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Entropy
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Modeling, Analysis, and Computation of Complex Fluids
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Modeling, Analysis, and Computation of Complex Fluids

A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Statistical Physics".

Deadline for manuscript submissions: 31 December 2025 | Viewed by 880

Special Issue Editor

Dr. Jia Zhao

E-Mail Website
Guest Editor
Department of Mathematics, University of Alabama, Tuscaloosa, AL 35487, USA
Interests: continuum, kinetic and multiscale theory of multiphase complex fluids; deep learning; mathematical biology; scientific computing; structure-preserving numerical PDEs

Special Issue Information

Dear Colleagues,

Multiphase complex fluids are ubiquitous in both natural and synthetic systems, such as emulsions, foams, biological materials, and advanced functional composites. They pose significant modeling, analysis, and computation challenges due to the couplings across multiple physical scales and phases.

This Special Issue of Entropy aims to highlight recent modeling, analysis, and computational developments in the study of multiphase complex fluids. Topics of interest include, but are not limited to, continuum, kinetic, and multiscale methods and models for complex fluids; multiphase fluid models such as phase-field models; non-equilibrium thermodynamics; and emerging applications in soft matter and biological systems. Research that leverages entropy-based principles, variational structures, and deep learning techniques to better understand the interplay between microstructure and macroscopic behavior is particularly welcome.

Dr. Jia Zhao
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 250 words) can be sent to the Editorial Office for assessment.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Entropy is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • multiphase flows
  • complex fluids
  • continuum and kinetic theory
  • multiscale modeling
  • phase-field methods
  • non-equilibrium thermodynamics
  • structure-preserving numerical methods
  • entropy-based modeling
  • soft matter physics
  • scientific computing

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Further information on MDPI's Special Issue policies can be found here.

Published Papers (2 papers)

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Research

24 pages, 2224 KB  
Article
Positivity-Preserving Hybridizable Discontinuous Galerkin Scheme for Solving PNP Model
by Diana Morales and Zhiliang Xu
Entropy 2025, 27(11), 1175; https://doi.org/10.3390/e27111175 - 20 Nov 2025
Viewed by 225
Abstract
We introduce a hybridizable discontinuous Galerkin (HDG) scheme for solving the Poisson–Nernst–Planck (PNP) equations. The log-density formulation as introduced by Metti et al. in their paper “Energetically stable discretizations for charge transport and electrokinetic models. J. Comput. Phys. 2016, 306, 1-18” is utilized [...] Read more.
We introduce a hybridizable discontinuous Galerkin (HDG) scheme for solving the Poisson–Nernst–Planck (PNP) equations. The log-density formulation as introduced by Metti et al. in their paper “Energetically stable discretizations for charge transport and electrokinetic models. J. Comput. Phys. 2016, 306, 1-18” is utilized to ensure the positivity of the densities of the charged particles. We further prove that our fully discrete scheme is energy stable and mass conserving. Numerical simulations are provided to demonstrate the accuracy of the scheme in one and two spatial dimensions. A derivation of an HDG-DG space–time scheme is given, with implementation and convergence analysis left to future work. Full article
(This article belongs to the Special Issue Modeling, Analysis, and Computation of Complex Fluids)
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33 pages, 2187 KB  
Article
Glymphatic Clearance in the Optic Nerve: A Multidomain Electro-Osmostic Model
by Shanfeng Xiao, Huaxiong Huang, Robert Eisenberg, Zilong Song and Shixin Xu
Entropy 2025, 27(11), 1174; https://doi.org/10.3390/e27111174 - 20 Nov 2025
Viewed by 423
Abstract
Effective metabolic waste clearance and maintaining ionic homeostasis are essential for the health and normal function of the central nervous system (CNS). To understand its mechanism and the role of fluid flow, we develop a multidomain electro-osmotic model of optic-nerve microcirculation (as a [...] Read more.
Effective metabolic waste clearance and maintaining ionic homeostasis are essential for the health and normal function of the central nervous system (CNS). To understand its mechanism and the role of fluid flow, we develop a multidomain electro-osmotic model of optic-nerve microcirculation (as a part of the CNS) that couples hydrostatic and osmotic fluid transport with electro-diffusive solute movement across axons, glia, the extracellular space (ECS), and arterial/venous/capillary perivascular spaces (PVS). Cerebrospinal fluid enters the optic nerve via the arterial parivascular space (PVS-A) and passes both the glial and ECS before exiting through the venous parivascular space (PVS-V). Exchanges across astrocytic endfeet are essential and they occur in two distinct and coupled paths: through AQP4 on glial membranes and gaps between glial endfeet, thus establishing a mechanistic substrate for two modes of glymphatic transport, at rest and during stimulus-evoked perturbations. Parameter sweeps show that lowering AQP4-mediated fluid permeability or PVS permeability elevates pressure, suppresses radial exchange (due mainly to hydrostatic pressure difference at the lateral surface and the center of the optic nerve), and slows clearance, effects most pronounced for solutes reliant on PVS–V export. The model reproduces baseline and stimulus-evoked flow and demonstrates that PVS-mediated export is the primary clearance route for both small and moderate solutes. Small molecules (e.g., Aβ) clear faster because rapid ECS diffusion broadens their distribution and enhances ECS–PVS exchange, whereas moderate species (e.g., tau monomers/oligomers) have low ECS diffusivity, depend on trans-endfoot transfer, and clear more slowly via PVS–V convection. Our framework can also be used to explain the sleep–wake effect mechanistically: enlarging ECS volume (as occurs in sleep) or permeability increases trans-interface flux and accelerates waste removal. Together, these results provide a unified physical picture of glymphatic transport in the optic nerve, yield testable predictions for how AQP4 function, PVS patency, and sleep modulate size-dependent clearance, and offer guidance for targeting impaired waste removal in neurological disease. Full article
(This article belongs to the Special Issue Modeling, Analysis, and Computation of Complex Fluids)
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