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A multicomponent model is developed for wax deposition onto a cold finger from a stirred wax‐containing oil. It utilizes Coutinho's thermodynamic equations for wax component concentrations and energy and mass transport equations within the deposit and from the oil and is the first cold‐finger model to predict both deposit thickness growth and aging by selective precipitation of heavier wax components. While it captures well deposit thickness growth, it requires preventing re‐dissolution of deposited wax to avoid shrinkage not observed in experiments. The model predicts deposit aging reasonably well but with quantitative deviations for the heavier wax of up to a factor of two. Possible explanations include the inadequacy of Hayduk‐Minhas and Cussler's hindered‐diffusion models to the soluble multicomponent wax diffusivities. Using pseudo two‐ and one‐component representation can reasonably predict the deposit thickness and aging of multi‐component deposits. This work shows an improved approach to modeling wax deposition and aging. [ABSTRACT FROM AUTHOR]

To meet the challenge of efficient modeling of film blowing with realistic constitutive equations for commercial thermoplastic melts, we present a multistage optimization modeling framework that integrates polymerization reaction modeling, rheology modeling, and bubble-shape prediction. A direct link is thereby created between the polymer architecture and the bubble shape of low-density polyethylene (LDPE) through a three-stage modeling protocol. Stage 1 aims to get complete polymer structure information from a limited set of linear and nonlinear rheological data and the measured averaged molecular weight. An optimization loop uses the Tobita algorithm for polymer reaction and the BoB model for rheology to minimize the deviation between experimental data and model predictions. Stage 2 is designed to obtain a representative reduced ensemble of LDPE in the Rolie-double-poly (RDP) model to reduce the computational cost of rheology calculations during processing. The parameters of the reduced molecular components are obtained by fitting the RDP model to a wide range of rheology data predicted by the BoB model applied to the full ensemble of polymer architectures obtained in stage 1. In stage 3, the reduced-ensemble RDP model is coupled to measured temperature profiles using time–temperature superposition, and the bubble shape and strain rate history of a fluid particle in the bubble are obtained by minimizing error in the momentum balance equations. We show that each stage of the process yields successful fitting, and at the end, we obtain an a priori prediction of height-dependent bubble radius and velocity in agreement with experiment. With this multistage optimization strategy, we link the polymer compositions to the bubble properties during the film blowing of LDPE. [ABSTRACT FROM AUTHOR]

This work presents a framework governing the development of an efficient, accurate, and transferable coarse-grained (CG) model of a polyether material. The framework combines bottom-up and top-down approaches of coarse-grained model parameters by integrating machine learning (ML) with optimization algorithms. In the bottom-up approach, bonded interactions of the CG model are optimized using deep neural networks (DNN), where atomistic bonded distributions are matched. In the top-down approach, optimization of nonbonded parameters is accomplished by reproducing the temperature-dependent experimental density. We demonstrate that developed framework addresses the thermodynamic consistency and transferability issues associated with the classical coarse-graining approaches. The efficiency and transferability of the CG model is demonstrated through accurate predictions of chain statistics, the limiting behavior of the glass transition temperature, diffusion, and stress relaxation, where none were included in the parametrization process. The accuracy of the predicted properties are evaluated in context of molecular theories and available experimental data. [ABSTRACT FROM AUTHOR]

To estimate yield stress and other rheological properties relevant to modeling of wax deposition in pipelines where flow is continuous, but stress varies across the pipe radius, model wax-oil mixtures are cooled at multiple cooling rates under constant shear stress until a temperature is reached, at which flow is arrested by gelation due to wax crystal formation. From these data, combined with a measurement of temperature-dependence of precipitated wax concentration by differential scanning calorimetry, an apparent yield stress σ y , below which flow is arrested at each temperature, is related to the concentration of precipitated wax C p and the cooling rate. Results are reported for multiple concentrations in oil of two independent wax mixtures: a many-component commercial wax mimicking the composition of field oil, and a simpler six-alkane mixture. These transient rheological data are fit to a pseudo "Herschel–Bulkley" constitutive equation from which it is found that the yield stresses obtained during flow under cooling are generally an order of magnitude, or more, lower than the yield stresses obtained in the previous work in flow at a comparable constant temperature after cooling in the absence of flow. We also find a strong decrease in the arrest temperature with a decreasing cooling rate, with no convergence even at the lowest cooling rate of 0.0625 °C min−1, indicating that under slower cooling, flow continues even under low stresses. The cooling-rate-dependent yield stress obtained in our study under constant stress provides a challenge to the recent models of gelation under flow stress and is of relevance to wax deposition in pipelines. [ABSTRACT FROM AUTHOR]

We use all-atom molecular dynamics simulations to extract ΔGeff, the free energy of binding of potassium ions K+ to the partially charged polyelectrolyte poly(acrylic acid), or PAA, in dilute regimes. Upon increasing the charge fraction of PAA, the chains adopt more extended conformations, and simultaneously, potassium ions bind more strongly (i.e., with more negative ΔGeff) to the highly charged chains to relieve electrostatic repulsions between charged monomers along the chains. We compare the simulation results with the predictions of a model that describes potassium binding to PAA chains as a reversible reaction whose binding free energy (ΔGeff) is adjusted from its intrinsic value (ΔG) by electrostatic correlations, captured by a random phase approximation. The bare or intrinsic binding free energy ΔG, which is an input in the model, depends on the binding species and is obtained from the radial distribution function of K+ around the charged monomer of a singly charged, short PAA chain in dilute solutions. We find that the model yields semi-quantitative predictions for ΔGeff and the degree of potassium binding to PAA chains, α, as a function of PAA charge fraction without using fitting parameters. [ABSTRACT FROM AUTHOR]

Direct ink writing is used to print multiple polydimethylsiloxane (PDMS) mixtures with fumed silica or as a two-part commercial liquid silicone rubber (LSR) mixed with polyethylene glycol (PEG) or as a two-part commercial vulcanizing (RTV) silicone. We correlate their printability into a hollow slump cone with rheological measurements, including (1) a shear rate up-ramp followed by (2) a down-ramp in the shear rate, (3) creep tests, and (4) large-amplitude oscillatory shear (LAOS) with increasing amplitude. The PDMS-fumed silica mixtures fail to print even at the highest fumed silica loading used (9 wt. %), while LSR-PEG with 4 or 6 wt. % PEG prints well, and one of the two RTV silicone components is printable, as is the mixture due in part to its rapid chemical curing. The large differences in printability of these materials do not correlate well with any single rheological test. They do correlate with a combination of a measure of material strength, given by either the yield stress σ y cr from creep tests or the "flow stress" σ f at which G′ and G″ cross-over in LAOS, and of material recoverability given by the dynamic yield stress σ y − in test 2. The latter is measured during a down-ramp in the shear rate after reaching a maximum shear rate of 1000 s−1, the highest shear rate in the print nozzle. [ABSTRACT FROM AUTHOR]

To predict the complex rheology and shear-rate inhomogeneities of lamellar gel networks, we propose a simple thixotropic constitutive model with an elastoplastic stress and a smoothly decreasing modulus near a solid boundary, motivated by the analysis of the effect of confinement and shear flow on lamellae orientation near surfaces. We show that the model qualitatively captures the important features of the lamellar gel shear rheology observed in experiments [Datta et al., J. Rheol. 64(4), 851–862 (2020)]. These include thixotropic shear thinning that is intermediate between constant viscosity and constant stress, a power-law slow creep under small constant shear stress and abrupt transition to fast creep at higher stress, as well as partial recovery of strain upon stress removal. In addition, the model correctly predicts a gap-dependent rheology and roughly predicts the amplitude dependence of storage and loss moduli in oscillatory tests despite having only a single thixotropic time constant. Most importantly, the introduction of the modulus gradient enables the model to predict the unique shear-banding phenomenon of lamellar gel networks wherein a thin, fast-shearing band exists near the boundary that widens only slowly with increased apparent shear rate until a very high rate is reached, while the bulk moves as a plug [Datta et al., J. Rheol. 64(4), 851–862 (2020)]. We discuss the influence of a lower modulus near the boundary and its possible origin in the underlying lamellar structure of the material. [ABSTRACT FROM AUTHOR]

Using PYS, TraPPE, OPLS-L, and Flexible-Williams (FW) force field models, atomistic simulations at temperatures ranging from 450 K to 600 K are performed to predict the melt density ρ, the persistence length Np, the nematic coupling constant α, and crystallization dynamics for pentacontane (C50). The coupling constant α arises from packing entropy of rodlike Kuhn segments and increases with increasing ρ and Np. Together with a self-consistent field theory, Np and α are then used to predict the isotropic-to-nematic (IN) transition temperature for polyethylene (PE) oligomers as a function of chain length. The nematic phase is found to be metastable since the IN transition temperature lies below the crystal melting temperatures for C50 in simulations using different force fields. Finally, isothermal simulations of crystallization for PE C50 oligomers and C1000 polymers show that crystal nucleation may be much accelerated by quenching below the IN transition temperature, where chains in the isotropic state first rapidly form nematic ordered domains, within which crystalline order then grows. We also find that the PYS, TraPPE, and FW models overpredict the melting temperature for C50 by around 50 K, while the most flexible OPLS-L model gives a melting temperature within around 10 K of the experimental value. Although giving a more accurate melting temperature, the slow crystallization kinetics of the OPLS-L model may limit its application in direct simulations of PE crystallization. [ABSTRACT FROM AUTHOR]

Using first-principles density functional theory calculations, the mechanical and electronic properties of the three main (β12, χ3, and striped) phases of single-layer borophene sheets are calculated under in-plane uniaxial/biaxial strain, including the harmonic strain-energy regions of β12, χ3, and striped phases over the strain ranges of −3.5%–3.5%, −4.5%–4.5%, and −2.5%–2.5%, respectively, along the x direction (the direction of the highest bond orientation). We introduce a method by which the nonlinear behavior of these and any other two-dimensional materials can be investigated even above their ultimate strains, beyond which no-uniform plastic deformation occurs. Defining an appropriate deformation, and utilizing both continuum modeling and special equations based on the density functional theory, a method of computing second-, third-, and fourth-order elastic constants of the three different phases of borophene is presented that utilizes rectangular unit cells, which can substitute for any two-dimensional unit cell. Using this new method, 4 independent second-order, 6 third-order, and 9 fourth-order elastic constants are calculated, which is the complete set of elastic constants for two-dimensional structures. The electronic band structure of borophene shows anisotropic electronic behavior. Despite the metallic character of borophene sheets, applying directional strain based on deformation matrices creates a bandgap in some regions of the Brillouin zones, opening up the possibility of mechanical control of electronic properties. [ABSTRACT FROM AUTHOR]

We develop a general framework for transport of polyions, solvent and salt, with intended application to Layer-by-Layer (LbL) assembly of polyelectrolyte monolayers (PEMs). The formulation for the first time includes electrostatics, chemical potential gradients, and mechanical stress gradients as driving forces for mass transport. The general model allows all species to be mobile throughout the process and avoids the assumptions of stepwise instantaneous equilibrium and/or immobilized structures typical of previous approaches, while reducing to these models in appropriate limits. A simple constitutive equation is derived for a mixture of oppositely charged polyelectrolytes that accounts for network strand dilution and cross-chain ion pairing by appending reactive terms to the Smoluchowski probability diffusion equation for network strand end-to-end vectors. The resulting general framework encompasses the Poisson equation describing the electrostatic potential distribution, an osmotic pressure balance, a stress constitutive equation, and a generalized flux law of polymer transport. The computational domain is split into a PEM phase and an external solution phase with an appropriate boundary condition derived for the interface between the two. The mobile species (water and small salt ions) are taken to be in a state of dynamic equilibrium with their distributions enslaved to the perturbations in the two polyion compositions. The proposed model captures the swelling response of PEM films to external solutions. For the first time, we studied the effects of the temporal evolution of electrostatic and stress distribution on the rate of chain loss and absorption during rinsing and dipping of an idealized and arbitrarily selected and rigid brush layer into external solutions. The temporal evolution provides a kinetic basis for the ability of LbL films to grow under conditions that thermodynamics alone suggests would cause them to be washed away and to account for partial desorption during washing. The proposed transport framework constitutes a solid basis for eventual quantitative modeling of LbL assembly and transport in polyion networks more generally. [ABSTRACT FROM AUTHOR]

After reviewing and organizing the literature on the problem of inertial cross-stream migration of rigid spheres in various geometries including tubes and channels, we use Dissipative Particle Dynamics (DPD) simulations to study the simplest case of migration of a single neutrally or non-neutrally buoyant sphere with diameter 20% of the gap in plane Poiseuille flow and assess the potential and limitations of DPD simulations for this and similar problems. We find that the neutrally buoyant sphere lags by up to 6% behind the surrounding fluid and is focused at a position around 50% of the distance between the channel center and the wall. With Re increasing from around 100 to 500, the sphere migrates closer to the channel center. With flow driven by gravity, a much denser non-neutrally buoyant sphere leads the surrounding fluid and is focused at a position closer to the wall, around 60% the distance from the channel center to the wall, in qualitative agreement with previous work. The lower values of the Schmidt number Sc in DPD simulations relative to real fluids, due to the relatively large diffusivity of DPD beads, are shown to not significantly affect the consistency of our DPD results with literature results although they make results noisy at low Re (i.e., ≲ 50). However, the increase in Ma and Wi with increasing Re leads to compressible flow effects and in some cases viscoelastic effects at high Re depending on the DPD parameters chosen. Even for optimally chosen parameters, we require Re ≲ 500 to avoid strong compressibility effects. Thus, the relative simplicity of the DPD method for complex fluid flows is offset by the need to control the effects of unphysically high values of other parameters, such as Ma and Wi, which seriously limits the range of conditions under which DPD simulations give valid results in fluid transport problems. [ABSTRACT FROM AUTHOR]

Reversible ion binding equilibria in polyelectrolyte solutions are strongly affected by interactions between dissociated ionic species. We examine how the structural correlations between ionic groups on polyelectrolytes impact the counterion binding. Treating the electrostatic correlation free energy using the classical Debye-Hückel expression leads to complete counterion dissociation in the concentrated regime. This unphysical behavior is shown to stem from improper regularization of the self-energy of dissociated ions and polyions and is mitigated by smearing point-like charges across a finite width. The influence of the self-energy on counterion binding is elaborated on by generalizing the Debye-Hückel free energy to polyelectrolytes with variable fractal dimension and stiffness. In the dilute regime, a greater propensity for binding is found for chains with more compact architectures, which in turn reduces the harsh self-repulsions of tightly packed arrangements of charge. In the concentrated regime, the effects of electrostatic correlations weaken due to screening and the extent of binding is governed by a balance of short-ranged interactions and the translational entropy of ions. [ABSTRACT FROM AUTHOR]

We present a one-parameter model that fits quantitatively the mean velocity profiles from experiments and numerical simulations of drag-reduced wall-bounded flows of dilute solutions of polymers and non-Brownian fibers in the low and modest drag reduction regime. The model is based on a viscous mechanism of drag reduction, in which either extended polymers or non-Brownian fibers increase the extensional viscosity of the fluid and thereby suppress both small and large turbulent eddies and reduce momentum transfer to the wall, resulting in drag reduction. Our model provides a rheological interpretation of the upward parallel shift S+ in the mean velocity profile upon addition of polymer, observed by Virk. We show that Virk’s correlations for the dependence on polymer molecular weight and concentration of the onset wall shear stress and slope increment on the Prandtl-Karman plot can be translated to two dimensionless numbers, namely an onset Weissenberg number and an asymptotic Trouton ratio of maximum extensional viscosity to zero-shear viscosity. We believe that our model, while simple, captures the essential features of drag reduction that are universal to flexible polymers and fibers, and, unlike the Virk phenomenology, can easily be extended to flows with inhomogeneous polymer or fiber concentration fields.

A thorough study is made of the dependences on salt concentration and polymer chain lengths of the low-frequency plateau of coacervates of poly (diallyl dimethyl ammonium chloride), PDADMAC, and poly (sodium 4-styrenesulfonate), PSS. The reliability and reproducibility of these measurements are carefully checked by determining the frequency-dependent stress limits of the rheometer through the use of reference fluids and by repeat experiments with coacervates. Long-time frequency sweeps show that coacervates with less salt are more repeatable than those with higher salt. A low-frequency plateau reliably appears only below a critical salt concentration, and the magnitude of the plateau depends strongly on salt concentration and chain lengths of both polycation and polyanion. It is only present for the molecular weight of the polycation, PDADMAC, higher than 100 kDa, but the magnitude of the plateau is more strongly influenced by the chain length of the polyanion, PSS. Possible causes of the low-frequency plateau are discussed. [ABSTRACT FROM AUTHOR]

We examine linear and nonlinear shear and extensional rheological properties using a "micelle-slip-spring model" [T. Sato et al., J. Rheol. 64, 1045–1061 (2020)] that incorporates breakage and rejoining events into the slip-spring model originally developed by Likhtman [Macromolecules 38, 6128–6139 (2005)] for unbreakable polymers. We here employ the Fraenkel potential for main chain springs and slip-springs to address the effect of finite extensibility. Moreover, to improve extensional properties under a strong extensional flow, stress-induced micelle breakage (SIMB) is incorporated into the micelle-slip-spring model. Thus, this model is the first model that includes the entanglement constraint, Rouse modes, finite extensibility, breakage and rejoining events, and stress-induced micelle breakage. Computational expense currently limits the model to micellar solutions with moderate numbers of entanglements (≲ 7), but for such solutions, nearly quantitative agreement is attained for the start-up of the shearing flow. The model in the extensional flow cannot yet be tested owing to the lack of data for this entanglement level. The transient and steady shear properties predicted by the micelle-slip-spring model for a moderate shear rate region without significant chain stretch are fit well by the Giesekus model but not by the Phan–Thien/Tanner (PTT) model, which is consistent with the ability of the Giesekus model to match experimental shear data. The extensional viscosities obtained by the micelle-slip-spring model with SIMB show thickening followed by thinning, which is in qualitative agreement with experimental trends. Additionally, the extensional rheological properties of the micelle-slip-spring model with or without SIMB are poorly predicted by both the Giesekus and the PTT models using a single nonlinear parameter. Thus, future work should seek a constitutive model able to capture the behavior of the slip-spring model in shear and extensional flows and so provide an accurate, efficient model of micellar solution rheology. [ABSTRACT FROM AUTHOR]

We review theories of polyelectrolyte (PE) coacervation, which is the spontaneous association of oppositely charged units of PEs and phase separation into a polymer‐dense phase in aqueous solution. The simplest theories can be divided into "physics‐based" and "chemistry‐based" approaches. In the former, PEs are treated as charged, long‐chain, molecules, defined by charge level, chain length, and chain flexibility, but otherwise lacking chemical identity, with electrostatic interactions driving coacervation. The "chemistry‐based" approaches focus on the local interactions between the species for which chemical identity is critical, and describe coacervation as the result of competitive local binding interactions of monomers and salts. In this article, we show how these approaches complement each other by presenting recent approaches that take both physical and chemical effects into account. Finally, we suggest future directions toward producing theories that are made quantitatively predictive by accounting for both long range electrostatic and local chemically specific interactions. [ABSTRACT FROM AUTHOR]

Brownian dynamics simulations of single-patch Janus particles under sedimentation equilibrium reveal that the phases found at fixed temperature and volume fraction are extremely sensitive to small changes in lateral box dimension. We trace this sensitivity to an uncontrolled parameter, namely, the pressure component parallel to the hexagonally ordered layers formed through sedimentation. We employ a flexible-cell constant-pressure scheme to achieve explicit control over this usually overlooked parameter, enabling the estimation of phase behavior under given pressure anisotropy. Our results show an increase in the stability range of an orientationally ordered lamellar phase with lateral layer compression and suggest a novel mechanism to control solid-solid phase transitions with negligible change in system volume, thus showing prospect for design of novel structures and switchable crystals from anisotropic building blocks. [ABSTRACT FROM AUTHOR]