Zeitschrift

Transport Phenomena

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Sprache: Englisch

Erstveröffentlichung: 1. Januar 2026

Erscheinungsweise: 4 Hefte pro Jahr

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Über diese Zeitschrift

Transport Phenomena (TP) was launched in 2025, alongside its sibling journal Open Transport (OT), to serve as a leading general science venue dedicated to advancing the understanding of flow, heat, and diffusion, and their complex interplay in all states of matter—solid, liquid, or gas.

Both journals share an identical scientific scope, editorial team, and editorial standards, differing only in their publishing models.

Aims and Scope
Transport Phenomena serves the global transport community as its leading general science hybrid title, showcasing the latest advances in fluid dynamics, heat transfer and mass transfer.

With enthusiasm, Transport Phenomena publishes intriguing, elegant, fascinating and important advances in and between these three cognate transport sciences.
Rooted respectively in the conservation principles of momentum, energy and mass, Transport Phenomena attracts contributions from all subdisciplines of the physical and biological sciences, applied mathematics and thus, from all branches of engineering.

Transport Phenomena deepens our understanding across the transport sciences, and advances its applications. The journal conducts rigorous and fair peer-review and aims to attract original, tenure accruing contributions, through which the journal endeavors to bring out the very best in the transport community.

Transport Phenomena is a subscription journal with the option of open access publication. All contributions submitted for publication in Transport Phenomena are single-blind peer reviewed. The publication language is English. The publication frequency is continuously.

Explore TEAPOT Press

Joint Special Collections open for subm issions:

Tribute to James C. Wu for Seven Decades of Pioneering Research
Guest editors: Joseph C. Majdalani (Auburn University, USA), Vigor Yang (Georgia Institute of Technology, USA)
Submission Deadline: June 30, 2026

Vortex Fluids Mechanics
Guest editor: Wang Fang (Beihang University, Beijing, China)
Webpage: https://icvfm2025.scimeeting.cn/en/web/index/28196_2433696
Submission Deadline: June 30, 2026

Plasma Droplets
Guest editor: Yang Li u (City College of New York, USA)
Webpage: https://schedule.aps.org/dfd/2025/events/Z08
Submission Deadline: June 30, 2026

Recent Advancements in Physical Sciences
Guest editor : Dharmendra Tripathi (National Institute of Technology, Uttarakhand, India)
Webpage: https://nituk.ac.in/icraps26/
Submission Deadline: June 30, 2026

Recent Advancements in Applied Mathematics and Computational Sciences
Guest editor: Dharmendra Tripathi (National Institute of Technology, Uttarakhand, India)
Webpage: https://sites.google.com/view/raamc202 6/publication
Submission Deadline: June 30, 2026

Tribute to Dav id Vernon Boger (1939–2025)
Guest editors: Alan Jeffrey Giacomin (University of Nevada, Reno, USA), Natalie Germann (University of Stuttgart, Germany), Nhan Phan-Thien (National University of Singapore, Singapore, and Zhejiang University, China), Rosanna Pasquino (University ofN aples Federico II, Italy)
Webpage: https://www.icr2027.com/En/Menu/TechnicalSessions
Submission Deadline: July 31, 2026
75th Anniversary of the German Society of Rheology
Guest editors: Jane Awayes (TU Berlin, Main Symposium Organizer), Oliver Löschke (TU Berlin, DRG Board Member, Symposium Organizer), Erik Wassner (BASF, DRG President), Hans-Joachim Schmid (Paderborn University, DRG Board Member)
Webpage: https://drg-rheol ogie.de/aktuelles/veranstaltungen/75-jahre-drg-symposium/
Submission Deadline: October 8, 2026

All submissions to the Special Collections must be made electronicall y via online submis sion system EditorialMa nager.

Article Types
Article, Letter, Review, Perspective, Tutorial, Book Review, Editorial, Announcement, Special Collection

Key Strengths
The following topical strengths reflect the journal’s broad and interdisciplinary scope :
3D printing flows, Acoustics, Aerodynamics, Aerosols, Aerospace and aeronautical flows, Artificial intelligence and flows, Artistic flows, A stronomical flows, Astrophysical flows, Biofluid mechanics, Bioinspired flows, Biomedical flows, Biomicrofluidics, Boiling, condensation, and evapora tion, Bursting, Capillary flows, Catalytic conversion, Cavitation and cavitating flows, Cel l biomechanics and flows, Chaotic flows, Chemically reacting flows, C ivil Structure, Clouds, CO₂ flows, Colloids, Combustion flows, Compl ex fluids, Compressible flows, Computational fluid dynamics, Computational fluid physics, Computers and fluids, Confined flo ws, Contact lines, Continuum mechanics, Convection, Convective heat transfer, Cou pled transport, Creep, compliance, and recovery, Cryogenic flows, Crystallization and flows, Data-driven fluids research, Diffusion and diffusivity, Digital twin flows, Drag reduction, Droplets, Electrical and magnetic effects in fluid flows, Electrokinetics, Electrothermal flows,Em ulsi ons , Enhanced oil recovery, Experiments in fluids, Field-driven motion, Film flows, Flow control, Flow instability and transition, Flow orientation and anisotropy, Flow through porous media, Flows over patterned substrates, Flows with other transport phenomena, Flows with complex boundary conditions,F low visualization, Fluid mechanics, Fluid physical properties, Fluid–structure interaction s , Foam, bubble, and film m echanics, Food, Fracking, Fracture and flows, Free surface flows, Fuel cell processes, Gels, Ge ophysical flo ws, Georheology, Glasses, History of transport phenomena, Hydraulics, Hydraulic fracture, Hydrodynamics, Hydrophobicity, Ioni c conduction, Imbibition, Interfacial flows, Jet flows, Kitchen flows, Knud sen flows, Laminar flows, Liquid crystals, Lubrication and tribology, Machine learning, Marangoni flows, Mathematics of fluids, Membrane separation, Meteorological flows, Micro- and nanofluid mechanics, Microfluidics, Microreactor flows, Mineral exploration flows, Mining flows, Mixing, Mole cu lar liquids, Molecular theory, Multiphase flows, Musical instruments, Nanofluidics, Nanoparticle dynamics, Neuromorphic flows, Oil and gas flows, Partic ulate and granular flows, Petrochemical exploration flows, Pharmaceutical and pharmalogical transport, Philosophy of transport phenomena, Physical geometry and flows, Physics of plasma, Polymer processing, Polymeric liquids, Processing flows, Pr opulsion, Quantum h eat transport, Quantum hydrodynamics, Rad iative heat transfer, Reactive flows, Relativistic fluid mechanics, Rh eology, Rotating flows, Sedim entation, Shock wave phenomena, Smart fluid behavior, Soft matter, Solar t hermal flows, Solvent exchange, Speech and hearing, Statistical mechanics of flows, Statisti cs of flows, Stratified flows, Supercooled liquids, Supercritical fluids, Superfluidity, Superhydrophobicity, Suspensions, Swarming flows, Swimming, Thermodiffusion, Thermodynamics of flows, Thermoelectric effects, Topological transport, Transonic flows, Transportation, Turbulent flows,Vis cou s and non-Newtonian flows, Viscoelasticity, Vortex dynamics, Waves, Wearable fluidics, Wicking, Wind

Sibling journal: Open Transport.

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Does “non-detect” sorption matter to contaminant transport in groundwater?

21. April 2026

Ana Sofia Piña Santillan, Alejandro G. Marangoni, Erica Pensini

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Sulfolane is a groundwater-miscible pollutant that is widely reported to exhibit negligible sorption onto minerals. Yet sub-monolayer uptake can evade detection in conventional batch tests while still affecting plume evolution over transport distances. Here we combine synchrotron soft X-ray spectroscopy, electronic-structure calculations, and transport modeling to test whether “undetectable” sorption can matter at the aquifer scale. Using O K-edge X-ray absorption spectroscopy (XAS) in a liquid flow cell with silicon nitride windows, we observe a sulfolane signal after flushing with water, consistent with slow desorption or irreversible retention on experimental timescales despite negligible sorption inferred from batch measurements. Complementary electronic-structure calculations support the plausibility of sub-monolayer sulfolane association on hydrated motifs representative of calcite and iron hydroxides, for which laboratory studies have reported no detectable uptake. We quantify transport implications of low-capacity interactions using two frameworks: (i) a capacity-limited storage model that represents finite interfacial capacity and (ii) a kinetic sink model that treats uptake as rate-limited removal rather than instantaneous equilibrium partitioning. Across soils spanning specific surface areas and site densities, even sub-monolayer surface excess can attenuate dissolved concentrations over kilometer-scale distances under plausible parameter combinations. Under sustained releases, the solid phase can accumulate inventories comparable to the dissolved mass while progressively saturating capacity along the flow path. This distributed surface reservoir is poised to desorb under changing conditions (e.g., dilution or geochemical shifts), sustaining long-term residual aqueous concentrations even when equilibrium sorption appears negligible. Although focused on sulfolane, the same mechanism may apply to other mobile groundwater contaminants.
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Drag reduction study of imposed axial flow in Taylor Couette flow

17. März 2026

Md Abdur Razzak, Khoo Boo Cheong, C.M. Jonathan Tay, Naseeb Ahmed Siddiqui

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This study investigates effect of externally imposed axial-flow in Taylor-Couette flow (TCF) with smooth rotating inner-cylinder and stationary outer-cylinder for radius ratio = 0.5, and Re = 60 to 650. Previous studies by Razzak et al. [M. A. Razzak, B. C. Khoo, and K. B. Lua, “Numerical study on wide gap Taylor Couette flow with flow transition,” Phys. Fluids , vol. 31, no. 11, 2019, M. A. Razzak, B. C. Khoo, and K. B. Lua, “Numerical study of Taylor Couette flow with longitudinal corrugated surface,” Phys. Fluids , vol. 32, no. 5, 2020, Drag reduction study of naturally occurring oscillating axial flow induced by helical corrugated surface in Taylor–Couette flow,” Phys. Fluids , vol. 35, no. 8, p. 083608, 2023] showed that macroscale corrugated surfaces in TCF passively generate axial secondary flows and reduce drag without external power, but their complex design limits practical use in turbomachinery. To overcome this, present study applies external axial-flow without altering cylinder geometry to evaluate its effect on torque and power. Unlike earlier periodic-boundary studies, parabolic inlet velocity and outflow condition are imposed at the cylinder ends. Three axial-flow types are examined steady (non-zero), oscillating with non-zero mean, and oscillating with zero-mean and results are compared with baseline TCF(no axial-flow) from Razzak et al. [M. A. Razzak, B. C. Khoo, and K. B. Lua, “Numerical study on wide gap Taylor Couette flow with flow transition,” Phys. Fluids , vol. 31, no. 11, 2019] for same radius and aspect ratios. Based on results, Taylor-vortices are found to be stretched along axial direction under the application of axial-flows. This was found to suppress the strength of jet impingement at the inner wall resulting in torque and power reduction for Re ≤ 450 and Re ≥ 540. In contrast, within range 450 < Re < 540, stronger naturally induced axial-flows in baseline case achieve better suppression, leading to lower torque than the externally applied axial-flow cases. Among the three axial-flow types, steady axial-flow yields the greatest vortex stretching and jet impingement suppression, resulting in the highest torque and power savings. Adding oscillation with non-zero mean slightly weakens these effects, while zero-mean oscillation offers the least suppression and torque reduction. Overall, stronger imposed axial-flow can further enhance drag reduction, offering a geometry-independent control for TCF.
Open Access
Pattern suppression and recovery under one-way versus two-way chemotactic coupling in hybrid partial differential equation–ordinary differential equation models

13. März 2026

Jiguang Yu, Louis Shuo Wang, Zonghao Liu, Jingfeng Liu

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We study coupled mass transport in a tumor–microenvironment regime with two motile densities ( S , R ) and non-motile state switching ( P , A ). The populations diffuse and undergo chemotactic drift; ( P , A ) follow pointwise ODE switching. A decoupled inhibitory field D satisfies a damped Neumann heat equation, giving maximum-principle bounds and exponential decay. Together with the pointwise invariant P + A , these identities yield global existence, positivity, and long-time reduction to limiting ( S , R ) kinetics with a unique globally attracting coexistence state. Neumann eigenmode reduction gives closed dispersion relations. The base ( S , R ) reaction–diffusion (RD) block remains stable for all nonconstant modes for any d S , d R > 0, excluding classical Turing destabilization. Chemotaxis is posed via a diffusive cue c , since ∇ A is undefined for non-diffusive A . In one-way damped coupling, the linearized mode matrix is block triangular and leaves the ( S , R ) spectrum unchanged. Two-way coupling adds a feedback rank-one mobility correction, induces effective cross-diffusion, and admits mode growth. We give explicit trace/determinant criteria for unstable Laplacian modes and the resulting instability thresholds.
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Spontaneous axis-switching swirling in transonic core-annular flow of highly differentiated fluids

4. März 2026

Wayne Strasser, Aleck Tilbrook, Daniel Wilson

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Forcing fluids to interact at high speeds creates a multitude of instabilities. Prior studies considered the consequences of these instabilities for core-annular flow (CAF) or atomization systems. However, the existence of spontaneous axis-switching swirling (SASS) modalities in CAF have never been explored. We computationally demonstrate this new behavior for a CAF of steam surrounded by a cold non-Newtonian fuel. Wave pile-up created 3-D fuel surface disturbances which eventually became thin slender lobes with radial modal deformation. Those slender lobes were subject to further instabilities and resulted in oscillatory tangential velocities that were a large fraction of the core steam velocity and orthogonal to the axially flowing base fuel wave. Since these tangential velocities were not externally imposed by atomizer geometry or boundary conditions, it was concluded that they are self-generating. Frequency analysis revealed that SASS tended to operate at the base wave frequency. We additionally explored numerical uncertainty with our previously validated computational tool and found that SASS behavior can be achieved on a coarse, limited mesh at relatively low simulation times.
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From columns to heaps: dimensionless similarity with particle-size-distributed Damköhler numbers and dual-porosity flow

2. März 2026

Juan J. Segura

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This work develops a unified, dimensionless framework for comparing reacting systems that are geometrically similar but differ in size, particle size distribution (PSD), and internal pore structure of the solid reactant, with emphasis on hydrometallurgical heap leaching. For two heaps operated under dynamically similar hydrodynamic conditions, the dimensionless residence time distribution (RTD) of the liquid is identical. However, differences in PSD and internal porosity break microscopic similarity and can strongly alter heap-scale conversion. Using the shrinking-core model (SCM), we show how a PSD induces a distribution of particle-scale Damköhler numbers that controls the heap-averaged conversion. We derive explicit change-of-variable expressions mapping a PSD in particle diameter to Damköhler-number distributions for (i) external film (convection) control, (ii) intraparticle diffusion control, and (iii) mixed control approximated by additive resistances. We then couple SCM kinetics to dual-porosity hydrology (mobile/immobile liquid domains) and identify the additional dimensionless groups governing interporosity exchange. Two numerical examples illustrate the approach: (1) transforming a lognormal PSD into external- and diffusion-controlled Damköhler distributions, and (2) a toy column/heap calculation comparing conversion trajectories for different PSDs under film versus diffusion control. Finally, we outline a practical workflow for column-test interpretation, combining SCM diagnostics with tracer-derived RTD and exchange parameters. The framework explains the heightened sensitivity of diffusion-controlled systems to PSD tails and dual porosity and provides a compact set of dimensionless groups for robust scale-up from columns to industrial heaps.
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A conservative master equation in logarithmic size for fragmentation population-balance equations: jump transport, drift–diffusion asymptotics, and particle-size distribution inference

24. Februar 2026

Juan J. Segura

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Fragmentation population-balance equations describe how particle-size distributions evolve under breakage and daughter fragment redistribution. By log-size we mean the logarithmic internal coordinate ξ = ln( x / x 0 ), where x is a size-like variable taken proportional to a conserved mass. From a standard self-similar fragmentation class we derive an exact conservative transport equation in ξ for the normalized mass fraction : a state-dependent pure-jump master equation (nonlocal internal-coordinate mass transfer). We also give an explicit Gorini–Kossakowski–Sudarshan–Lindblad (GKSL) factorization whose diagonal sector reproduces this master equation, used here as an optional structure-preserving operator representation and constrained parameterization for inverse modeling. In a controlled small-jump regime, the nonlocal jump transport reduces to a drift–diffusion (Fokker–Planck) operator in log-size space. Under detailed-balance conditions this operator admits the standard symmetrization to a self-adjoint Schrödinger-type spectral problem, motivating compact parametric hypothesis classes for distribution shapes. We then present two inverse routes: (i) time-resolved parametric fitting of transport/spectral parameters, and (ii) a regularized steady inversion that reconstructs an effective potential from a measured steady PSD. We include numerical benchmarks: forward simulation of the jump transport model (continuous-time Markov chain discretization) and its drift–diffusion reduction, quantitative discrepancy metrics, and inverse parameter recovery on an Airy half-line synthetic benchmark under multiplicative noise.
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Eyring’s rate theory and its connection to entropy scaling: viscosity and self-diffusion of hydrocarbons, alcohols, and water

19. Februar 2026

Maximilian Fleck, Marcelle B. M. Spera

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Eyring’s absolute rate theory relates fluid flow with the activation energy necessary for a molecule to go from one equilibrium position to another. Developed nearly a century ago, it remains a powerful approach for understanding transport processes in liquids. This work presents a revision of Eyring’s theory by replacing the vaporization-based parts of the theory with a residual approach that conceptualizes transport as local (re)movement of molecules within the system rather than removal from it. In this new approach, the energy barrier corresponds to the difference between a molecule with and without intermolecular interactions, effectively treating it as the residual property related to an ideal gas reference state. Furthermore, we explore the physical connections between Eyring’s absolute rate theory and Rosenfeld excess entropy scaling, revealing that both approaches describe complementary aspects of the same transport phenomena. It is tempting to link both theories. The activation parameters in Eyring’s theory, particularly the energy of activation, are shown to relate to the residual entropy used in entropy scaling. This provides a pathway to establish entropy scaling on a more rigorous physical foundation while offering deeper insights into the molecular mechanisms governing viscous flow. In comparison to experimental data, the revised theory demonstrated significant predictive power for viscosity across a wide range of thermodynamic conditions and species, including associating liquids. Moreover, parameters are transferable to other properties, such as self-diffusion.
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Entropy-time geodesics as a universal framework for transport and transition phenomena

16. Februar 2026

Sami Lakka

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We develop a geometric framework for irreversible transport phenomena in which macroscopic evolution equations arise from the combined structure of a thermodynamic state metric and an Onsager-based dissipation metric. The construction begins by defining a pseudo-Riemannian manifold from the Hessian of an appropriate thermodynamic potential. When the enthalpy is used and written in variables ( S , P ), the resulting metric possesses a Lorentzian-type signature: entropy acts as a time-like coordinate, while pressure forms a spatial-like coordinate associated with mechanical response. Local irreversible dynamics are incorporated through the inverse Onsager matrix, which defines a positive-definite dissipation metric on the space of fluxes and gradients. A thermodynamic action integrating these two geometric layers yields geodesic evolution equations. For a Newtonian fluid with constant viscosity, the resulting Euler–Lagrange equations reproduce the incompressible Navier–Stokes equations without requiring an externally imposed constitutive closure. Within this framework, turbulence scaling emerges from competition between inertial curvature and dissipation metric stiffness. The Kolmogorov length scale appears as a minimum geometric resolution length where these contributions balance, providing a geometric interpretation of energy cascade termination and dissipation onset. Finite-time singularities in the classical PDE formulation correspond to curvature divergences in the transport geometry; however, the thermodynamic proper time diverges in such limits, suggesting that blow-up is dynamically suppressed in single-phase continua. Breakdown occurs only when the thermodynamic metric itself becomes degenerate, such as at cavitation or critical points where compressibility or heat capacity diverge, corresponding to a change in manifold topology. Although derived explicitly for fluid flow, the framework is general: by choosing different thermodynamic potentials and Onsager matrices, the same geometric formulation applies to heat conduction, diffusion, electrochemical transport, and other irreversible processes. The results provide a unified thermodynamic geometric basis for transport equations, clarify the conditions under which continuum models remain valid, and offer a new interpretation of turbulence scaling and phase-transition-induced breakdown.
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The study of coherent Rayleigh-Brillouin scattering in multiple flow regimes using unified gas-kinetic scheme

16. Februar 2026

Xiaozhe Xi, Junzhe Cao, Kun Xu

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Coherent Rayleigh-Brillouin scattering (CRBS) holds great promise for the characterization of gas properties and the investigation of gas kinetic processes. The CRBS spectrum exhibits a strong dependence on the Knudsen number (Kn), revealing its inherently multiscale nature. In the unified gas-kinetic scheme (UGKS), collisions are intrinsically coupled with free transport during flux construction, endowing the method with distinct multiscale capabilities. Specifically, the UGKS reduces to a Boltzmann solver when the relaxation time τ ≥Δ t , and to the gas-kinetic scheme (GKS)-a Navier–Stokes solver-when τ ≪Δ t , thereby accommodating flow regimes without constraints on the molecular mean free path or collision time. In this study, the UGKS is extended to simulate CRBS phenomena, with the governing equation formulated based on the Bhatnagar–Gross–Krook (BGK)-Shakhov model. Detailed derivations are provided. To account for the additional perturbation source term, a second-order accurate numerical algorithm is developed using the Strang splitting method within the UGKS framework. The proposed model is validated against argon CRBS experiments, demonstrating excellent agreement. Building on this validated framework, the impact of incident signal intensity on CRBS spectra across a range of Knudsen numbers is systematically examined, accompanied by an in-depth analysis of the underlying physical mechanisms. This work broadens the applicability of computational fluid dynamics (CFD)-based CRBS simulations and provides a reliable numerical foundation for exploring high-intensity, multiscale gas-kinetic phenomena in future research.
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Ten lectures on turbulence: 1. turbulent structures

6. Februar 2026

Cunbiao Lee

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This paper discusses the structure of turbulence, categorizing it into elementary structures and composite structures, while also outlining the discovery processes of these structures. It strives to present the different viewpoints regarding their formation, with a focus on describing their dynamic roles in the process of turbulence formation. This paper does not critique past interpretations, as researchers at the time had limited and possibly one-sided evidence. The author also presents an own understanding of the physical processes and dynamic relationships involved in the formation of these structures, offering reasonable explanations for these processes.
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Scale-dependent velocity fluctuations generated by molecular collisions

6. Februar 2026

Tristan Barkman

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A discrete binomial random-walk description of molecular collisions is used to quantify the variance of coarse-grained velocity fields arising solely from collision-induced momentum exchange. Closed-form expressions for the growth of velocity variance as functions of coarse-graining scale and time are derived and shown to imply a power-law decay of variance with averaging scale. Particle-based ensemble simulations validate the predicted scaling and temporal behaviour; surrogate ensemble tests demonstrate that phase/temporal coherence is required for the observed integrated transfer diagnostics. The analysis is intentionally restricted to collision-generated fluctuations in quiescent fluids and does not model cascade dynamics; implications for possible amplification under inertial dynamics are discussed cautiously. All data and the minimal verification instructions required to reproduce the summary tables are embedded in Appendix.
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Dynamics of motions and deformations of an arbitrary-geometry flexural floe in ocean waves

6. Februar 2026

Andrei Ludu

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This paper develops a comprehensive mathematical framework for modeling the coupled hydroelastic dynamics of sea-ice floes of arbitrary shape and non-uniform thickness under linear ocean wave forcing, with particular emphasis on oblique wave incidence. We simultaneously incorporate all six rigid-body motions (heave, surge, sway, roll, pitch, and yaw) and the complete spectrum of flexural deformation modes within a unified Green’s function formulation. The water flow is modeled using potential theory governed by Laplace’s equation, while the floe obeys the generalized Kirchhoff-Love plate equation with spatially varying flexural rigidity. We formulate the coupled fluid-structure interaction problem through kinematic velocity-matching conditions and dynamic pressure-continuity conditions at the ice-water interface. The submerged floe geometry is represented as a non-axisymmetric, piece-wise smooth orientable surface parameterized by a piece-wise differentiable draft function, accommodating realistic irregular features including thickness variations, keels, and submerged ridge structures. The elastic eigenproblem with free-edge boundary conditions yields a complete orthogonal basis of deformation modes, accounting for added-mass effects through modified natural frequencies. By decomposing the velocity potential into partial potentials associated with incident waves, scattered waves, rigid motions, and elastic modes, we reduce the problem to a system of Fredholm integral equations of the second kind for surface density functions on all boundary segments. We derive the complete 6 × 6 mass, added-mass, and hydrostatic stiffness matrices for floes of arbitrary geometry, enabling analysis of fully coupled dynamics. A numerical implementation is developed and validated against multiple floe geometries, including elliptical disk-cone configurations and complex asymmetric shapes with variable thickness and ice keels. Results demonstrate that oblique wave incidence excites all six rigid degrees of freedom, with significant energy exchange between rigid motions and flexural modes near resonance conditions. The Response Amplitude Operators (RAOs) reveal geometry-dependent resonance phenomena and strong coupling between modes for non-symmetric configurations. Energy budget analysis quantifies the distribution among heave, surge, sway, roll, pitch, and elastic deformation modes across the frequency spectrum.
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On the cocycle structure of the Boltzmann distribution

4. Februar 2026

Chuan-Tsung Chan, Chan-Yi Chang, Zhong-Tang Wu

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Based on a cocycle structure, we identify a new derivation of the Boltzmann distribution for finite energy-level systems from the maximal entropy principle (MEP). Our approach does not rely on the method of the Lagrange multiplier, and it provides a more transparent way to understand the dependence on the energy levels of the temperature T = 1/ β for the equilibrium distribution. Finally, we make two curious observations associated with our derivations.
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Closed form solution of plane turbulent boundary flow – solution process, validity conditions and extension

3. Februar 2026

Bo Hua Sun

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The Prandtl mixing length plane turbulent boundary flow is governed by the nonlinear ordinary differential equation (ODE): d u + d y + + κ 2 y + 2 d u + d y + 2 = 1 $\frac{\mathrm{d}{u}^{+}}{\mathrm{d}{y}^{+}}+{\kappa }^{2}{{y}^{+}}^{2}{\left(\frac{\mathrm{d}{u}^{+}}{\mathrm{d}{y}^{+}}\right)}^{2}=1$ with boundary condition y + = 0 : u + = 0. Although van Driest first derived the closed-form solution for this ODE in 1956 (E. R. van Driest, “On turbulent flow near a wall,” J. Aeronaut. Sci. , vol. 23, no. 11, pp. 1007–1011, 1956), but the lack of detailed solution process led to its long-term neglect in subsequent fluid mechanics textbooks and research. As a result, the problem of finding the solution has remained an open question in the community. In this work, we independently rederive the solution and provide a complete, step-by-step solution process. Furthermore, we explicitly clarify the validity conditions of the solution (i.e., smooth wall, zero pressure gradient, fully developed turbulent flow, incompressible flow) and propose a modified analytical extension that conforms well to direct numerical simulation (DNS) results. The proposed modification incorporating van Driest-type damping into the solution framework is physically motivated, and this extension is semi-empirical, thus should be interpreted as a model enhancement/refinement rather than an exact mathematical solution. The present work not only supplements the missing solution details of van Driest’s solution but also improves its applicability.
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Axial symmetric Navier Stokes equations and the Beltrami/antiBeltrami spectrum in view of Physics Informed Neural Networks

30. Januar 2026

Pietro Fré

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In this paper, I further continue an investigation on Beltrami Flows began in 2015 with A. Sorin and amply revised and developed in 2022 with M. Trigiante. Instead of a compact 3-torus T 3 = R 3 / Λ ${T}^{3}={\mathbb{R}}^{3}/{\Lambda}$ where Λ is a crystallographic lattice, as done in previous work, here I considered flows confined in a cylinder with identified opposite bases. In this topology I considered axial symmetric flows and found a complete basis of axial symmetric harmonic 1-forms that, for each energy level, decomposes into six components: two Beltrami, two antiBeltrami and two closed forms. These objects, that are written in terms of trigonometric and Bessel functions, constitute a function basis for an L 2 space of axial symmetric flows. I have presented a general scheme for the search of axial symmetric solutions of Navier Stokes equation by reducing the latter to a hierachy of quadratic relations on the development coefficients of the flow in the above described functional basis. It is proposed that the coefficients can be determined by means of a Physics Informed like Neural Network optimization recursive algorithm. Indeed the present paper provides the theoretical foundations for such an algorithmic construction that is planned for a future publication.
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Constraints on constitutive relations in turbulence modeling

30. Januar 2026

Varangrat Juntasaro

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The formulation of constitutive relations is central to turbulence modeling, yet their evolution has always been constrained by requirements of physical consistency, mathematical well-posedness and numerical stability. This review integrates these constraints into a unified framework, tracing how they have shaped the trajectory of turbulence closures from classical formulations to contemporary data-driven approaches. Fundamental principles including conservation laws, realizability, invariance, dimensional homogeneity, memory effects and asymptotic consistency delineate the admissible space of models while simultaneously guiding their refinement. Historical progress, from the Boussinesq approximation through nonlinear eddy-viscosity models to explicit algebraic stress closures, demonstrates the progressive incorporation of such constraints as corrective mechanisms that enhance robustness and predictive fidelity. In parallel, recent advances in physics-informed and machine learning-based models confirm that these same constraints remain indispensable for ensuring generalizability, physical admissibility and solver compatibility. By framing turbulence modeling through the lens of constraints, this review highlights their dual role as both limitations and design principles while underscoring their continuing relevance in shaping next-generation hybrid frameworks that unite physical rigor with data-driven adaptability.
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Liouville spectral gap and bifurcation-driven Lagrangian–Eulerian decoupling with nondiffusive turbulence closures

29. Januar 2026

Nicola de Divitiis

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In fully developed homogeneous and isotropic turbulence, the Lagrangian and Eulerian descriptions of motion, although formally equivalent, become statistically decoupled. In this work, by invoking Liouville theorem, we show that the joint probability density function (PDF) of the Eulerian and Lagrangian fields, evolving from arbitrary initial conditions, relaxes exponentially toward a factorized form given by the product of the corresponding marginal PDFs. This relaxation is governed by a genuine spectral gap of the Liouville operator, whose magnitude is primarily set by the bifurcation rate of the velocity-gradient dynamics, whereas the contribution of Lyapunov exponents is shown to be significantly smaller. As a consequence, Eulerian–Lagrangian correlations decay rapidly, and if the joint PDF is initially factorized, its factorized structure is preserved at all subsequent times, with each marginal evolving independently under the corresponding dynamics. We further show that the formal equivalence between the two descriptions implies the invariance of the relative kinetic energy between arbitrarily chosen points. When combined with the asymmetric statistics of instantaneous finite-scale Lyapunov exponents in incompressible turbulence, this property provides a quantitative interpretation of particle-pair separation and of the turbulent energy cascade. Finally, these results naturally lead to nondiffusive closure relations for the von Kármán–Howarth and Corrsin equations, which coincide with those previously proposed by the author, thereby providing an independent theoretical validation of those closures.
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Functional trends and rheological evaluation of polyurethane microcapsules in dermato-cosmetic applications

12. Januar 2026

Sharadwata Pan, Andreas Wierschem, Natalie Germann, Thomas Becker

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To date, natural and synthetic polymer-based microcapsules have been used extensively in various dermato-cosmetic applications, with an emphasis on the targeted delivery of active ingredients, including therapeutic and aesthetic interventions. Although numerous polymer candidates have been comprehensively investigated, polyurethane based microcapsules have received comparatively minor attention, despite possessing a multitude of intrinsic benefits. However, in recent years, although there has been an upsurge of studies involving polyurethane, predominantly as a capsule wall or shell component, towards tangible dermato-cosmetic applications, these are only intermittently documented. In the current review, we target this lacuna, explore, and collate only the most contemporary trends and advances (2017-to date) in the field. In addition, despite the significance, and pertaining to the acute deficiency of rheological studies targeting polyurethane-based microcapsules in dermato-cosmetic applications, we critically examine and lay a comprehensive interpretation, based on the current state-of-the-art, inevitability for systematic inquiries, and identification of several target domains that need urgent attention. Finally, we deliberate on the challenges and the impending projections from a diverse outlook. We focus on a steady and more sustainable path forward via incorporation of green raw materials, cumulative domain-optimized and customer-focused applications, and a significantly improved understanding of the microcapsule mechanical behavior via implementation of novel rheological characterization procedures.
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Designing flaxseed oil-in-water emulsion-based stimuli-responsive edible films

6. Januar 2026

Ezgi Pulatsu, Leticia Lam Hon Wah, Chibuike C. Udenigwe

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Emulsions are useful for formulating compartmentalized structures with tunable characteristics, making their dried state a potential stimuli-responsive edible substrate for four-dimensional (4D) printing applications. Yet, establishing component, microstructure, and response relationships is crucial for controlled transformations under stimulus exposure, thereby enabling the technology for edible applications. The oil phase incorporation requires particular attention, due to its hydrophobicity and its impact on the response behavior, which can be determined by the swelling rate during water immersion tests. This study focused on flaxseed oil-in-water (O/W) emulsion-based edible films, stabilized by gelatin and lecithin. The dried films based on two oil-to-water (O:W) ratios (5:95 and 10:90 v/v), were submerged in distilled water (pH: 4, 7, and 10). The film-forming emulsions were yield stress fluids exhibiting solid-like properties in the linear viscoelastic region. Network strength and connectivity of emulsions were significantly different based on complex modulus as a function of frequency ( p < 0.05). The films were characterized via thickness (0.19–0.66 mm), weight (0.41–1.18 g), moisture content, opacity, and color. The film matrix properties affected the response behavior of the samples depending on the swelling media. The film survivability depended on the swelling medium pH ( p < 0.05). All samples remained intact overnight at pH 4 and 7. Only sample 5O95W-10 swelled up to 60 min at pH 10, which can be attributed to longer gel setting time and the presence of more protein and emulsifier allowing better network connectivity. Swelling rates of the films were similar at pH 4 and pH 7 ( p > 0.05), and their governing mechanism was less Fickian diffusion. Understanding the effects of the oil phase and the pH of the swelling medium on the response behavior provides insights for tailoring these films as novel substrates for 4D printing and enables controlled transformations.
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Effects of long-chain branching, short-chain branching, and polydispersity on pressure sensitive rheology of polymer melts

22. Dezember 2025

Lilian Lin, Matthew Joe, Heon E. Park

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The rheological behavior of polymer melts under high pressure is a critical factor in many industrial processes like injection molding and extrusion, yet it is often inadequately characterized. At operating pressures that can exceed 100 MPa, viscosity can increase by orders of magnitude, making atmospheric-pressure data insufficient for accurate process simulation. This pressure-induced viscosity increase is highly dependent on molecular architectures of the materials. This study aims to deconstruct the influence of specific structural features such as short-chain branching (SCB), long-chain branching (LCB), and polydispersity on the pressure sensitivity of the viscosity of polyethylene. Utilizing a high-pressure sliding plate rheometer (HPSPR) to ensure accurate measurements under uniform shear and pressure, we characterized four distinct polyethylene melts. All samples, regardless of their structure, exhibited piezorheologically simple behavior, allowing the application of time–pressure superposition over the entire shear rate range. A key finding is that the long-chain branched sample, known from the literature to be thermorheologically complex, was found to be piezorheologically simple. This dichotomy is explained by the different physical mechanisms of temperature and pressure. The pressure sensitivity of the viscosity, quantified by the pressure–viscosity coefficient, was found to be strongly dependent on molecular branching. Both SCB and LCB significantly increase the pressure sensitivity while polydispersity had a negligible effect. These results demonstrate that molecular branches are the dominant structural parameter controlling the rheological response of polyethylene to pressure, providing crucial insights for the development of more accurate predictive models for high-pressure polymer processing.
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Orthogonal superposition of oscillatory shearing upon steady shear flow from polymer rotarance theory: normal stresses

12. Dezember 2025

Myong Chol Pak, Wi Song Pak, Hak Chol Pak, Alan Jeffrey Giacomin

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One of the most intriguing experiments in polymer physics, is the superposition of small shearing oscillations upon steady shear flow. This experiment allows us to explore how the steady shear flow affects the complex viscosity, and the complex components of the first and second normal stress differences. The novelty of this paper is its exploration of the how the direction of this superposition matters to the complex components of the first and second normal stress differences in orthogonal superposition. Whereas, these complex components of the normal stress differences have been measured in parallel superposition, these have not been measured in orthogonal. Previously, we derived material functions from rotarance theory for the (previously measured) normal stress responses to the parallel superposition of small-amplitude oscillatory shear flow upon steady shear flow [ Phys. Fluids , 37 , 033133 (2025)]. The novelty of this work is that we arrive at analytical expressions for the (not previously measured) orthogonal superposition counterparts. We choose rotarance theory for our exploration, for its unique diversity of macromolecular structure. By rotarance theory , we mean accounting for the elasticity of polymeric liquids by considering, and by only considering, the physics of macromolecular orientation. We find that both the first and second normal stress difference responses in orthogonal superposition differ importantly from their parallel superposition counterparts.
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Third rank permeability in chiral solids

24. November 2025

Roderic S. Lakes

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Effects of a third rank permeability term in chiral solids are studied. Fluid flow through such materials acquires vorticity upon emergence from the material. Materials of interest include chiral surface lattices such as the gyroid, chiral rib lattices, and granular materials comprised of sugar crystals, quartz sand, wheat or beans. A characteristic length scale is associated with the chirality. The length scale can be obtained by several methods. Contacts with nonlocal permeability, elasticity and piezoelectricity are explored.
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An excellent closed-form approximate solution to the Blasius equation

14. November 2025

Ekachai Juntasaro

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An approximate analytical solution for the laminar boundary layer on a flat plate governed by the Blasius equation is presented. Although the numerical solution of the Blasius equation is well established, no closed-form analytical solution has yet been found. In this study, the approximate analytical solutions are developed by extending Lin's (1999) exponential formulation of the dimensionless streamwise velocity to include quadratic and cubic exponents. Both proposed forms satisfy the boundary conditions at the wall and the free-stream, and the corresponding analytical expressions for the dimensionless stream function, shear stress, and cross-stream velocity are derived. Comparison with the numerical Blasius solution shows that the quadratic form provides a reasonable approximation, while the cubic form exhibits excellent agreement over the entire range of the similarity variable η which is defined as η = y U ∞ / ν x $\eta =y\sqrt{{U}_{\infty }/\left(\nu x\right)}$ , where x and y are the wall-parallel and wall-normal coordinates respectively, U ∞ is the free-stream velocity and ν is the kinematic viscosity. The maximum residual of the cubic solution is on the order of 10 −3 at the wall, indicating high accuracy. The proposed cubic analytical solution thus provides a compact and explicit expression that closely represents the Blasius solution, offering a practical alternative for engineering applications requiring analytical evaluation of boundary-layer quantities.
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Hele-Shaw flow with pressure and shear rate dependent viscosity

14. November 2025

Benedetta Calusi, Liviu Iulian Palade

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This paper investigates the behavior of a fluid characterized by a viscosity simultaneously depending on pressure and shear rate within a Hele-Shaw cell featuring a sharp corner geometry. The study extends previous analyses conducted on purely pressure-dependent (piezo-viscous) and yield-stress fluids, providing a new perspective on confined complex flows. Motivated by practical applications related to designing biomedical devices and flows of relevance to bio-medicine area, thin film technologies, injection molding – to name only a few – the flow configuration considered here can highlight essential features of complex fluid behavior in narrow-gap geometries around a sharp edge. Starting from the governing equations for an incompressible generalized Newtonian fluid and employing an appropriate rheological model, we derive the modified flow equations adapted to the Hele-Shaw flow. A particular solution is obtained near the corner region. Numerical simulations complement the theoretical results, illustrating the influence of the rheological parameters on the flow behavior.
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Chemical wires: reaction-diffusion waves as analogues of electron drift

6. November 2025

Mahala Wanner, Augustus R. Thomas, John F. Lindner, Niklas Manz

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We use chemical reaction-diffusion waves in narrow channels to model electron drift in wires. By varying the initial conditions of an excitable Belousov–Zhabotinsky (BZ) medium, we achieve careful, quantitative control of BZ wave speeds in the range of electron drift speeds in conductors, a few millimeters per minute. We compare the speeds of the easily observable BZ waves and their computer simulations with theoretical electron drift speeds to explore the effects of wire radius, electric current, and material composition. Such BZ waves are compelling visual analogues of electron drift.

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Founding Editor-in-Chief

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Founding Deputy Editors

Natalie Germann, University of Stuttgart, Institute of Process System Engineering, Stuttgart, Germany

Rossana Pasquino, Department of Chemical Engineering, Materials and Industrial Production, University of Naples Federico II, Naples, Italy

Nhan Phan-Thien (Phan Thiện Nhân), Department of Mechanical Engineering, National University of Singapore, Singapore and Department of Engineering Mechanics, Zhejiang University (浙江大学), China

Chunxiao Xu (许春晓), Institute of Fluid Mechanics, Tsinghua University, Beijing, China

Founding Senior Associate Editors

Kathleen A. Feigl, Department of Mathematical Sciences, Michigan Technological University, Houghton, MI, USA

Zhaohui Yao (姚朝晖), Engineering Science Department, University of Chinese Academ y of Sciences, Beijing, China

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Rashmi Dubey (रश्मि दुबे), University of Petroleum and Energy Studies, Dehradun, India

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N.K. Anand (एन. के. आनंद) (Texas A&M University, USA)

Robert C. Armstrong (Massachusetts Institute of Technology, USA)

Dietmar Auhl, (Technische Universität Berlin, Germany)

Matteo Aureli (University of Nevada, Reno, USA)

Chandler Benjamin (Texas A&M University, USA)

Bofeng Bai (白博峰) (Xi'an Jiaotong University, China)

Antony N. Beris (University of Delaware, USA)

Roger T. Bonnecaze (University of Texas at Austin, USA)

Pierre J. Carreau (Ecole Polytechnique de Montréal, Canada)

Suman Chakraborty (সুমনচক্রবর্তী) (Indian Institute of Technology Kharagpur, India)

Lin Chen (陈林) (Chin ese Ac ad e my of Science, China)

Mikhael Gorokhovski (Михаил Гороховский) (École Centrale de Lyon, France)

Ezgi Pulats u ( University of Ottawa, Canada)

Pierre Sagaut (Aix-Marsei lle Université, France)

Norman J. Wagner (University of Delaware, USA)

Shiyi Chen (陈十一) (Eastern Institute of Technology, Ningbo, China)

Pamela L. Cook (University of Delaware, USA)

Daniel Curtis (Swansea University, UK)

Daniel De Kee (University of Toronto, Canada)

Bingqing Deng (邓冰清) (University of Chinese Academy of Sciences, China)

Dimitris Drikakis (Δημήτρης Δρικάκης) (University of Nicosia, Cyprus)

Randy H. Ewoldt (University of Illinois at Urbana-Champaign, USA)

Dixia Fan (范迪夏) (Westlake University, China)

Xiande Fang (方贤德) (Nanjing University of Aeronautics and Astronautics, China)

Peter Fischer (ETH Zurich, Switzerland)

Ian Frigaard (University of British Columbia, Canada)

Jochen Fröhlich (TU Dresden, Germany)

Peter H. Gilbert (Queen's University, Canada)

Joe D. Goddar d (University of California San Diego, USA)

Mikhael Gorokhovski (Михаил Горох овский) (École Centrale deLyon, Fra nce)

Ole Hassager (T echnical University of Denmark, Denmark)

Jane E. Hillston (University of Edinburgh, UK)

Qian Huang (黄茜) (Sichuan University, China)

Camiel H.C. Janssen (National Autonomous University of Mexico, Mexico)

William P. Jon es (Imperial College London, UK)

Yogesh M. Joshi (योगेश मो जोशी) Indian Institute of Technology Kanpur, India)

Roland Kádár (Chalmers University of Technology, Sweden)

Mona Kanso (منى قانصو) (Massachusetts Institute of Technology, USA)

Sangtae Kim (Purdue University, USA)

Daniel J. Klingenberg (University of Wisconsin-Madison, USA)

Chanyut Ko litawon g (ชาญยุทธ โกลิตะวงษ์) (King Mongkut's University of Technology North Bangkok, Thailand)

Jörg Läuger (Anton Paar Germany GmbH, Germany)

Cunbiao Lee (李存标) (Peking University, China)

Pohseng Lee (李宝胜)( National University o f Singapore, Singapore)

Sunwei Li (李孙伟) (Shenzhen International Graduate School (SIG S), Tsinghua Univ ersity, Shenzhen, China)

E.J. (Ted) Lig htfoot (Ted Lightfoot Consulting LLC, USA)

Moubin Liu (刘谋斌) (Peking University, China)

Joseph Majdalani (Auburn University, USA)

Alexander Ya. Malkin (Александр Яковлевич Малкин) (Russian Academy of Sciences, Moscow, Russia)

Niklas Manz (The Wooster College, Ohio, USA)

Arthur B. McDonald (Queen's University, Kingston, Canada)

Helmut Münstedt (Friedrich-Alexander-Universität Erlangen-Nürnberg, Germany)

Bernd R. Noack (Shenzhen University, China)

Tim A. Osswald (University of Wisconsin-Madison, USA)

Myong Chol Pak (박명철) (Kim Il Sung Universi ty, DPR Korea)

Liviu lulian Palade (Université de Lyon, France)

Heon Park (박희언) (Western Michigan University, USA)

Tony Paxton (Imperial College London, UK)

Van-Sang Pham (Phạm Văn Sáng) (Hanoi Un iversity of Science and Technology, Vietnam)

Ezgi Pulatsu ( Unive rsity of Ottawa, Canada)

Klaus Rademann (Humboldt-Universität zu Berlin, Germany)

Graça Raposo (Institut Curie CNRS, Fr ance)

Simon A. Rogers (University of Illinois Urbana-Champaign, USA)

Chaimongkol Saengow (ชัยมงคล แซ่โง้ว) (Sirindhorn International Institute of Technology (SIIT), Thammasat University, Thailand)

Pierre Sagaut (Aix-Marseille Université, France)

Leonard Sagis (Wageningen University, The Netherlands)

Richard Saurel, (Aix-Marseille University, France)

Simon Song (송시몬) (Hanyang University, South Korea)

Bohua Sun (孙博华) (Chinese Academy of Sciences, China)

Roger I. Tanner (University of Sydney, Australia)

Tim K.T. Tse (謝錦添) (The Hong Kong University of Science and Technology, Hong Kong)

Lìh-Shēng Turng (童立生) (University of Wisconsin - Madison, USA)

David C. Venerus (New Jersey Institute of Technology, USA)

Jan Vermant (ETH Zurich, Switzerland)

Manfred H.H. Wagner (Technische Universität Berlin, Germany)

Norman J. Wagner (U nivers ity of Delaware, USA)

Lewis E. W edgewood (University of Illinois at Chicago, USA)

Manfred W ilhelm (Karslruhe Institute of Technology, Germany)

Norbert Willenbacher (Karlsruhe Institute of Technology, Germany)

Paula Wood-Adams (University of British Columbia, Canada)

Gerald J. Wang (Carnegie Mellon University, USA)

Liying Yang (楊立英) (Chinese Academy of Sciences, China)

Vigor Yang (杨威迦) (Georgia Tech, USA)

Alexander L. Yarin (University of Illinois at Chicago, Chicago, Illinois, USA)

A-Man Zhang (张阿漫) (Harbin Engineering University, China)

Luoding Zhu (祝罗丁) (Indiana University, Indianapolis, IN, USA)

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eISSN: 3052-878X

ISSN: 3052-8798

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