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28 pages, 4958 KiB

Open AccessFeature PaperArticle

A Thermodynamically Consistent, Microscopically-Based, Model of the Rheology of Aggregating Particles Suspensions

by Soham Jariwala, Norman J. Wagner and Antony N. Beris

Entropy 2022, 24(5), 717; https://doi.org/10.3390/e24050717 - 17 May 2022

Cited by 6 | Viewed by 2848

Abstract

In this work, we outline the development of a thermodynamically consistent microscopic model for a suspension of aggregating particles under arbitrary, inertia-less deformation. As a proof-of-concept, we show how the combination of a simplified population-balance-based description of the aggregating particle microstructure along with [...] Read more.

In this work, we outline the development of a thermodynamically consistent microscopic model for a suspension of aggregating particles under arbitrary, inertia-less deformation. As a proof-of-concept, we show how the combination of a simplified population-balance-based description of the aggregating particle microstructure along with the use of the single-generator bracket description of nonequilibrium thermodynamics, which leads naturally to the formulation of the model equations. Notable elements of the model are a lognormal distribution for the aggregate size population, a population balance-based model of the aggregation and breakup processes and a conformation tensor-based viscoelastic description of the elastic network of the particle aggregates. The resulting example model is evaluated in steady and transient shear forces and elongational flows and shown to offer predictions that are consistent with observed rheological behavior of typical systems of aggregating particles. Additionally, an expression for the total entropy production is also provided that allows one to judge the thermodynamic consistency and to evaluate the importance of the various dissipative phenomena involved in given flow processes. Full article

(This article belongs to the Special Issue Modeling and Simulation of Complex Fluid Flows)

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10 pages, 273 KiB

Open AccessArticle

Derivation of Two-Fluid Model Based on Onsager Principle

by Jiajia Zhou and Masao Doi

Entropy 2022, 24(5), 716; https://doi.org/10.3390/e24050716 - 17 May 2022

Cited by 2 | Viewed by 2270

Abstract

Using the Onsager variational principle, we study the dynamic coupling between the stress and the composition in a polymer solution. In the original derivation of the two-fluid model of Doi and Onuki the polymer stress was introduced a priori; therefore, a constitutive [...] Read more.

Using the Onsager variational principle, we study the dynamic coupling between the stress and the composition in a polymer solution. In the original derivation of the two-fluid model of Doi and Onuki the polymer stress was introduced a priori; therefore, a constitutive equation is required to close the equations. Based on our previous study of viscoelastic fluids with homogeneous composition, we start with a dumbbell model for the polymer, and derive all dynamic equations using the Onsager variational principle. Full article

(This article belongs to the Special Issue Modeling and Simulation of Complex Fluid Flows)

11 pages, 5286 KiB

Open AccessArticle

An Experimental and Numerical Investigation on Bubble Growth in Polymeric Foams

by Daniele Tammaro, Massimiliano M. Villone, Gaetano D’Avino and Pier Luca Maffettone

Entropy 2022, 24(2), 183; https://doi.org/10.3390/e24020183 - 26 Jan 2022

Cited by 6 | Viewed by 2824

Abstract

The cellular morphology of thermoplastic polymeric foams is a key factor for their performances. Three possible foam morphologies exist, namely, with closed cells, interconnected cellular structure, and open cells. In the gas foaming technology, a physical blowing agent, e.g.,

{CO}_{2}

or [...] Read more.

The cellular morphology of thermoplastic polymeric foams is a key factor for their performances. Three possible foam morphologies exist, namely, with closed cells, interconnected cellular structure, and open cells. In the gas foaming technology, a physical blowing agent, e.g.,

{CO}_{2}

or

N_{2}

, is used to form bubbles at high pressure in softened/melted polymers. As a consequence of a pressure quench, the bubbles grow in the liquid matrix until they impinge and possibly break the thin liquid films among them. If film breakage happens, the broken film may retract due to the elastic energy accumulated by the polymeric liquid during the bubble growth. This, in turn, determines the final morphology of the foam. In this work, we experimentally study the growth of

{CO}_{2}

bubbles in a poly(e-caprolactone) (PCL) matrix under different pressure conditions. In addition, we perform three-dimensional direct numerical simulations to support the experimental findings and rationalize the effects of the process parameters on the elastic energy accumulated in the liquid at the end of the bubble growth, and thus on the expected morphology of the foam. To do that, we also extend the analytic model available in the literature for the growth of a single bubble in a liquid to the case of a liquid with a multi-mode viscoelastic constitutive equation. Full article

(This article belongs to the Special Issue Modeling and Simulation of Complex Fluid Flows)

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32 pages, 1214 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

Nonequilibrium Thermodynamics of Polymeric Liquids via Atomistic Simulation

by Brian Joseph Edwards, Mohammad Hadi Nafar Sefiddashti and Bamin Khomami

Entropy 2022, 24(2), 175; https://doi.org/10.3390/e24020175 - 25 Jan 2022

Cited by 3 | Viewed by 3463

Abstract

The challenge of calculating nonequilibrium entropy in polymeric liquids undergoing flow was addressed from the perspective of extending equilibrium thermodynamics to include internal variables that quantify the internal microstructure of chain-like macromolecules and then applying these principles to nonequilibrium conditions under the presumption [...] Read more.

The challenge of calculating nonequilibrium entropy in polymeric liquids undergoing flow was addressed from the perspective of extending equilibrium thermodynamics to include internal variables that quantify the internal microstructure of chain-like macromolecules and then applying these principles to nonequilibrium conditions under the presumption of an evolution of quasie equilibrium states in which the requisite internal variables relax on different time scales. The nonequilibrium entropy can be determined at various levels of coarse-graining of the polymer chains by statistical expressions involving nonequilibrium distribution functions that depend on the type of flow and the flow strength. Using nonequilibrium molecular dynamics simulations of a linear, monodisperse, entangled C₁₀₀₀H₂₀₀₂ polyethylene melt, nonequilibrium entropy was calculated directly from the nonequilibrium distribution functions, as well as from their second moments, and also using the radial distribution function at various levels of coarse-graining of the constituent macromolecular chains. Surprisingly, all these different methods of calculating the nonequilibrium entropy provide consistent values under both planar Couette and planar elongational flows. Combining the nonequilibrium entropy with the internal energy allows determination of the Helmholtz free energy, which is used as a generating function of flow dynamics in nonequilibrium thermodynamic theory. Full article

(This article belongs to the Special Issue Modeling and Simulation of Complex Fluid Flows)

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18 pages, 323 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

Fluctuation-Dissipation Theorems for Multiphase Flow in Porous Media

by Dick Bedeaux and Signe Kjelstrup

Entropy 2022, 24(1), 46; https://doi.org/10.3390/e24010046 - 27 Dec 2021

Cited by 14 | Viewed by 3312

Abstract

A thermodynamic description of porous media must handle the size- and shape-dependence of media properties, in particular on the nano-scale. Such dependencies are typically due to the presence of immiscible phases, contact areas and contact lines. We propose a way to obtain average [...] Read more.

A thermodynamic description of porous media must handle the size- and shape-dependence of media properties, in particular on the nano-scale. Such dependencies are typically due to the presence of immiscible phases, contact areas and contact lines. We propose a way to obtain average densities suitable for integration on the course-grained scale, by applying Hill’s thermodynamics of small systems to the subsystems of the medium. We argue that the average densities of the porous medium, when defined in a proper way, obey the Gibbs equation. All contributions are additive or weakly coupled. From the Gibbs equation and the balance equations, we then derive the entropy production in the standard way, for transport of multi-phase fluids in a non-deformable, porous medium exposed to differences in boundary pressures, temperatures, and chemical potentials. Linear relations between thermodynamic fluxes and forces follow for the control volume. Fluctuation-dissipation theorems are formulated for the first time, for the fluctuating contributions to fluxes in the porous medium. These give an added possibility for determination of the Onsager conductivity matrix for transport through porous media. Practical possibilities are discussed. Full article

(This article belongs to the Special Issue Modeling and Simulation of Complex Fluid Flows)

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16 pages, 2833 KiB

Open AccessArticle

Crooks Fluctuation Theorem for Single Polymer Dynamics in Time-Dependent Flows: Understanding Viscoelastic Hysteresis

by Yuecheng Zhou, Folarin Latinwo and Charles M. Schroeder

Entropy 2022, 24(1), 27; https://doi.org/10.3390/e24010027 - 24 Dec 2021

Cited by 1 | Viewed by 2961

Abstract

Nonequilibrium work relations have fundamentally advanced our understanding of molecular processes. In recent years, fluctuation theorems have been extensively applied to understand transitions between equilibrium steady-states, commonly described by simple control parameters such as molecular extension of a protein or polymer chain stretched [...] Read more.

Nonequilibrium work relations have fundamentally advanced our understanding of molecular processes. In recent years, fluctuation theorems have been extensively applied to understand transitions between equilibrium steady-states, commonly described by simple control parameters such as molecular extension of a protein or polymer chain stretched by an external force in a quiescent fluid. Despite recent progress, far less is understood regarding the application of fluctuation theorems to processes involving nonequilibrium steady-states such as those described by polymer stretching dynamics in nonequilibrium fluid flows. In this work, we apply the Crooks fluctuation theorem to understand the nonequilibrium thermodynamics of dilute polymer solutions in flow. We directly determine the nonequilibrium free energy for single polymer molecules in flow using a combination of single molecule experiments and Brownian dynamics simulations. We further develop a time-dependent extensional flow protocol that allows for probing viscoelastic hysteresis over a wide range of flow strengths. Using this framework, we define quantities that uniquely characterize the coil-stretch transition for polymer chains in flow. Overall, generalized fluctuation theorems provide a powerful framework to understand polymer dynamics under far-from-equilibrium conditions. Full article

(This article belongs to the Special Issue Modeling and Simulation of Complex Fluid Flows)

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Review

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26 pages, 620 KiB

Open AccessReview

Some Recent Advances in Energetic Variational Approaches

by Yiwei Wang and Chun Liu

Entropy 2022, 24(5), 721; https://doi.org/10.3390/e24050721 - 18 May 2022

Cited by 9 | Viewed by 3043

Abstract

In this paper, we summarize some recent advances related to the energetic variational approach (EnVarA), a general variational framework of building thermodynamically consistent models for complex fluids, by some examples. Particular focus will be placed on how to model systems involving chemo-mechanical couplings [...] Read more.

In this paper, we summarize some recent advances related to the energetic variational approach (EnVarA), a general variational framework of building thermodynamically consistent models for complex fluids, by some examples. Particular focus will be placed on how to model systems involving chemo-mechanical couplings and non-isothermal effects. Full article

(This article belongs to the Special Issue Modeling and Simulation of Complex Fluid Flows)

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32 pages, 1028 KiB

Open AccessEditor’s ChoiceReview

Stochastic Hydrodynamics of Complex Fluids: Discretisation and Entropy Production

by Michael E. Cates, Étienne Fodor, Tomer Markovich, Cesare Nardini and Elsen Tjhung

Entropy 2022, 24(2), 254; https://doi.org/10.3390/e24020254 - 9 Feb 2022

Cited by 18 | Viewed by 3057

Abstract

Many complex fluids can be described by continuum hydrodynamic field equations, to which noise must be added in order to capture thermal fluctuations. In almost all cases, the resulting coarse-grained stochastic partial differential equations carry a short-scale cutoff, which is also reflected in [...] Read more.

Many complex fluids can be described by continuum hydrodynamic field equations, to which noise must be added in order to capture thermal fluctuations. In almost all cases, the resulting coarse-grained stochastic partial differential equations carry a short-scale cutoff, which is also reflected in numerical discretisation schemes. We draw together our recent findings concerning the construction of such schemes and the interpretation of their continuum limits, focusing, for simplicity, on models with a purely diffusive scalar field, such as ‘Model B’ which describes phase separation in binary fluid mixtures. We address the requirement that the steady-state entropy production rate (EPR) must vanish for any stochastic hydrodynamic model in a thermal equilibrium. Only if this is achieved can the given discretisation scheme be relied upon to correctly calculate the nonvanishing EPR for ‘active field theories’ in which new terms are deliberately added to the fluctuating hydrodynamic equations that break detailed balance. To compute the correct probabilities of forward and time-reversed paths (whose ratio determines the EPR), we must make a careful treatment of so-called ‘spurious drift’ and other closely related terms that depend on the discretisation scheme. We show that such subtleties can arise not only in the temporal discretisation (as is well documented for stochastic ODEs with multiplicative noise) but also from spatial discretisation, even when noise is additive, as most active field theories assume. We then review how such noise can become multiplicative via off-diagonal couplings to additional fields that thermodynamically encode the underlying chemical processes responsible for activity. In this case, the spurious drift terms need careful accounting, not just to evaluate correctly the EPR but also to numerically implement the Langevin dynamics itself. Full article

(This article belongs to the Special Issue Modeling and Simulation of Complex Fluid Flows)

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