used a geometrical concentric annulus for the sake of simplicity. The results of the current work indicate that neglecting the converging characteristics of the actual spinneret can lead to significant underestimation of the wall shear rate. Using the equations derived in our work, we were able to predict not only the velocity profile but also the wall shear rate and the elongation rate; the influence of the spinneret design on the membrane morphology and properties were also examined. © 2011 American Institute of Chemical Engineers AIChE J, 2012     

Relative viscosity models and their application to capillary flow data of highly filled hard‐metal carbide powder compounds

The rheological behavior of highly filled polymer systems used in powder injection molding (PIM) technology strongly influences the final properties of the products. In this study, the capillary flow data of multi‐component polymer binders—based on polyethylene, paraffin, ethylene‐based copolymers, and polyethylene glycol—compounded with three various hard‐metal carbide powders were employed. The rheology of such highly filled (up to 50 vol%) multiphase systems is necessarily a complex phenomenon characterized by strain dependent, non‐Newtonian properties complicated by flow instabilities and yield. Over 15 mathematical models proposed for highly filled systems were tested, some of them calculating the maximum filler loading. Due to the complex structure of the filler (irregular shape, particle size distribution) and a multi‐component character of the binder, the applicability of these models varied with the powder‐binder systems studied. However, the particular values of maximum loadings are in good accordance with the predictions based on powder characteristics. Simple modification of Frankel‐Acrivos model to the systems containing unimodal hard‐metal carbide powders with particles of an irregular shape and broad particle size distribution gave precise agreement between experimental data and model prediction. POLYM. COMPOS., 26:29–36, 2005. © 2004 Society of Plastics Engineers.     

Modeling of three‐dimensional flow and heat transfer in polystyrene foam extrusion dies

A three‐dimensional mathematical model was developed to investigate the nonisothermal, non‐Newtonian polymer flow through the dies used in the polystyrene foam extrusion process. The model, based on the computational fluid dynamics (CFD) code, Polyflow, allowed for the shear rate and temperature dependence of the shear viscosity of the blowing agent laden polystyrene melt. The model also accounted for viscous heating. The shear viscosity of the polystyrene‐blowing agent mixture was measured experimentally at several temperatures. The model was used to calculate pressure, flow, and temperature distributions in two different dies used for industrial‐scale extrusion of polystyrene foams. The article presents a selection of computed results to illustrate the effect of die design on uniformity of flow at the die exit, the overall pressure drop in the die, relative magnitudes of pressure drop in the land section versus the rest of the die, and temperature distribution in the die. POLYM. ENG. SCI., 2008. © 2008 Society of Plastics Engineers.     

The effect of a concentration‐dependent viscosity on particle transport in a channel flow with porous walls

The transport of a dilute suspension of particles through a channel with porous walls, accounting for the concentration dependence of the viscosity, is analyzed. In particular, we study two cases of fluid permeation through the porous channel walls: (1) at a constant flux and (2) dependent on the pressure drop across the wall. We also consider the effect of mixing the suspension first compared with point injection by considering inlet concentration distributions of different widths. We find that a pessimal inlet distribution width exists that maximizes the required hydrodynamic pressure for a constant fluid influx. The effect of an external hydrodynamic pressure, to compensate for the reduced transmembrane pressure difference due to osmotic pressure, is investigated. © 2014 American Institute of Chemical Engineers AIChE J, 60: 1891–1904, 2014     

Characteristics of air–water two‐phase flow in a 3‐mm smooth tube

Two‐phase flow pattern and friction characteristics for an air–water system in a 3.17 mm smooth tube are reported in this study. The range of mass flux is between 50 and 700 kg/m²s. The experimental data show that the two‐phase friction multipliers are strongly related to the flow pattern. For a stratified‐wavy flow pattern, a mass‐flux dependence of the two‐phase multipliers is seen. For a non‐stratified flow pattern, the two‐phase frictional multipliers are comparatively independent of mass flux. Correlations of the frictional multipliers are developed for stratified and non‐stratified flow. To use the appropriate correlation in different regime, a simple criterion is proposed.     

Synthesis,characterization of polyacrylate‐g‐carbon black and its application to soap‐free waterborne coating

Polyacrylate‐g‐Carbon Black (abbrev. as gCB) was prepared by free radical polymerization of acrylate monomers on the carbon black surface, which was initiated by a redox system consisting of cerium ammonium nitrate and hydroxymethyl carbon black. gCB was ascertained by X‐ray Photoelectron Spectrometry (XPS). The optimum conditions of synthesis were studied. The stabilities of gCB dispersing in water were studied by zeta potential measurement and spectrophotometric analysis. The results showed that gCB could disperse in water better than the ungrafted carbon black. gCB could be dispersed in the soap‐free hydrosol forming a colored soap‐free water‐borne coating with satisfactory comprehensive performance. © 2001 John Wiley & Sons, Inc. J Appl Polym Sci 81: 1100–1106, 2001     

A facile dip‐coating approach to prepare SiO2/fluoropolymer coating for superhydrophobic and superoleophobic fabrics with self‐cleaning property

In this study, a facile, two‐step dip‐coating approach was reported for the fabrication of the superhydrophobic and superoleophobic cotton fabrics. It was confirmed that the superhydrophobic and superoleophobic composite thin film containing modified‐SiO₂ nanoparticles and fluoropolymer had been successfully fabricated on the cotton fabrics surface, the results demonstrated that the treated cotton fabrics showed good performances, such as superhydrophobicity and superoleophobicity, low water and oil absorption ability, self‐cleaning property and good laundering durability, so forth. The above approach can be applied to potentially advance superhydrophobic and superoleophobic fabrics materials for a variety of applications. © 2014 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2015 , 132, 41458.     

Corrosion‐resistant coating development with potential application in equipment of low‐temperature waste heat recovery

In order to improve corrosion resistance of a condensing heat exchanger, a fluoropolymer, perfluoroalkoxy alkane (PFA), fine powder in 30 wt% aqueous slurry was coated on metal coupons and a coating of high quality finish was obtained. The coating was characterized by microscopy and thickness measurements. The thickness of the coating can be controlled by the number of layers used for the application of wet spray. Hot acid bath corrosion tests showed that the coated coupon possesses the highest adhesion strength and excellent corrosion resistance (1.8–6.7 × 10^?3 mm/year), comparable to super alloys such as Inconel (1.1–26.2 × 10^?3 mm/year) and Hastelloy (0.3–19.8 × 10^?3 mm/year). A heat transfer coefficient analysis showed that across a heat transfer metal tube coated with PFA, the heat transfer resistance of the gas side film is one order of magnitude larger than the resistance from the coated layer. The developed coating could provide an alternative material solution for condensing heat exchangers used in low‐grade waste heat recovery.     

Thermal radiation effect on unsteady MHD free convection flow past a vertical plate with temperature‐dependent viscosity

This article investigates the influence of radiation and temperature‐dependent viscosity on the problem of unsteady MHD flow and heat transfer of an electrically conducting fluid past an infinite vertical porous plate taking into account the effect of viscous dissipation. The governing equations are converted into a system of nonlinear ordinary differential equations via a local similarity parameter which is taken as a function of time. The resulting system of coupled nonlinear ordinary differential equations is solved numerically using the fourth order Runge–Kutta integration scheme with the shooting method. The numerical results for the velocity and the temperature are displayed graphically showing the effects of various parameters. The results show that increasing the Eckert number and decreasing the viscosity of air leads to a rise in the velocity, while increasing in the magnetic or the radiation parameters is associated with a decrease in the velocity. Also, an increase in the Eckert number leads to an increase in the temperature, whereas an increase in radiation parameter leads to a decrease in the temperature.     

Numerical simulation and experimental validation of liquid‐film‐flow characteristics in dip coating for non‐Newtonian fluids

The film‐flow problem in dip coating is simulated numerically for non‐Newtonian fluids based on Carreau–Yasuda (CY) and Herschel–Bulkley (HB) constitutive equations, with particular focus on coating‐film‐thickening phenomena and on the evolution of free surface and flow field under different sets of conditions. Finite element method (FEM) is combined with remeshing technique using a commercial code (Polyflow). Numerical predictions of the final film thickness and free surface for HB and CY fluids are successfully compared with experiments under the given conditions. Results show that the combination of FEM‐remeshing technique could be useful for dip‐coating design and optimization. Effects of coating fluid properties and withdrawal speed on film thickening and free surface shape and location are also discussed. Flow fields under different conditions are presented to analyze the evolution of the entire flow field and flow characteristics in detail. POLYM. ENG. SCI. 56:1070–1078, 2016. © 2016 Society of Plastics Engineers