Research

Jump to: Review

29 pages, 531 KiB

Open AccessArticle

Adsorption of Wormlike Chains onto Partially Permeable Membranes

by

Alexander Semenov

and

Irina Nyrkova

Polymers 2023, 15(1), 35; https://doi.org/10.3390/polym15010035 - 22 Dec 2022

Cited by 1 | Viewed by 681

Abstract

Reversible adsorption of a single stiff wormlike macromolecule to flat membranes with various permeabilities is considered theoretically. It is shown that the adsorbed layer microstructure is significantly different from either a flexible chain or a stiff chain adsorption at a solid surface. Close [...] Read more.

Reversible adsorption of a single stiff wormlike macromolecule to flat membranes with various permeabilities is considered theoretically. It is shown that the adsorbed layer microstructure is significantly different from either a flexible chain or a stiff chain adsorption at a solid surface. Close to the critical point, the adsorbing wormlike chain forms a strongly anisotropic proximal layer near the membrane in addition to a nearly isotropic distal layer. The proximal layer is characterized by the algebraic monomer concentration profile,

c (x) \propto {|x|}^{- β}

, due to the self-similar distribution of aligned polymer loops. For a perfectly penetrable membrane,

β = 1

which is different from

β = 4 / 3

obtained for semiflexible chain adsorption at a solid surface. Moreover, we establish that the critical exponent for a partially permeable membrane depends on its properties (porosity w) and propose an asymptotically exact theory (based on the generalized Edwards equation) predicting this dependence,

β = β (w)

. We also develop a scaling theory elucidating, in particular, an intricate competition of loops and tails in both proximal and distal sublayers. Full article

(This article belongs to the Special Issue Polymer Theory and Simulation)

► Show Figures

Graphical abstract

12 pages, 11669 KiB

Open AccessFeature PaperArticle

Liquid Fraction Effect on Foam Flow through a Local Obstacle

by

,

,

and

Polymers 2022, 14(23), 5307; https://doi.org/10.3390/polym14235307 - 05 Dec 2022

Cited by 1 | Viewed by 1079

Abstract

An experimental study of quasi-two-dimensional liquid foams with varying liquid fractions is presented. Experiments are conducted in a Hele-Shaw cell with a local permeable obstacle placed in the center and filling 35, 60 and 78% of the cell gap. Foam velocity is calculated [...] Read more.

An experimental study of quasi-two-dimensional liquid foams with varying liquid fractions is presented. Experiments are conducted in a Hele-Shaw cell with a local permeable obstacle placed in the center and filling 35, 60 and 78% of the cell gap. Foam velocity is calculated using a standard cross-correlation algorithm. Estimations of the liquid fraction of the foam are performed using a new simplified method based on a statistical analysis of foam cell structures. The pattern of the foam velocity field varies with increasing liquid fraction, responsible for significant variation of the foam’s rheology. The local permeability decreases with increasing obstacle height and liquid fraction. In case of high liquid fraction (

5.8 \times 10^{- 2}

), the permeability coefficient tends to zero for obstacles filling more than 78% of the cell gap. Full article

(This article belongs to the Special Issue Polymer Theory and Simulation)

► Show Figures

Figure 1

22 pages, 494 KiB

Open AccessArticle

Capillary Thinning of Viscoelastic Threads of Unentangled Polymer Solutions

by

Alexander Semenov

and

Irina Nyrkova

Polymers 2022, 14(20), 4420; https://doi.org/10.3390/polym14204420 - 19 Oct 2022

Cited by 3 | Viewed by 892

Abstract

In this paper, we theoretically consider the process of the capillary thinning of a polymer fluid thread bridging two large immobile droplets in the regime of highly stretched polymer chains. We first derive a new relation between the pressure p and the flow [...] Read more.

In this paper, we theoretically consider the process of the capillary thinning of a polymer fluid thread bridging two large immobile droplets in the regime of highly stretched polymer chains. We first derive a new relation between the pressure p and the flow velocity v in unentangled polymer solutions, which is called the anti-Bernoulli law: it shows that p is higher where v is faster. Using this equation, it is shown that the flow field is asymptotically irrotational, in particular, in the thread/droplet transition zones (in the case, the negligible solvent viscosity and inertial effects). On this basis, we predict the free surface profile and the thread thinning law for the FENE-P model of polymer dynamics. The predictions are compared with recent theoretical results and some experimental data on capillary thinning. Full article

(This article belongs to the Special Issue Polymer Theory and Simulation)

► Show Figures

Figure 1

15 pages, 3053 KiB

Open AccessArticle

The Problem of Filling a Spherical Cavity in an Aqueous Solution of Polymers

by

Oxana A. Frolovskaya

and

Vladislav V. Pukhnachev

Polymers 2022, 14(20), 4259; https://doi.org/10.3390/polym14204259 - 11 Oct 2022

Cited by 1 | Viewed by 755

Abstract

The problem of filling a spherical cavity in a liquid has attracted the attention of many authors. The study of bubble behavior in liquid allows to estimate the consequences of cavitation processes, which can lead to the intensive destruction of the material surface. [...] Read more.

The problem of filling a spherical cavity in a liquid has attracted the attention of many authors. The study of bubble behavior in liquid allows to estimate the consequences of cavitation processes, which can lead to the intensive destruction of the material surface. Regarding this connection, it becomes necessary to study the influence of impurities, including polymeric additives on the strengthening or suppression of cavitation. In this paper, this problem is considered in three models of a relaxing fluid. It is shown that for all models, the cavity filling time is finite if the surface tension is not equal to zero. This result was previously established for the cases of ideal and viscous fluids. However, the relaxation factor can significantly change the flow pattern by slowing down the filling process and lowering the level of energy accumulation during the bubble collapse. Full article

(This article belongs to the Special Issue Polymer Theory and Simulation)

► Show Figures

Figure 1

19 pages, 1319 KiB

Open AccessArticle

Recursive Settling of Particles in Shear Thinning Polymer Solutions: Two Velocity Mathematical Model

by

Vladimir Neverov

and

Vladimir Shelukhin

Polymers 2022, 14(19), 4241; https://doi.org/10.3390/polym14194241 - 10 Oct 2022

Viewed by 904

Abstract

Processing of the available experimental data on particles settling in shear-thinning polymer solutions is performed. Conclusions imply that sedimentation should be recursive, since settling also occurs within the sediment. To capture such an effect, a mathematical model of two continua has been developed, [...] Read more.

Processing of the available experimental data on particles settling in shear-thinning polymer solutions is performed. Conclusions imply that sedimentation should be recursive, since settling also occurs within the sediment. To capture such an effect, a mathematical model of two continua has been developed, which corresponds to experimental data. The model is consistent with basic thermodynamics laws. The rheological component of this model is a correlation formula for gravitational mobility. This closure is justified by comparison with known experimental data available for particles settling in vertical vessels. In addition, the closure is validated by comparison with analytical solutions to the Kynch one-dimensional equation, which governs dynamics of particle concentration. An explanation is given for the Boycott effect and it is proven that sedimentation is enhanced in a 2D inclined vessel. In tilted vessels, the flow is essentially two-dimensional and the one-dimensional Kynch theory is not applicable; vortices play an important role in sedimentation. Full article

(This article belongs to the Special Issue Polymer Theory and Simulation)

► Show Figures

Figure 1

24 pages, 2841 KiB

Open AccessArticle

Flows of Dense Suspensions of Polymer Particles through Oblique Bifurcating Channels: Two Continua Approach

by

Vladimir Shelukhin

and

Andrey Antonov

Polymers 2022, 14(18), 3880; https://doi.org/10.3390/polym14183880 - 17 Sep 2022

Viewed by 843

Abstract

A two-velocity mathematical model is proposed for dense suspension flows through channel bifurcations. Equations agree with thermodynamic laws and they are suitable for both heavy and light particles. The pulsatile mode of injection of particles is considered. In the 2D-case, we address the [...] Read more.

A two-velocity mathematical model is proposed for dense suspension flows through channel bifurcations. Equations agree with thermodynamic laws and they are suitable for both heavy and light particles. The pulsatile mode of injection of particles is considered. In the 2D-case, we address the issue of partitioning particles and study how a loss of particles into the side branch depends on the bifurcation angle. A qualitative agreement with experiment data are established. We capture the Zweifach–Fung effect. We treat polymer particles as a phase enjoying the rheology of the Bingham viscoplastic material. We prove that the polymer particle distribution between two branches correlates with the averaged-in-time Bingham number in these branches. Full article

(This article belongs to the Special Issue Polymer Theory and Simulation)

► Show Figures

Figure 1

17 pages, 352 KiB

Open AccessArticle

Model for Aqueous Polymer Solutions with Damping Term: Solvability and Vanishing Relaxation Limit

by

Evgenii S. Baranovskii

and

Mikhail A. Artemov

Polymers 2022, 14(18), 3789; https://doi.org/10.3390/polym14183789 - 10 Sep 2022

Cited by 4 | Viewed by 727

Abstract

The main aim of this paper is to investigate the solvability of the steady-state flow model for low-concentrated aqueous polymer solutions with a damping term in a bounded domain under the no-slip boundary condition. Mathematically, the model under consideration is a boundary value [...] Read more.

The main aim of this paper is to investigate the solvability of the steady-state flow model for low-concentrated aqueous polymer solutions with a damping term in a bounded domain under the no-slip boundary condition. Mathematically, the model under consideration is a boundary value problem for the system of strongly nonlinear partial differential equations of third order with the zero Dirichlet boundary condition. We propose the concept of a full weak solution (velocity–pressure pair) in the distributions sense. Using the method of introduction of auxiliary viscosity, the acute angle theorem for generalized monotone nonlinear operators, and the Krasnoselskii theorem on the continuity of the superposition operator in Lebesgue spaces, we obtain sufficient conditions for the existence of a full weak solution satisfying some energy inequality. Moreover, it is shown that the obtained solutions of the original problem converge to a solution of the steady-state damped Navier–Stokes system as the relaxation viscosity tends to zero. Full article

(This article belongs to the Special Issue Polymer Theory and Simulation)

Review

Jump to: Research

50 pages, 589 KiB

Open AccessReview

Review: Kirkwood–Riseman Model in Non-Dilute Polymeric Fluids

by

George David Joseph Phillies

Polymers 2023, 15(15), 3216; https://doi.org/10.3390/polym15153216 - 28 Jul 2023

Viewed by 389

Abstract

In two prior articles, I demonstrated from extensive simulational studies by myself and others that the Rouse model of polymer dynamics is invalid in polymer melts and in dilute solution. However, the Rouse model is the foundational basis for most modern theories of [...] Read more.

In two prior articles, I demonstrated from extensive simulational studies by myself and others that the Rouse model of polymer dynamics is invalid in polymer melts and in dilute solution. However, the Rouse model is the foundational basis for most modern theories of polymeric fluid dynamics, such as reptation/scaling models. One therefore rationally asks whether there is a replacement. There is, namely by extending the Kirkwood–Riseman model. Here, I present a comprehensive review of one such set of extensions, namely the hydrodynamic scaling model. This model assumes that polymer dynamics in dilute and concentrated solution is dominated by solvent-mediated hydrodynamic interactions; chain crossing constraints are taken to create only secondary corrections. Many other models assume, contrariwise, that in concentrated solutions, the chain crossing constraints dominate the dynamics. An extended Kirkwood–Riseman model incorporating interchain hydrodynamic interactions is developed. It yields pseudovirial series for the concentration and molecular weight dependencies of the self-diffusion coefficient

D s

and the low-shear viscosity

η

. To extrapolate to large concentrations, rationales based on self-similarity and on the Altenberger–Dahler positive-function renormalization group are presented. The rationales correctly predict how

D_{s}

and

η

depend on polymer concentration and molecular weight. The renormalization group approach leads to a two-parameter ansatz that correctly predicts the functional forms of the frequency dependencies of the storage and loss moduli. A short description is given of each of the papers that led to the hydrodynamic scaling model. Experiments supporting the aspects of the model are noted. Full article

(This article belongs to the Special Issue Polymer Theory and Simulation)

► Show Figures

Graphical abstract

Journal Menu

Journal Browser

Special Issue "Polymer Theory and Simulation"

Share This Special Issue

Special Issue Editor

Special Issue Information

Keywords

Published Papers (8 papers)

Research

Review

Further Information

Guidelines

MDPI Initiatives

Follow MDPI