arXiv subjects

Benjamin Reichert

Publications and source records attributed to Benjamin Reichert.

10 recordsLinked to original sources

arXiv2026

A hybrid Volume of Fluid Phase-Field method for Direct Numerical Simulations of soluble surfactant-laden interfacial flows

We present a hybrid Volume-of-Fluid (VoF) Phase-Field method for general soluble surfactant-laden interfacial flows. The scheme retains the VoF method for interface tracking and momentum solution, while a diffused Phase-Field serves as a smooth carrier for surfactant transport, enabling consistent coupling between bulk and interfacial concentration fields without computing surface derivatives. Adsorption/desorption kinetics are incorporated through regularized source terms localized at the interface, and surface tension can be specified for general equations of state. The method is fully adaptive via quadtree/octree Adaptive Mesh Refinement, enabling efficient simulations in planar, axisymmetric, and three-dimensional domains with high parallel scalability. Rigorous validation against analytical solutions for surfactant transport on deforming interfaces and for diffusion-driven adsorption in the no-flow limit confirms accuracy and convergence. We then investigate the buoyancy-driven rise of a bubble in the presence of soluble surfactants, in axisymmetric and three-dimensional configurations. By independently varying the Biot and Damk\"ohler numbers, we recover the correct asymptotic limits corresponding to clean-interface and insoluble-surfactant dynamics, and characterize the intermediate soluble regime. The resulting Marangoni stresses, induced by non-uniform interfacial concentrations, significantly reduce interfacial mobility, leading to measurable reductions in terminal velocity and pronounced modifications of the bubble trajectory. These results demonstrate the robustness of the method in capturing the interplay between hydrodynamics, bulk and interfacial transport, and Marangoni stresses in realistic three-dimensional geometries.

physics.flu-dyn↗

arXiv2025

Orbiting, colliding and merging droplets on a soap film: toward gravitational analogues

Modern telescopes provide breathtaking images of nebulae, clouds and galaxies shaped by gravity-driven interactions between complex bodies. While such structures are prevalent on an astrophysical scale, they are rarely observed at the human scale. In this letter, we report the observations of the complex orbits, collision, and coalescence of droplets on a soap film, forming structures such as bridges and spiral arms, reminiscent of their astrophysical counterparts. These dynamics emerge from attractive forces caused by gravito-capillary-driven distortions of the supporting soap film. Long orbits and intricate coalescence mechanisms are enabled by the small dissipation in the soap film and the fluidic nature of the droplets and supporting film, respectively. The existence of stable droplets within the soap film featuring a universal radius, as well as the attractive potentials, are explained through a careful comparison of experimental data with models computing the distortions of the supporting soap film. This work opens perspectives to

physics.flu-dyn↗

arXiv2020

Density profile of a semi-infinite one-dimensional Bose gas and bound states of the impurity

We study the effect of the boundary on a system of weakly interacting bosons in one dimension. It strongly influences the boson density which is completely suppressed at the boundary position. Away from it, the density is depleted over the distances on the order of the healing length at the mean-field level. Quantum fluctuations modify the density profile considerably. The local density approaches the average one as an inverse square of the distance from the boundary. We calculate an analytic expression for the density profile at arbitrary separations from the boundary. We then consider the problem of localization of a foreign quantum particle (impurity) in the potential created by the inhomogeneous boson density. At the mean-field level, we find exact results for the energy spectrum of the bound states, the corresponding wave functions, and the condition for interaction-induced localization. The quantum contribution to the boson density gives rise to small corrections of the bound state energy levels. However, it is fundamentally important for the existence of a long-range Casimir-like interaction between the impurity and the boundary.

cond-mat.quant-gas↗

arXiv2020

Active volatile drops on liquid baths

In most experimental studies, active drops propel in a liquid bulk due to self-generated interfacial stresses of solutal origin. Here, we demonstrate the self-propulsion of a volatile drop on the surface of a liquid bath due to stresses of thermal origin. Evaporative heat pumping is converted into directed motion driven by thermocapillary stresses, which emerge on the drop surface as a result of a symmetry breaking of the drop temperature field. The dependence of the drop speed on the activity source, i.e. the evaporation flux, is derived with scaling arguments and captures the experimental data.

cond-mat.soft↗

arXiv2020

Analytical results for the capacitance of a circular plate capacitor

We study the classic problem of the capacitance of a circular parallel plate capacitor. At small separations between the plates, it is initially considered in 19th century by Kirchhoff who found the leading and the subleading term in the capacitance. Despite a large interest in the problem, one and a half century later, analytically was found only the second subleading term. Using the recent advances in the asymptotic analysis of Fredholm integral equations of the second kind with finite support, here we study the one governing the circular capacitor, known as the Love equation. We found analytically many new subleading terms in the capacitance at small separations. We also calculated the asymptotic expansion at large separations, thus providing the two simple expressions which practically describe the capacitance at all distances. The approach described here could be used to find exact analytical expansions for the capacitance to an arbitrary number of terms in both regimes of small and large separations.

math-ph↗

arXiv2019

Fluctuation-induced potential for an impurity in a semi-infinite one-dimensional Bose gas

We consider an impurity in a semi-infinite one-dimensional system of weakly-interacting bosons. We calculate the interaction potential for the impurity due to the end of the system, i.e., the wall. For local repulsive (attractive) interaction between the impurity and the Bose gas, the interaction potential is attractive (repulsive). At short distances from the wall it decays exponentially crossing over into a universal $1/r^2$ behavior at separations $r$ above the healing length. Our results can also be interpreted as a Casimir-like interaction between two impurities, where one of them is infinitely strongly coupled to the Bose gas. We discuss various scenarios for the induced interaction between the impurities using the scattering approach. We finally address the phenomenon of localization of the impurity near the wall. In the paper we mainly study the case of a static impurity, however the universal $1/r^2$ interaction also holds for a slowly moving impurity.

cond-mat.quant-gas↗

arXiv2019

Exact Results for the Boundary Energy of One-Dimensional Bosons

We study bosons in a one-dimensional hard-wall box potential. In the case of contact interaction, the system is exactly solvable by the Bethe ansatz, as first shown by Gaudin in 1971. Although contained in the exact solution, the boundary energy in the thermodynamic limit for this problem is only approximately calculated by Gaudin, who found the leading order result at weak repulsion. Here we derive an exact integral equation that enables one to calculate the boundary energy in the thermodynamic limit at an arbitrary interaction. We then solve such an equation and find the asymptotic results for the boundary energy at weak and strong interactions. The analytical results obtained from the Bethe ansatz are in agreement with the ones found by other complementary methods, including quantum Monte Carlo simulations. We study the universality of the boundary energy in the regime of a small gas parameter by making a comparison with the exact solution for the hard rod gas.

cond-mat.quant-gas↗

arXiv2019

Field-theoretical approach to the Casimir-like interaction in a one-dimensional Bose gas

We study the fluctuation-induced interaction between two impurities in a weakly-interacting one-dimensional Bose gas using the field theoretical approach. At separations between impurities shorter and of the order of the healing length of the system, the induced interaction has a classical origin and behaves exponentially. At separations longer than the healing length, the interaction is of a quantum origin and scales as the third power of the inverse distance. Finite temperature destroys the quasi-long-range order of the Bose gas and, accordingly, the induced interaction becomes exponentially suppressed beyond the thermal length. We obtain analytical expressions for the induced interaction at zero and finite temperature that are valid at arbitrary distances. We discuss experimental realizations as well as possible formation of bound states of two impurities, known as bipolarons.

cond-mat.quant-gas↗

arXiv2019

The Casimir-like effect in a one-dimensional Bose gas

The electromagnetic Casimir effect manifests as the interaction between uncharged conducting objects that are placed in a vacuum. More generally, the Casimir-like effect denotes an induced interaction between external bodies in a fluctuating medium. We study the Casimir-like interaction between two impurities embedded in a weakly interacting one-dimensional Bose gas. We develop a theory based on the Gross-Pitaevskii equation that accounts for the effect of quantum fluctuations. At small separations, the induced interaction between the impurities decays exponentially with the distance. This is a classical result that can be understood using the mean-field Gross-Pitaevskii equation. We find that at larger distances, the induced interaction crosses over into a power law dependence due to the quantum fluctuations. We obtain an analytic expression for the interaction that interpolates between the two limiting behaviors. The obtained result does not require any regularization.

cond-mat.quant-gas↗

arXiv2017

Quasiparticle decay in a one-dimensional Bose-Fermi mixture

In a one-dimensional weakly interacting Bose-Fermi mixture one branch of elementary excitations is well described by the Bogoliubov spectrum. Here we use the microscopic theory to study the decay of such quasiparticle excitations. The main scattering process which leads to their decay is the backscattering of a Bogoliubov quasiparticle off the Fermi sea, where a particle-hole pair is excited. For a low-momentum quasiparticle (phonon) of momentum $q$, we find that the decay rate scales as $q^3$ provided $q$ is smaller than the Fermi momentum $k_F$, while in the opposite case the decay behaves as $q^2$. If the ratio of the masses of fermions and bosons equals to the ratio of the boson-fermion and the boson-boson interaction strengths, the decay rate changes dramatically. It scales as $q^7$ for $q k_F$. For a high momentum Bogoliubov quasiparticle, we find a constant decay rate for $q k_F$. We also find an analytic expression for the decay rate in the crossover region between low and high momenta. The decay rate is a continuous, but nonanalytic function of the momentum at $q=k_F$. In the special case when the parameters of our system correspond to the integrable model, we observe that the decay rate vanishes.

cond-mat.quant-gas↗