Let A be m-accretive in a real Banach space X. Given closed sets K(t)⊂ X, we develop an existence theory for mild solutions of the constrained problem u'(t)+Au(t)∋ f(t,u(t)), u(t)∈ K_A(t):=K(t)∩D(A), where the forcing is Carathéodory on the effective tube K_A. We also assume joint measurability of f on the moving graph or a Carathéodory extension to a fixed cylinder. Under a linear-growth hypothesis and the corresponding regular- and exceptional-time subtangential conditions, we reduce the problem to a bounded effective tube with a common integrable bound. A first central result constructs a closed separable resolvent-invariant subspace preserving distances to the moving sets and the subtangential conditions, permitting use of the Scorza–Dragoni property for the reduced forcing. A second central ingredient is a two-level approximation. Mild solutions u_ε driven by w_ε are accompanied by auxiliary paths v_ε and current-time selectors x_ε satisfying x_ε(t)∈ K_A(t) and w_ε(t)=f(t,x_ε(t)) for almost every t in a closed regularity set of almost full measure. For every t there is also σ_ε(t)∈[(t-ε)^+,t] with v_ε(σ_ε(t))∈ K_A(σ_ε(t)). The current-time selectors identify the limiting forcing, while the lagged nodes guarantee viability. This yields well-posedness under time-dependent constraints for such forcings f when they are locally Lipschitz in the state variable. Further viability results follow under various compactness conditions. Application of the abstract viability theory yields comparison principles, nonautonomous Lyapunov pairs, periodic solutions, and time-dependent bounds for abstract reaction–diffusion systems.

Mass transfer of gaseous components from rising bubbles to the ambient liquid depends not only on the chemical potential difference of the transfer component but also on the interfacial free energy and composition. The latter is strongly affected by surface active agents that are present in many applications. Surfactants lead to local changes in the interfacial tension, which influence the mass transfer rates in two different ways. On the one hand, inhomogeneous interfacial tension leads to Marangoni stress, which can strongly change the local hydrodynamics, thus impacting the local mass transfer. On the other hand, the coverage by surfactant molecules results in a mass transfer resistance. This hindrance effect is not included in current continuum physical models. The present work provides the experimental validation of a recently introduced extended sharp-interface model for two-phase flows with mass transfer that also accounts for the mass transfer hindrance due to adsorbed surfactant. The crucial feature is to account for area-specific concentrations not only of adsorbed constituents but also of transfer species, and to model mass transfer as a series of two bidirectional sorption-type bulk-interface exchange processes. The resulting model is shown to quantitatively describe experimental measurements on mass transfer reduction for the dissolution of CO2 bubbles in different surfactant solutions.

Acoustic levitation enables contactless manipulation for applications in containerless processing in chemistry and materials science. Single-transducer levitators, consisting of an ultrasonic transducer and a reflector, offer a minimal hardware configuration but require precise control of the transducer-reflector distance H. We propose a distance stabilization system based on a motorized linear stage and a precision balance that measures the acoustic radiation force (ARF) as a time-averaged, surface-integrated force magnitude on the reflector. Because ARF versus H exhibits extremely narrow resonance peaks, micrometer-scale deviations markedly reduce force and destabilize levitation. In practice, high-power transducers are actively kept at resonance using resonance frequency tracking (RFT). As the tracked frequency changes, the wavelength changes as well and the optimal distance H shifts. We introduce a two-stage control strategy in order to robustly stabilize H. First, a physics-informed, one-sided adaptive hill climb algorithm locates the cavity resonance. Second, a physics-informed extremum-seeking controller maintains the experimentally determined resonance distance despite drift and disturbances, using only the absolute ARF feedback. Longterm validation at node index n =5 confirmed that ARF remained within the 95% tolerance bound for two hours, ensuring stable levitation. Performance was limited by the balance, mainly due to its internal averaging time. This occasionally caused convergence to local maxima or temporary loss of track during object insertion. The strategy presented enables robust, long-duration operation of acoustic levitators.

Reliable operation of resonant acoustic levitators requires knowledge of the acoustic field state because the optimum transducer-reflector distance and resonant operating condition shift with wavelength, temperature, object insertion, and mechanical alignment. Existing adjustment methods are limited, especially for compact closed-loop operation and architectures without a passive reflector. Here, we investigate transducer-mounted microelectromechanical system (MEMS) microphones as off-axis external sensors that acquire relative acoustic signals without placing sensors inside the levitation cavity. Using a linear microphone configuration, we performed transducer-reflector distance sweeps over resonance modes n = 5-8 and compared microphone amplitude with acoustic radiation force measured by a precision balance and with peak-to-peak transducer current. The channel-mean microphone-voltage maxima occurred within two sampled distance increments, or at most 30 micrometers, of the force maxima. At the microphone-derived peak positions, at least 98.3

The level set method relies on the representation of sharp interfaces as zero level sets of an appropriate class of level set functions. The advection of such a sharp interface within a flow field v is then governed by the linear transport equation partial derivative t phi + v & centerdot; del phi= 0 in the simplest setting. A convenient choice for the level set function is, at least locally, the signed distance to the interface as its gradient has unit length. It thus gives the interface normal field from which further geometric quantities such as the curvature can be computed. While the signed distance of the interface hence is a geometrically convenient level set function, its time evolution is not governed by the linear transport equation. Several modifications of the linear level set equation have been proposed in order to compute the signed distance function or to stabilize the norm of the gradient of a level set function on the interface. The velocity extension level set method is a prominent approach used for efficient numerical approximation of the local signed distance function of the moving interface. We present a rigorous mathematical formulation of the velocity extension level set method and prove that it indeed provides the smooth local signed distance function of the interface. A key is to derive a first-order fully nonlinear PDE that is equivalent to the linear transport equation with extended velocity. The main challenge to be overcome is the fact that the velocity extension level set method on the one hand requires enough regularity near the interface to have basic geometric quantities well-defined, while on the other hand the problem should have a unique solution in the full spacial domain so that it is a wellposed problem for numerical methods. For this purpose, we combine techniques of viscosity solutions to Hamilton-Jacobi equations with the classical method of characteristics, and develop a novel local comparison principle to obtain partial regularity of viscosity solutions, confirming that the viscosity solution is locally smooth and consistent with the local signed distance function in a time-global tubular neighborhood of the interface. (c) 2026 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).

We study Maxwell-Stefan diffusion with additive friction coefficients f_ij=g_i+g_j. In mass fractions, the system isolates the constrained pair-friction block; in mole fractions, it is the classical ideal isothermal/isobaric Maxwell-Stefan system at constant total molar concentration. Additivity makes the constrained pair-friction dissipation species-diagonal; conversely, species-diagonality on one interior barycentric constraint space forces a pair-sum representation. At operator level, the positive constrained relaxation operator is a scalar shift of a compression of G=diag[g_1,…,g_N]. Its scalar resolvent yields both an explicit constrained inverse and interlacing spectral roots, which form global real-analytic coordinates on the open simplex and whose differentials are left eigen-covectors. In root coordinates the principal part is diagonal, no self-square gradient term occurs, and scalar comparison yields invariant rectangles and separation from the simplex boundary. For regularity we introduce entropy-stabilized one-sided multi-EPD truncations: Euler-Poisson-Darboux entropies cancel mixed quadratic production, while for N≥4 a truncation-weighted mixing-entropy correction supplies transverse coercivity. Caccioppoli and logarithmic estimates, shrinking, and critical mass yield Hölder continuity up to the Neumann boundary. The mixing entropy also symmetrizes the moment system; frozen conormal estimates give spatial Lipschitz bounds. Together with time Hölder control and short-interval maximal regularity, this yields global strong solvability on bounded C^2+α domains with 0<α<1, for each N≥2, d≥2, and p>d+2, for all uniformly positive, compatible initial concentrations in the natural trace class. Solutions become classical for positive times and converge exponentially to equilibrium in relative entropy, L^2, and C^1().

A compressible, non-isothermal dilute polymer solution is formulated as a Class-II binary mixture with separate solvent and polymer mass and momentum balances and with total energy and entropy balances for the complete mixture. The entropy exploitation is sharpened by a balance-anchoring axiom introduced here: in a fixed balance representative, each selected binary dissipative product contains a constitutive factor from an unclosed balance flux or source. Polymer configuration is resolved first by a connector distribution and then by its conformation tensor. Population kinematics fix polymer transport and, by moments, yield a two-velocity upper-convected rate; objectivity verifies covariance rather than selecting it. Within the total entropy balance, configurational transport and deformation powers cancel their chemical-potential and elastic partial-stress counterparts when deformation and stress-decomposition weights match. A Gordon–Schowalter test independently requires the affine upper-convected choice for the stated dumbbell free energy and Kramers stress unless an additional reversible channel is supplied. Coordinated stress–interaction changes shift the local entropy flux/production pair by a divergence, exposing representation dependence of local mechanism-wise production. An entropy-invariant Class-II-to-Class-I reduction selects a descendant entropy flux preserving the parent production and yields thermo-chemical, configurational-stress and partial-viscous-stress diffusion terms. The omitted quadratic relative-inertia flux is paired with relative kinetic-energy storage and transport and is a reversible truncation, not missing entropy production. The resulting compressible non-isothermal Hookean stress and temperature equations reduce to Oldroyd-B/UCM only after one-velocity, incompressible and isothermal limits.

We consider elliptic transmission problems in several space dimensions near an interface which is C^1,1 diffeomorphic to an axisymmetric reference-interface with a singular point of cusp type. We establish the regularity of the gradient and of the Hessian in L^p spaces up to the cusp point for local weak solutions. We obtain regularity thresholds which are different according to whether the cusp is inward or outward to the subdomain, and which depend explicitly on the opening of the interface at the cusp. Our results allow for source terms in the bulk and on the interface.

In this work, we revisit the Generalised Navier Boundary Condition (GNBC) introduced by Qian et al. in the sharp interface volume-of-fluid context. We replace the singular uncompensated Young stress by a smooth function with a characteristic width $\varepsilon \gt 0$ that is understood as a physical parameter of the model. Therefore, we call the model the 'contact region GNBC' (CR-GNBC). We show that the model is consistent with the fundamental kinematics of the contact angle transport described by Fricke, K & ouml;hne and Bothe. We implement the model in the geometrical volume-of-fluid solver Basilisk using a 'free angle' approach. This means that the dynamic contact angle is not prescribed, but reconstructed from the interface geometry and subsequently applied as an input parameter to compute the uncompensated Young stress. We couple this approach to the two-phase Navier-Stokes solver and study the withdrawing tape problem with a receding contact line. It is shown that the model allows for grid-independent solutions and leads to a full regularisation of the singularity at the moving contact line, which is in accordance with the thin film equation subject to this boundary condition. In particular, it is shown that the curvature at the moving contact line is finite and mesh converging. As predicted by the fundamental kinematics, the parallel shear stress component vanishes at the moving contact line for quasi-stationary states (i.e. for $\dot heta _d=0$ ), and the dynamic contact angle is determined by a balance between the uncompensated Young stress and an effective contact line friction. Furthermore, a nonlinear generalisation of the model is proposed, which aims at reproducing the molecular kinetic theory of Blake and Haynes for quasi-stationary states.

We consider the local kinematics at fluid interfaces in two-phase flows within the sharp interface framework. In the considered case with phase change and slip at the interface, the governing velocity field is discontinuous at the phase boundary with possible jumps of the normal and the tangential components. This causes the associated initial value problems for the kinematic differential equation, governing the motion of fluid elements, to be ill-posed in general. Motivated by a corresponding example, where the velocity field is physically consistent regarding the balance of mass and momentum as well as the entropy inequality, we employ concepts from differential inclusions, to rigorously define co-moving sets within this framework. Based on this general two-phase flow setting, we proof a natural extension of the Reynolds transport theorem to this case.

For the moving average process Xn=ρξn−1+ξn, n∈N, where ρ∈R and (ξi)i≥−1 is an i.i.d. sequence of standard normally distributed random variables, we study the persistence probabilities P(X0≥0,…,XN≥0) for N→∞. We exploit the fact that the exponential decay rate λρ of that quantity, called the persistence exponent, is given by the leading eigenvalue of a concrete integral operator. This makes it possible to study the problem with purely functional-analytic methods. In particular, using methods from perturbation theory, we show that the persistence exponent λρ can be expressed as a power series in ρ. Finally, we consider the persistence problem for the Slepian process, transform it into the moving average setup, and show that our perturbation results are applicable.

The occurrence of extremely thin concentration boundary layers at fluid interfaces for high local Péclet numbers is a severe obstacle for efficient and accurate numerical simulation of mass transfer processes in two-phase fluid systems. Especially challenging are liquid-liquid systems, in which thin concentration boundary layers can appear on both sides of the fluid interface under convection-dominated conditions. In those cases, the one-sided species concentrations at the interface are a-priori not even known approximately, but are determined by a conjugate mass transfer problem governed by interfacial jump conditions. To the best of the authors' knowledge we for the first time introduce a two-sided Subgrid-Scale (SGS) boundary layer model for conjugate mass transfer at fluid interfaces. It accurately computes the local mass transfer rates on moderate or coarse mesh resolutions even when very high concentration gradients in interface vicinity occur. For this purpose, SGS modeling is applied on both sides of an interface transmissive to passive scalars, such as the interface in a two-phase fluid system, enabling the accurate capture of conjugate mass transfer across thin boundary layer on one or on both sides of the interface. We implement our approach in the unstructured Finite-Volume Arbitrary Lagrangian / Eulerian Interface-Tracking (ALE-IT) OpenFOAM module twoPhaseInterTrackFoam. We have made twoPhaseInterTrackFoam publicly available in our previous publication (Schwarzmeier et al., 2025).

An analytical derivation of the buoyancy-induced initial acceleration of a spherical gas bubble in a host liquid is presented. The theory makes no assumptions further than applying the two-phase incompressible Navier-Stokes equations, showing that neither the classical approach using potential theory nor other simplifying assumptions are needed. The result for the initial bubble acceleration as a function of the gas and liquid densities, classically built on potential theory, is retained. The result is reproduced by detailed numerical simulations. The accelerated, although stagnant state of the bubble induces a pressure distribution on the bubble surface which is different from the result related to the Archimedean principle, emphasizing the importance of the non-equilibrium state for the force acting on the bubble.

Bubbles and bubbly flows are omnipresent in nature and technology, showing a multitude of phenomena, which can be either beneficial or a hindrance. In any case, for their control and their applications, it is crucial to understand their fundamentals and therefore from the very beginning of the International Journal of Multiphase Flow they have been central. In this synoptic review we give some examples for the fascinating fluid dynamics of bubbles and bubbly flows, starting from their nucleation and cavitation phenomena, then going to single bubble phenomena, and finally to bubbly flows, in which the collective effects of bubbles are key, and to mass transfer in such bubbly flows. The review ends with an outlook on future direction and open issues in the research on bubbles and bubbly flows.

Metal energy carriers recently gained growing interest in research as a promising storage and transport material for renewable electricity. Within the development of a metal-fueled circular energy economy, research involves a model hierarchy spanning from micro to macro scales, making the transfer of information among different levels of complexity a crucial task for the implementation of the new technology. Chemical reactor networks (CRNs) are models of reduced complexity and a promising approach to accomplish the scale-bridging task. This holds if valid information from CRNs can be obtained on a much denser set of operating conditions than available from experiments and elaborated simulation methods like Computational Fluid Dynamics (CFD). An approach for CRN calibration from recent literature, including model error quantification, is further developed to construct a CRN model of a laboratory reactor for flash ironmaking, using data from the literature. By introducing a meta model of a CRN parameter, a simple CRN model on an extended set of operating conditions has successfully been calibrated. This way, the employed coupled calibration and uncertainty quantification framework has proven promising for the task of scale-bridging in the model hierarchy under investigation.

We provide an implementation of the unstructured Finite-Volume Arbitrary Lagrangian / Eulerian (ALE) Interface-Tracking method for simulating incompressible, immiscible two-phase flows as an OpenFOAM module. In addition to interface-tracking capabilities that include tracking of two fluid phases, an implementation of a Subgrid-Scale (SGS) modeling framework for increased accuracy when simulating sharp boundary layers is enclosed. The SGS modeling framework simplifies embedding subgrid-scale profiles into the unstructured Finite Volume discretization. Our design of the SGS model library significantly simplifies adding new SGS models and applying SGS modeling to Partial Differential Equations (PDEs) in OpenFOAM.

We revisit the sharp-interface continuum thermodynamics of two-phase multicomponent fluid systems, accounting for partial mass and partial momentum balances both in the bulk phases and on the interface. This allows to describe the transfer of species between the individual bulk phases and the interface, i.e. ad- and desorption processes. In fact, the transfer of any constituent between the two bulk-phases is considered as a series of ad- and desorption processes. In this framework, all species transfer processes are coupled via the interfacial thermodynamics. As a consequence, the influence of surface active species on the transfer of other constituents can be captured in detail. The derivation of this model class relies on an axiomatic form of the entropy principle which, at the same time, allows for an efficient closure process. This form of the entropy principle has been introduced for one-phase fluid systems in (Bothe, Dreyer, Acta Mechanica 226, 2015) as the result of intense joint work of the late Wolfgang Dreyer and the present author.

Since viscoelastic two-phase flows arise in various industrial and natural processes, developing accurate and efficient software for their detailed numerical simulation is a highly relevant and challenging research task. We present a geometrical unstructured Volume-of-Fluid (VOF) method for handling two-phase flows with viscoelastic liquid phase, where the latter is modeled via generic rate-type constitutive equations and a one-field description is derived by conditional volume averaging of the local instantaneous bulk equations and interface jump conditions. The method builds on the plicRDF-isoAdvector geometrical VOF solver that is extended and combined with the modular framework DeboRheo for viscoelastic computational fluid dynamics (CFD). A piecewise-linear geometrical interface reconstruction technique on general unstructured meshes is employed for discretizing the viscoelastic stresses across the fluid interface. DeboRheo facilitates a flexible combination of different rheological models with appropriate stabilization methods to address the high Weissenberg number problem. Program summary Program Title: DeboRheo CPC Library link to program files: https://doi.org/10.17632/gsgdrjm2md.1 Developer's repository link: https://gitlab.com/deborheo/deborheorelease/ Licensing provisions: GPLv3 Programming language: C ++ Nature of problem: DNS of viscoelastic two-phase flows encounters major challenges due to abrupt changes of physical properties and rheological behaviors of the two phases at the fluid interface, and viscoelastic flows characterized with high Weissenberg numbers introduce additional numerical challenges. Solution method: A geometrical unstructured Volume-of-Fluid (VOF) method for handling two-phase flows with a viscoelastic liquid phase, where the latter is modeled by generic rate-type constitutive equations. Appropriate stabilization techniques are included to address the High Weissenberg Number Problem (HWNP).