Polymer Flow Research Articles

Recent developments on multiscale simulations for rheology and complex flow of polymers

AbstractThis review summarized the multiscale simulation (MSS) methods for polymeric liquids. Since polymeric liquids have multiscale characteristics of monomeric, mesoscopic, and macroscopic flow scales, MSSs that relate different hierarchical levels are adequate to reproduce flow properties accurately. Our review includes pioneering studies to the most advanced MSS studies on rheology predictions and flow simulations of polymeric liquids. We discuss two major types of MSS methods: the bottom-up and model-embedded MSS methods. The former method mainly connects all-atom molecular dynamics models and mesoscopic models to predict rheological properties. In contrast, the latter method, where a microscopic or mesoscopic model is embedded in a macroscopic computational domain, is designed to predict macroscopic flow properties. Finally, we also discuss MSS methods using machine learning techniques. Graphical abstract

A Relaxation Scheme for the Simulation of Two‐Phase Flows With Inaccessible Pore Volume in Polymer Flooding

ABSTRACTThe simulation of polymer injection in a reservoir is of paramount importance in enhanced oil recovery. Despite decades of research, the computation of polymer flows in porous media remains a challenging task. The main difficulty lies in the necessity to take into account the effect of inaccessible pore volumes (IPV), for which standard closure laws give rise to a weakly hyperbolic or even non‐hyperbolic system. In the latter case, exponential instabilities may appear at the continuous level, which must be addressed at the discrete level so as to prevent a premature stop of the numerical simulations. The notion of IPV was introduced by engineers in order to account for the following observation: when a polymer solution is injected into an initial core saturated with water, the breakthrough of the polymer at the exit occurs before that of the water in which it is injected. It seems that due to their large size, the polymer molecules cannot insinuate themselves into all pores as well as water. Having less volume to flood, the polymer molecules see their speed increased, hence the ad hoc acceleration factor associated with the polymer. In this work, we propose a relaxation method that guarantees some practical robustness for all IPV laws. This is achieved by replacing the original system by a relaxation model which is always hyperbolic. The designed relaxation model involves two parameters which enable us not only to adjust the correct amount of numerical dissipation, but also to ensure positivity for some critical quantities such as water saturation and polymer concentration. Extensive numerical tests are performed in order to compare the relaxation scheme to the more classical upwind scheme for several IPV laws.

An investigation of the behaviour of polymer fluids in the American Petroleum Institute filter press

The American Petroleum Institute (API) filter press test has been used for decades in the construction industry as part of the quality control regime for bentonite-based excavation support fluids. The industry has carried over the use of this test to polymer fluids despite the lack of published evidence of its suitability for these fluids and the very different mechanisms by which polymer fluids and bentonite slurries achieve excavation support. This paper presents the first systematic investigation of this issue through a combination of laboratory testing and theoretical analysis. The investigation demonstrates the very different behaviours of bentonite slurries and polymer fluids. In contrast to the results for bentonite slurries, API filter press results for polymers are shown to be highly sensitive to the filter paper used. In particular, repeatability testing revealed a substantial variation in the polymer fluid loss rates attributable to three primary factors: (a) the filter paper pore size; (b) filter paper damage resulting from the applied test pressure; (c) apparent ‘clogging’ of the filter paper pore space. Furthermore, the study demonstrates the poor repeatability of the API filter press test for polymer fluids even when filter papers of the same type are used. Interestingly, analysis of polymer flow with respect to filter paper pore size and the applied pressure showed that the filter papers were behaving as porous media rather than a simple bundle of capillaries; their behaviour could not be modelled using a simple capillary bundle model. Importantly, this finding shows that the filter press may provide a rapid method of assessing the apparent viscosity of polymer fluids in porous media at high shear rates – data that cannot be obtained by rotational viscometry, and would otherwise require resort to permeameter testing of coarse soils. The investigation demonstrates that the filter press test is not useful for the on-site quality control of polymer fluids but, given the theory presented in the paper, it can be a useful laboratory tool that provides valuable insight into polymer fluid flow behaviour in soils of high hydraulic conductivity, the most challenging soils for polymer fluid support.

Characteristics of shear stress fluctuations in polymer solutions and their relation to turbulent structures in channel flows

In this study, the wall shear stress in the channel flow of polyacrylamide polymers was investigated through electrochemical experiments, and the effects of the polymer concentration were evaluated at different Reynolds numbers. The objective was to explore the relationship between the changes in the drag reduction and near-wall turbulence structure induced by the polymer. The experiments were conducted using polymer concentrations of 0, 20, 50, 100, and 150 ppm, and a drag reduction of approximately 23% was achieved at a bulk Reynolds number of Reb = 18 750. In the electrochemical method, the working electrode was arranged spanwise, and simultaneous measurements were performed for eight electrodes to discuss the scale of the near-wall low-speed streaks and burst events. A comprehensive analysis of the correlation of the wall shear stress in the streamwise direction and the cross-spectrum of two points in the spanwise direction revealed that large streamwise and spanwise scales of near-wall low-speed streaks were generated at high polymer concentrations. Furthermore, the results obtained using the variable interval time averaging technique indicated that polymer incorporation suppressed the wall shear stress fluctuations and weakened both the intensity and frequency of the bursting events.

Two‐phase flows simulations in a space‐time framework for injection molding applications: Comparison with experimental results

AbstractHigh‐resolution numerical simulations of the injection molding process are crucial for precise process and part behavior prediction and tool fabrication. However, the complex flow behavior with high shear rates, rapid cooling as well as the nonlinear material properties post many challenges, and efficient high‐resolution numerical analysis is still subject to research. This study presents a simplified numerical description of the polymer flow and cooling during the injection phase, aiming for efficient and yet accurate simulations of the process. The in‐house finite‐element solver XNS is used to simulate the polymer and air flows, as a two‐phase flow, using the level‐set method. The injected polymer is characterized as a shear‐thinning flow using the non‐Newtonian Cross‐Williams‐Landel‐Ferry rheology model. To reduce the computational time, other polymer model effects such as a precise crystallization kinetics model during the injection phase have been neglected as a result of the findings of a previous study. Heading towards more efficient computations, we use a space‐time discretization, which has a higher convergence rate than commonly used time discretizations and can allow future mesh refinement in time, particularly convenient for our application. The results of the simulation are compared to the propagation of the flow front in an injection molding process of a plate part. The flow front is traced in‐situ by three aligned infrared sensors that detect the temperature increase from the mold wall. The time of flow front propagation between two sensors is in good agreement with experimental results. The peak temperature is calculated lower as compared to the experiment; however the temperature gradients are in good agreement validating the numerical model presented here.

Multiphysics modeling and simulation of monolayer flow and die swelling in industrial tube extrusion process

AbstractIn a regular extrusion process for thermoplastic specimen, the material behavior in dies and its rheological properties have a major influence on the mechanical properties and the quality of the extruded product. This study outlines the multiphysical model, which has been adapted to address the specific issues associated with polyamide 12 polymer extrusion. A series of numerical simulations, based on the modeling of material behavior, have been conducted using the computational code Comsol Multiphysics®. These simulations have been applied to the study of polymer melt flows through an industrial extrusion die. The objective of this study is to analyze the influence of the imposed extrusion parameters on the physical field distribution and the material displacement within the die. The die swell at the exit of the extrusion die has been investigated as a function of the imposed pressure. The progression of the polymer flow front inside the extrusion tool and the swelling rates have been analyzed. In particular, the phenomenon of delayed swelling at high pressure has been highlighted at high pressure.Highlights Polymer swelling at industrial extrusion die exit is investigated. Polymer melt extrusion within industrial extrusion tool is numerically simulated. Flow front progression and extrudate swell are analyzed. Effect of extrusion pressure on instabilities and die swell is highlighted.

Influence of polymer flow rate, mold cavity volume and injection speed on selected properties of polypropylene molded parts

Influence of the height of the molding cavity and the injection speed for three PP grades with different mass melt flow rate (MFR) on the molded parts mass and longitudinal shrinkage, before and after UV aging, was investigated. It was shown that the mass of the molded parts depends on the flow rate of the material and the volume of the molding cavity, while shrinkage depends only on the volume of the mold cavity and is greater after aging.

Entropy optimization of a FENE-P viscoelastic model: a numerically guided comprehensive analysis

AbstractThe influence of polymers on entropy generation processes is substantial, particularly in the fields of fluid dynamics and rheology. The FENE-P (Finitely Extensible Nonlinear Elastic-Peterlin) model describes the polymer’s dynamics as a result of the interaction between the stretching caused by the velocity gradient and the elastic force that restores the polymer to its equilibrium position. Models such as FENE-P aid in understanding and predicting polymer flow behaviour allowing for the reduction of entropy generation by optimizing system designs. A continuum approach is employed to express the heat flux vector and polymer confirmation tensor of the model. The study investigates the complex relationship between polymer conformation, flow dynamics, and heat transfer taking into account the thermophoresis (Soret effect) and mass diffusion-thermal diffusion coupling (Dufour effect) phenomena to optimize processes by reducing entropy. This study illuminates polymer’s significance in entropy minimization, improving engineering design methodologies and applications in materials science, chemical engineering, and fluid dynamics. As result, the presence of polymers leads to a substantial decrease in the total entropy of the system. This understanding provides opportunities for enhancing heat transfer systems, thereby facilitating the development of more efficient and sustainable technology.

Response Surface Methodology to Explore the Influence Mechanism of Fiber Diameter in a New Multi-Needle Electrospinning Spinneret.

Multi-needle electrospinning is an efficient method for producing nanofiber membranes. However, fluctuations in the fluid flow rate during the process affect membrane quality and cause instability, an issue that remains unresolved. To address this, a multi-stage flow runner spinneret needs to be developed for large-scale nanofiber membrane production. This paper uses COMSOL finite element software to simulate polymer flow in the spinneret runner. From this, the velocity field distribution and velocity instability coefficient were obtained, providing theoretical guidance for optimal spinneret design. In addition, response surface analysis (RSM) was used to experimentally explore the process parameters, and then residual probability plots were used for reliability verification to evaluate the effect of each process parameter on fiber diameter. These process parameters can guide the controlled production of nanofibers during multi-needle electrospinning.

Raising Two More Fundamental Questions Regarding the Classical Views on the Rheology of Polymer Melts.

The current paradigm of polymer flow assumes that (i) the effect of the molecular weight of the macromolecules, M, and of the temperature, T, on the expression of the viscosity of polymer melts separate; (ii) the molecular weight for entanglement, Mc, is independent of T; and (iii) the determination of Mc by the break in the log viscosity curve against log M unequivocally differentiates un-entangled melts from entangled melts. We use reliable rheological data on monodispersed polystyrene samples from very low molecular weight (M/Mc = 0.015) to relatively high molecular weight (M/Mc = 34) to test the separation of M and T in the expression of the viscosity; we reveal that an overall illusion of the validity of the separation of T and M is mathematically comprehensible, especially at high temperature and for M > 2Mc, but that, strictly speaking, the separation of M and T is not valid, except for certain periodic values of M equal to Mc, 2Mc, 4Mc, 8Mc, 16Mc, etc. (period doubling) organized around a "pole reference" value MR = 4Mc. We also reveal, for M < Mc, the existence of a lower molecular weight limit, M'c = Mc/8 for the onset of the macromolecular behavior (macro-coil). The discrete and periodic values of M that validate the separation of the effect of M and T on the viscosity generate the fragmentation of the molecular range into three rheological ranges. Likewise, we show that the effect of temperature is also fragmented into three rheological ranges for T > Tg: Tg < T< (Tg + 23°), (Tg + 23°) < T < TLL and T > TLL' where TLL is the liquid-liquid temperature. Our conclusion is that the classical formulation of the viscosity of polymer melts is so overly simplified that it is missing important experimental facts, such as period doubling for the separation of T and M, TLL, M'c, and Mc, resulting in its inability to understand the true nature of entanglements. We present in the discussion of the paper the alternative approach to the viscoelastic behavior, "the duality and cross-duality" of the Dual-conformers, showing how this model formalism was used to test mathematically and invalidate the separation of T and M in the classical formulation of viscosity.

Numerical Modeling of Reservoir Rock Treatment Processes with Polyacrylamide

Increasing the quantities of crude oil extracted from depleted deposits can be achieved using tertiary exploitation methods, namely water injection and polyacrylamide plugs. The adsorption on the surface of the rocks determined the reduction of the mobility of the polymer but also the modification of the gel structure by the modification (crossing) of the polymer (of the polymer chains), which led to clogging (blocking of the pores) and increasing the possibility of fluid flow. Polyacrylamide as a polymer to improve the final recovery factor aims to achieve a good flow of crude oil. In this article, the equations of polymer flow through sands and limestones have been established.

Influence of Polymer Flow on Polypropylene Morphology, Micro-Mechanical, and Tribological Properties of Injected Part

This research investigates the micro-mechanical and tribological properties of injection-molded parts made from polypropylene. The tribological properties of polymers are a very interesting area of research. Understanding tribological processes is very crucial. Considering that the mechanical and tribological properties of injected parts are not uniform at various points of the part, this research was conducted to explain the non-homogeneity of properties along the flow path. Non-homogeneity can be influenced by numerous factors, including distance from the gate, mold and melt temperature, injection pressure, crystalline structure, cooling rate, the surface of the mold, and others. The key factor from the micro-mechanical and tribological properties point of view is the polymer morphology (degree of crystallinity and size of the skin and core layers). The morphology is influenced by polymer flow and the injection molding process conditions. Gained results indicate that the indentation method was sufficiently sensitive to capture the changes in polypropylene morphology, which is a key parameter for the resulting micro-mechanical and tribological properties of the part. It was proven that the mechanical and tribological properties are not equal in varying regions of the part. Due to cooling and process parameters, the difference in the indentation modulus in individual measurement points was up to 55%, and the tribological properties, in particular the friction coefficient, showed a difference of up to 20%. The aforementioned results indicate the impact this finding signifies for injection molding technology in technical practice. Tribological properties are a key property of the part surface and, together with micro-mechanical properties, characterize the resistance of the surface to mechanical failure of the plastic part when used in engineering applications. A suitable choice of gate location, finishing method of the cavity surface, and process parameters can ensure the improvement of mechanical and tribological properties in stressed regions of the part. This will increase the stiffness and wear resistance of the surface.

Pore-scale flooding experiments reveal the thermally regulated flow fields of the curdlan solution

Polymers can enhance oil recovery depending on viscoelasticity. In a field, during polymer flow through porous strata, continuous shear forces result in severe viscosity loss. However, polymers with great shear resistance result in limited migration distance. One solution to the above dilemma is to regulate viscosity, which enables a polymer to migrate long distances through pores with low viscosity and subsequently maintain high viscosity in deep reservoirs. The viscosity of curdlan can be regulated by changing temperature. By curdlan, we mean a biopolymer that shows applications in food industry. However, regarding oil reservoirs, it is unclear whether curdlan viscosity can be effectively regulated in pores. To reveal the feasibility of curdlan viscosity regulation to enhance oil recovery, flooding experiments combined with micro-particle image velocimetry were conducted in a two-dimensional pore network to investigate flow fields of curdlan solutions (0.25%, 0.5%, 1%, and 2%, w/v) at different temperatures (40, 65, and 85 °C). As a result, at 40 °C, curdlan solution (0.25%) easily migrated with low viscosity loss and low adsorption [88.3% original throat diameter (OTD)], and the mobility of curdlan was higher than hydrolyzed polyacrylamide. After heating (65 °C), the viscoelasticity, adsorption (55.1% OTD), and flow resistance (injection pressure, 2.2–8.8 kPa) of curdlan increased, and the greater adsorption capacity of curdlan than xanthan gum led to a more homogeneous flow field [average velocity ratio (Rm), from 2.6 to 1.1]. Since a homogeneous flow field indicated better sweep efficiency, curdlan regulated by temperature could achieve both long-distance migration and improved sweep efficiency in deep strata. These results suggested that viscosity regulation by curdlan could potentially improve oil recovery in water-flooded reservoirs.

Assessing Rheology Effects and Pore Space Complexity in Polymer Flow Through Porous Media: A Pore‐Scale Simulation Study

AbstractNon‐Newtonian fluid flow within porous media, exemplified by polymer remediation of contaminated groundwater/aquifer systems, presents complex challenges due to the fluids' complex rheological behavior within 3D tortuous pore structures. This paper introduces a pore‐scale flow simulator based on the OpenFOAM open‐source library, designed to model shear‐thinning flow within porous media. Leveraging this developed solver, extensive pore‐scale flow simulations were conducted on μ‐CT images of various real and synthetic porous media with varying complexity for both power‐law and Cross‐fluid models. We focused on the macroscale‐averaged deviation between bulk viscosity and the in‐situ viscosity, commonly denoted by a shift factor. We provided an in‐depth evaluation of the shift factor's dependency on the fluid's rheological attributes and the rock's pore space complexity. The least‐squares fitted values of the shift factor fell in the range of 1.6–9.5. Notably, the most pronounced shift factor emerged for extreme flow behavior indices. Our findings highlight not just the critical role of rheological parameters, but also demonstrate how the shift factor fluctuates based on tortuosity, characteristic pore length, and the cementation exponent. In particular, less porous/permeable systems with smaller characteristic pore lengths exhibited larger shift factors due to higher variations of shear rate and local viscosity in narrower flow paths. Additionally, the shift factor increased as rock became more tortuous and heterogeneous. The introduced pore‐scale simulation proves instrumental in determining the macroscopic averaged shift factor. This, in consequence, is vital for precise computations of viscosity and pressure drop when dealing with non‐Newtonian fluid flow in porous media.

Design, Manufacturing, and Comparative Analysis of a Mini Extruder for Polymer Flow Characterization: A Case Study on HDPE and PMMA Polymers

Polymer extrusion is one of the most widely used polymer processing methods and the sole option for many standard products. The modern extrusion machine has a very sophisticated design; for example, the extrusion screw has different zones and complex geometry. Determining the proper processing settings is always a challenge for engineers. Additionally, complex rheological properties of the polymers in extrusion sometimes yield challenging and unpredictable problems to troubleshoot. For convenience, a small-scale extrusion machine can be used to troubleshoot and analyze the polymers rather than the large manufacturing machines that are hard to work with. This study has produced a small-scale extrusion machine that is easy to manufacture without deviating from the extrusion process's nature. The extruder, whose production details are given, was tested with two different polymers: HDPE and PMMA. The correct temperature and screw rotation speed were determined with the extruder for the proper process parameters. In addition, the temperature-viscosity relationship of the polymers' flow nature was also determined.

MODEL-BASED ANALYSIS TO EVALUATE THE EFFECT OF POLYMER PROPERTIES AND PHYSICAL PHENOMENA ON POLYMER FLOODING OPERATIONS

Polymer flooding, known for enhancing heavy oil displacement, may encounter efficiency-limiting physical phenomena. This work assesses the impact of key factors like viscosity, shear rate, and adsorption in field applications using a model-based approach on the EPIC001 case, a real offshore Brazilian heavy oil reservoir. In simulation results, increasing the displacing fluid viscosity using apparent or zero-shear functions, oil production and economic returns show improvements over waterflooding. The shear rate effect slightly increases oil production and enhances injectivity loss due to shear-thinning in polymer flow. However, modeling it increases computation costs, as it extends simulation run time from minutes to days, making it impractical for intensive processes like production optimization. An analysis of the method’s effectiveness shows that it varies based on the adsorption level considered. At its highest value, even with a higher oil recovery factor, the economic return was lower than using waterflooding. Combining shear rate and adsorption has a minimal impact on field indicators when compared to adsorption alone. This work enhances the comprehension of physical phenomena and non-Newtonian behavior in tertiary polymer flooding on heavy oil reservoirs and its impact on the production forecast. It also highlights important considerations for modeling-based procedures.

Water Diffusion in Additively Manufactured Polymers: Analysis of the Capillary Effect

Additive manufacturing (AM) is an advanced manufacturing method that produces objects by sequential layering. Material extrusion AM (MEAM) with continuous-fibre reinforcement is becoming more widely used in naval structures, which are exposed to the marine environment. However, the water diffusion process and the effect of water ageing on the mechanical performance of AM materials are not yet well understood because of their complex internal structure, caused by defects generated during manufacturing. Current research on diffusion is mostly based on experimental methods for conventionally manufactured materials without considering AM-induced defects. The objective of this study is to explore how the defects inherent to MEAM affect water diffusion in a composite material by the capillary effect. Results from a numerical study of capillary flow in MEAM polymer are applied as a boundary condition in the subsequent finite-element analysis. The study illustrates that flow in the capillary reaches the steady state quicker compared to the saturation time in the matrix, predicted by Fick’s diffusion equation. It is demonstrated that the capillary effect can significantly affect the water diffusion in MEAM parts and reduce the saturation time to one-third compared to the case without accounting for this effect.

Numerical and experimental analysis of 3D printer hot ends

The design of the hot end plays a critical role in additive manufacturing, especially in material extrusion. Yet the melt flow behavior within the hot end assembly has not been explicitly presented regarding the hot end design. The present study intends to fill this knowledge gap by employing a two-phase approach to investigate the melt dynamics through three commercially available hot ends. The hot ends considered are E3D v6 Standard, v6 Gold, and Revo Six, which were chosen based on brand, design, and functionality. In Phase 1, an experimental apparatus was developed to assess the impact of feeding rate and extrusion temperature on the outlet temperature, outlet velocity, and under-extrusion percentage of extruded polymer. In Phase 2, the polymer flow through each hot end is explored utilizing a computational fluid dynamics model, which was validated using data obtained in Phase 1. It was determined that the filament feeding rate is the most influential parameter in polymer extrusion and that Revo Six’s symmetrical design affects the stability of extrusion. It was also revealed that the thermal evolution of the melted filament within the hot end assembly is directly affected by the length of the heating region and the polymer's material properties. The experimental and numerical procedures developed in this investigation can be useful to 3D printing users and manufacturers in selecting a hot end assembly based on application requirements.

Tailoring the Mass Density of 3D Printing Materials for Accurate X-ray Imaging Simulation by Controlled Underfilling for Radiographic Phantoms.

Additive manufacturing and 3D printing allow for the design and rapid production of radiographic phantoms for X-ray imaging, including CT. These are used for numerous purposes, such as patient simulation, optimization of imaging procedures and dose levels, system evaluation and quality assurance. However, standard 3D printing polymers do not mimic X-ray attenuation properties of tissues like soft, adipose, lung or bone tissue, and standard materials like liquid water. The mass density of printing polymers-especially important in CT-is often inappropriate, i.e., mostly too high. Different methods can be applied to reduce mass density. This work examines reducing density by controlled underfilling either realized by using 3D printing materials expanded through foaming during heating in the printing process, or reducing polymer flow to introduce microscopic air-filled voids. The achievable density reduction depends on the base polymer used. When using foaming materials, density is controlled by the extrusion temperature, and ranges from 33 to 47% of the base polymer used, corresponding to a range of -650 to -394 HU in CT with 120 kV. Standard filaments (Nylon, modified PLA and modified ABS) allowed density reductions by 20 to 25%, covering HU values in CT from -260 to 77 (Nylon), -230 to -20 (ABS) and -81 to 143 (PLA). A standard chalk-filled PLA filament allowed reproduction of bone tissue in a wide range of bone mineral content resulting in CT numbers from 57 to 460 HU. Controlled underfilling allowed the production of radiographic phantom materials with continuously adjustable attenuation in a limited but appropriate range, allowing for the reproduction of X-ray attenuation properties of water, adipose, soft, lung, and bone tissue in an accurate, predictable and reproducible manner.

Mechanical Transfer of Black Phosphorus on a Silk Fibroin Substrate: A Viable Method for Photoresponsive and Printable Biomaterials.

Despite the technological importance of semiconductor black phosphorus (BP) in materials science, maintaining the stability of BP crystals in organic media and protecting them from environmental oxidation remains challenging. In this study, we present the synthesis of bulk BP and the exploitation of the viscoelastic properties of a regenerated silk fibroin (SF) film as a biocompatible substrate to transfer BP flakes, thereby preventing oxidation. A model based on the flow of polymers revealed that the applied flow-induced stresses exceed the yield stress of the BP aggregate. Raman spectroscopy was used to investigate the exfoliation efficiency as well as the environmental stability of BP transferred on the SF substrate. Notably, BP flakes transferred to the SF substrate demonstrated improved stability when SF was dissolved in a phosphate-buffered saline medium, and in vitro cancer cell viability experiments demonstrate the tumor ablation efficiency under visible to near-infrared (Vis-nIR) radiation. Moreover, the SF and BP-enriched SF (SF/BP) solution was shown to be processable via extrusion-based three-dimensional (3D) printing. Therefore, this work paves the way for a general method for the transferring of BP on natural biodegradable polymers and processing them via 3D printing toward novel functionalities and complex shapes for biomedical purposes.