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Dieter Bothe

Publications and source records attributed to Dieter Bothe.

At least 19 recordsLinked to original sources
arXiv2026

Enriched Surface Thermodynamics for Sharp-Interface Fluid Models

A sharp interface can retain material and structural information about an unresolved fluid transition zone. We formulate a local thermodynamic framework for isotropic surfaces carrying constituent surface mass densities and a thickness descriptor. The distinction between densities of additive contents and internal descriptors determines the area conjugate, reversible surface stress, and Gibbs-Duhem relation. A volume-per-area thickness has a pressure-like conjugate, a mechanical work contribution, and a separate evolution equation. Independent, constrained, and rapidly equilibrating thicknesses require different kinematics and reductions. Material storage can be retained without retaining surface inertia. The balances and entropy production specify admissible exchange and structural relaxation. For a moving surface patch, an available-free-energy identity accounts for mechanical power and for the contributions of material and structural fluxes across its boundary. Equilibrium reduction retains the production and transport needed to follow the reduced state. An explicit mass-thickness free energy has a positive-definite material Hessian and gives coupled adsorption, expansion, compression, and dissipative relaxation. Pressure response yields conditional restrictions on reduced states and demonstrates that distinct independent and constrained states can share an entire pressure-tension curve. Geometric thickness realizations and finite-rate transfer are treated with their associated mechanical and balance requirements. The framework separates state selection, constitutive closure, reduction, and identification from observations.

physics.flu-dyn↗
arXiv2026

Numerical analysis of geometrical effect on drop deformation and breakup between rotating cylinders

This study numerically investigates the effects of geometrical curvature on drop deformation and breakup in shear flow between counter-rotating concentric cylinders. Simulations were performed using a geometric Volume-of-Fluid (VOF) method incorporating plicRDF interface reconstruction and isoAdvector interface advection, combined with adaptive mesh refinement. Three circular geometries with different values of the non-dimensional geometrical curvature, $κ_{\mathrm F}$, were considered and compared with a planar shear flow system. At fixed Reynolds and Capillary numbers ($Re$ and $Ca$), the breakup morphology differed substantially between the planar and circular systems. In the planar system, the drop underwent relatively symmetric neck thinning, whereas in the circular systems, the drop exhibited asymmetric deformation and pronounced azimuthal elongation. At higher curvature, the drop formed a thin filament that subsequently fragmented, producing multiple satellite drops. Analysis of the internal velocity field and the magnitude of the rate-of-deformation tensor revealed distinct flow and deformation structures associated with these breakup behaviors. Furthermore, the critical $Re$ for breakup, $Re_{\mathrm{cr}}$, decreased with increasing $κ_{\mathrm F}$ at nvestigated $Ca$ values. In contrast, the maximum dimensionless elongation length immediately before breakup at $Re=Re_{\mathrm{cr}}$ increased with $κ_{\mathrm F}$. These findings suggest that geometrical curvature affects not only the breakup threshold but also the deformation process leading to breakup, providing insights into drop breakup in curved shear flows.

physics.flu-dyn↗
arXiv2026

Continuum thermodynamics of chemically reacting multi-temperature fluid mixtures

We develop a continuum-thermodynamic model for chemically reacting, multi-velocity and multi-temperature fluid mixtures. Partial balances of mass, momentum and total energy are closed using a single entropy density depending jointly on the constituent mass and nonkinetic internal-energy densities. Its partial derivatives determine the constituent temperatures and chemical potentials. For the chosen entropy flux and separately treated volume deformation, the strengthened entropy principle yields a weighted Euler relation constraining the partial thermodynamic pressures. We construct thermodynamically consistent constitutive relations for viscosity, heat conduction, Maxwell--Stefan momentum exchange, thermal relaxation and nonlinear reaction kinetics. The baseline model includes thermo-diffusion and its reciprocal coupling; a fully coupled reciprocal completion is given within the stated isotropic co-factor class. An alternative formulation couples chemical conversion and energy redistribution through specified elementary processes. We identify the material functions required for closure and admissible shifts of constituent energy zeros. An ionization network with resolved electronic levels yields Saha-type ionization relations and Boltzmann excitation ratios under the stated detailed-balance assumptions, recovering the Saha--Eggert relation at common temperature. Competing electron- and heavy-particle processes can maintain stationary populations while transferring energy between groups at different prescribed temperatures.

physics.flu-dyn↗
arXiv2026

DeboRheo v2.0: Improved Robustness for Geometrical VOF Simulations of Viscoelastic Two-Phase Flows

We present DeboRheo v2.0, an unstructured, geometrically unsplit Volume-of-Fluid framework implemented in OpenFOAM for viscoelastic two-phase flows. Version 2.0 improves numerical robustness when large viscosity contrasts coincide with strongly deformed interfaces and thin viscoelastic lamellae or filaments. The revised interfacial viscosity treatment retains a sharp geometric interface while regularizing the viscous contribution to the momentum equation. The solver combines mass-momentum-consistent phase advection, optional SIMPLEC pressure-velocity coupling, and a modular rheological framework with conformation-tensor stabilization. We assess the method using two-dimensional, axisymmetric, and three-dimensional benchmarks governed by the Oldroyd-B and exponential Phan-Thien-Tanner models. The results agree well with published numerical and experimental data and demonstrate improved robustness for demanding viscoelastic free-surface configurations on unstructured meshes.

physics.flu-dyn↗
arXiv2026

acousticHelmholtzFoam: an MPI-parallel unstructured finite-volume solver for frequency-domain acoustics in heterogeneous two-phase media with perfectly matched layers

acousticHelmholtzFoam is an OpenFOAM application that computes time-harmonic acoustic pressure fields in heterogeneous gas-liquid media on unstructured polyhedral meshes. The complex pressure is stored as real and imaginary volume fields, the material coefficients are constructed from a volume-of-fluid phase fraction with geometric face-fraction averaging, and open boundaries are truncated by Cartesian perfectly matched layers (PMLs) whose damping tensor is generated by the companion utility setPMLFields. The two coupled real-valued equations are discretized with the cell-centred finite-volume operators of OpenFOAM and assembled explicitly, including processor couplings and boundary contributions, into a distributed PETSc matrix that is solved by default with the MUMPS sparse direct solver. The solver writes pressure amplitude, complex velocity, acoustic radiation pressure and time-averaged momentum flux for acoustic-force evaluation. This paper documents the implemented equations, the case interface, the assembly and solution algorithm, the build procedure and the test infrastructure. A layered gas-liquid-PML case with an analytical solution serves as an end-to-end regression: on 8000 cells the whole-domain relative complex-pressure error is $1.197\times10^{-3}$, and serial and MPI solutions on up to eight ranks agree to within $10^{-12}$ in relative $L_2$ norm. A single-axis acoustic-levitator height sweep with constant-volume spheroidal drops demonstrates the two-phase material input and the force output, and strong- and problem-size-scaling measurements characterize the direct-solver workflow. The numerical formulation and its verification are presented in a companion paper (arXiv:2610.01593).

physics.comp-ph↗
arXiv2026

An unstructured finite-volume Helmholtz method with perfectly matched layers for heterogeneous two-phase acoustics

This paper presents a cell-centred unstructured finite-volume method for time-harmonic two-phase acoustics. A volume-fraction representation supplies density and acoustic compressibility. Face fractions average available neighbouring planar interface cuts independently of velocity direction, retaining the established one-field face-density closure. Cartesian complex-coordinate stretching provides perfectly matched layers (PMLs). Real-imaginary splitting yields a real-valued block system, discretized with corrected non-orthogonal fluxes and consistent boundary contributions. Verification covers homogeneous waves, layered gas-liquid transmission with PML truncation, baffled-piston radiation with Kirchhoff far-field reconstruction, and resolved rigid-sphere radiation forces. Homogeneous-wave pressure converges at approximately second order on orthogonal meshes and on meshes with non-orthogonal interiors and orthogonal boundary cells. Reconstructed velocity converges at approximately second order on orthogonal meshes and with an observed order of about 1.7 on the latter mesh family. Under aligned refinement, the layered case's relative whole-domain complex-pressure $L_2$ error decreases to $2.657\times10^{-4}$. The resolved-sphere force differs from the Gorkov prediction by at most 1.5% over the tested Rayleigh size range. The results quantify the accuracy and current limitations of the heterogeneous Helmholtz-PML formulation.

physics.flu-dyn↗
arXiv2026

A Sharpened Entropy Principle for Two-Fluid Polymer Thermodynamics

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.

cond-mat.soft↗
arXiv2026

From a three-fluid junction to Young's law: Constitutive and rigid-support limits of wetting

Young's law on a rigid solid and the Neumann balance at a three-fluid junction describe different admissible motions. We connect them through an ordered continuum construction. An affine viscoelastic third phase first acquires permanent deformation memory in the no-relaxation limit at fixed modulus. Independently specified material-surface laws distinguish surface free energy from mechanical surface stress. On the deformable support, displacement of solid material and migration of the wet-dry partition give separate equilibrium conditions. Stiffening an anchored support suppresses displacement at a fixed macroscopic observation distance but leaves reversible migration possible. The surviving variation gives Young's law; the constrained mechanics remains as a reaction carrying normal and, in general, tangential capillary loads. Two complementary results substantiate this reduction. A clamped finite-strain model with circular liquid interfaces yields uniform convergence of reduced energies and recovery of the spatial Young angle for global almost minimisers. A separate quadratic half-space model gives convergence of stationary migration derivatives and a nonzero limiting traction distribution. The results explain how a local Neumann-like ridge can coexist with a Young angle measured against the distant wall, while distinguishing geometric convergence from the control of migration and reaction forces.

cond-mat.soft↗
arXiv2026

Global Strong Solutions for the Affine Darken Class of Maxwell-Stefan Diffusion Systems

The core-diagonal closure of Bothe and Druet identifies multicomponent Darken diffusion as a thermodynamically consistent Maxwell-Stefan model in which the constitutive data are species tracer diffusivities. Building on the Stieltjes-coordinate and De Giorgi regularity framework introduced in our recent preprint for additive Maxwell-Stefan frictions, we prove global maximal-$L^p$ strong well-posedness, without smallness assumptions, for the affine Darken class with composition-dependent scalar coefficients and uniformly positive tracer diffusivities. We show that this is exactly the maximal Darken class preserving the fixed Stieltjes eigenframe underlying the global argument. For general smooth, uniformly positive Darken tracer diffusivities we also derive the direct constrained flux form, exact mixing-entropy symmetrization, Fisher dissipation, composition-uniform normal ellipticity, and local strong well-posedness. Solutions in the affine class remain uniformly separated from the simplex boundary, become classical for positive times, and converge exponentially to equilibrium. Constant multiplicative frictions, including repeated factors, are covered by grouping species with equal factors.

math.AP↗
arXiv2026

Global Strong Solutions for the Ternary Maxwell-Stefan Diffusion System

We prove global strong well-posedness for the normalized isothermal, isobaric ternary Maxwell-Stefan diffusion system on bounded $C^{2+α_0}$ domains, for arbitrary positive constant binary frictions and compatible nonnegative initial data, without a smallness condition. For distinct frictions, trace--determinant variables produce two separated spectral roots satisfying scalar parabolic equations with antisymmetric quadratic coupling. Euler-Poisson-Darboux one-sided truncations, stabilized by the mixing entropy, yield boundary De Giorgi oscillation decay and positive-time Hölder regularity. The mixing-entropy Hessian then provides a local symmetrizer; conormal Schauder estimates give uniform $C^{1+a}$ control, and frozen maximal $L_p$-regularity yields a uniform terminal trace bound excluding finite-time breakdown. Repeated frictions reduce to triangular scalar parabolic systems. Every component with positive conserved mass is strictly positive for positive time.

math.AP↗
arXiv2026

Global Strong Solutions for Maxwell-Stefan Diffusion with Additive Friction Coefficients

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 $G=diag[g_1,\ldots,g_N]$. 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 $N\ge4$ 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 $N\ge2$, $d\ge2$, 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 $C^1(\barΩ)$.

math.AP↗
arXiv2026

Co-moving volumes and the Reynolds transport theorem for two-phase flows

We consider the local kinematics at fluid interfaces in sharp-interface two-phase flows with phase change and interfacial slip. In this setting the governing velocity field is discontinuous at the phase boundary, with possible jumps of both normal and tangential components, and the associated kinematic initial value problems may fail to be uniquely solvable. A physically consistent example exhibits this non-uniqueness and, in addition, rapid loss of boundary regularity: smooth initial control volumes can instantaneously develop edges, while their phasewise parts may form cusps. Motivated by these phenomena, we use concepts from differential inclusions to define co-moving volumes as attainable sets. For such attainable-set co-moving volumes in three-dimensional two-phase flows, we prove the Reynolds transport theorem first in boundary-integral form and then in divergence form. A key ingredient is a boundary-integral form of the single-phase Reynolds transport theorem for families of compact regular closed sets whose space-time tubes are Lipschitz domains. We also provide a short proof of this single-phase result by applying the divergence theorem in space-time; this proof does not require the motion to be generated by an ambient velocity field.

math.AP↗
arXiv2026

Existence and qualitative theory for nonlinear accretive evolutions with Carathéodory forcing

Let $A$ be $m$-accretive in a real Banach space $X$. Given closed sets $K(t)\subset X$, we develop an existence theory for mild solutions of the constrained problem \[ u'(t)+Au(t)\ni f(t,u(t)), \qquad u(t)\in K_A(t):=K(t)\cap\overline{D(A)}, \] 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 $u_\varepsilon$ driven by $w_\varepsilon$ are accompanied by auxiliary paths $v_\varepsilon$ and current-time selectors $x_\varepsilon$ satisfying $x_\varepsilon(t)\in K_A(t)$ and $w_\varepsilon(t)=f(t,x_\varepsilon(t))$ for almost every $t$ in a closed regularity set of almost full measure. For every $t$ there is also $σ_\varepsilon(t)\in[(t-\varepsilon)^+,t]$ with $v_\varepsilon(σ_\varepsilon(t))\in K_A(σ_\varepsilon(t))$. 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.

math.FA↗
arXiv2026

Non-intrusive MEMS microphone sensing of acoustic field state in resonant 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% of the corresponding maximum force was retained. Microphone amplitude localized the force maximum more sharply than peak-to-peak transducer current. In one frequency-shift experiment, microphone phase provided a proof of principle for correction-direction estimation, while envelope modulation captured channel-resolved field changes during object oscillation. Ring measurements showed channel-dependent responses as transducer-reflector tilt was varied, but did not provide a calibrated or unique tilt estimate. These results show the potential of external MEMS microphones as relative acoustic observables for resonance-related field-state assessment and provide a basis for compact transducer-side feedback. The principle may also be transferable to transducer-transducer and array-based architectures.

physics.app-ph↗
arXiv2025

A consistent treatment of dynamic contact angles in the sharp-interface framework with the generalized Navier boundary condition

In this work, we revisit the Generalized 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 $\varepsilon > 0$ 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, Köhne 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 regularization 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 $\dotθ_d=0$) and the dynamic contact angle is determined by a balance between the uncompensated Young stress and an effective contact line friction. Furthermore, a non-linear generalization of the model is proposed, which aims at reproducing the Molecular Kinetic Theory of Blake and Haynes for quasi-stationary states.

physics.flu-dyn↗
arXiv2025

A two-sided subgrid-scale model for mass transfer across fluid interfaces

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).

physics.comp-ph↗
arXiv2025

The initial acceleration of a buoyant spherical bubble revisited

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.

physics.flu-dyn↗
arXiv2025

A continuum thermodynamic model of the influence of non-ionic surfactant on mass transfer from gas bubbles

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. One 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 bi-directional sorption-type bulk-interface exchange processes. The resulting model is shown to quantitatively describe experimental measurements on mass transfer reduction for the dissolution of CO$_2$ bubbles in different surfactant solutions.

physics.flu-dyn↗