arXiv subjects

Jan Diekmann

Publications and source records attributed to Jan Diekmann.

6 recordsLinked to original sources

arXiv2026

Interface-dominated sliding compound drops

We investigate compound drops composed of two immiscible nonvolatile partially wetting liquids that slide down an inclined homogeneous smooth solid substrate based on a mesoscopic hydrodynamic two-layer model in full-curvature formulation. First, drops of one liquid stationarily sliding on a layer of the other liquid are briefly investigated with a focus on the dependence of drop velocity and interface profiles on inclination and mean thickness of the adaptive substrate. Then, stationary sliding compound drops are studied with a focus on the dependence of their configuration, velocity, dynamic Young and Neumann angles on three control parameters, namely, the inclination, the volume ratio and the viscosity ratio. The reasons for the encountered dependence of the velocity on configuration are clarified based on a discussion of the lateral dissipation profile. Finally, we briefly consider the time-periodic fusion-overtaking-splitting behavior found outside the existence range of the stationary sliding compound drops as determined by saddle-node bifurcations.

physics.flu-dyn↗

arXiv2024

Mesoscopic hydrodynamic model for spreading, sliding and coarsening compound drops

We revisit the mesoscopic hydrodynamic description of the dynamics of sessile partially wetting compound drops, i.e., of drops that consist of two immiscible nonvolatile partially wetting liquids and are situated on a smooth rigid solid substrate. We briefly discuss and complete existing dynamic models employing a gradient dynamics approach. Thereby, the underlying energy features capillarity and wettability contributions for all relevant interfaces in full-curvature formulation. Establishing transparent consistency relations between macroscopic and mesoscopic parameters, we obtain mesoscopic Neumann and Young laws that are also fully consistent with the macroscopic ones. In particular, we discuss the minimal requirements for the wetting energy that ensure the full spectrum of macroscopic parameters {for partially wetting cases} is addressed by the mesoscopic model. Subsequently, we distinguish long-wave and full-curvature variants of the dynamical model based on properties of the energy, and employ the latter to illustrate the usage of the mesoscopic model. As examples, we chose the spreading of individual compound drops on one-dimensional horizontal substrates, sliding compound drops on one-dimensional inclined substrates, and the coarsening of drop ensembles on one- and two-dimensional horizontal substrates. In each case, the discussion emphasizes occurring qualitative changes in the drop configurations.

physics.flu-dyn↗

arXiv2024

Drops of volatile binary mixtures on brush-covered substrates

We introduce a mesoscopic hydrodynamic model for drops of binary mixtures of volatile partially wetting liquids on brush-covered substrates, i.e., we model the coupled dynamics of spreading, evaporation, imbibition, diffusion and partial demixing of the two volatile components across the three phases - brush, drop and gas. The formulation of the model as gradient dynamics on an underlying free energy functional allows us to systematically account for cross-couplings between the six scalar fields needed to describe the dynamics of both components within each of the three phases. The energy accounts for concentration- and brush state-dependent capillarity and wettability, miscibility of the two components within drop and brush, and entropy in the gas. Finally, the usage of the model is illustrated by employing numerical time simulations to study the dynamics of a sessile drop.

physics.flu-dyn↗

arXiv2023

Drops on polymer brushes -- advances in thin-film modelling of adaptive substrates

We briefly review recent advances in the hydrodynamic modeling of the dynamics of droplets on adaptive substrates, in particular, solids that are covered by polymer brushes. Thereby, the focus are long-wave and full-curvature variants of mesoscopic hydrodynamic models in gradient dynamics form. After introducing the approach for films/drops of nonvolatile simple liquids on rigid smooth solid substrate, it is first expanded to an arbitrary number of coupled degrees of freedom, before considering the specific case of drops of volatile liquids on brush-covered solids. After presenting the model its usage is illustrated by briefly considering the natural and forced spreading of drops of nonvolatile liquids on a horizontal brush-covered substrate as well as drops sliding down a brush-covered incline. Finally, also volatile liquids are considered.

physics.flu-dyn↗

arXiv2023

Leading-logarithmic approximation by one-loop renormalization group within Matsubara formalism

We demonstrate how to devise a Matsubara-formalism-based one-loop approximation to the flow of the functional renormalization group (FRG) that reproduces identically the leading-logarithmic parquet approximation. This construction of a controlled fermionic FRG approximation in a regime not accessible by perturbation theory generalizes a previous study from the real-time zero-temperature formalism to the Matsubara formalism and thus to the de facto standard framework used for condensed-matter FRG studies. Our investigation is based on a simple model for the absorption of x rays in metals. It is a core part of our construction to exploit that in a suitable leading-logarithmic approximation the values of the particle-hole susceptibility on the real- and on the imaginary-frequency axes are identical.

cond-mat.str-el↗

arXiv2020

Parquet approximation and one-loop renormalization group: Equivalence on the leading-logarithmic level

We investigate the functional renormalization group (FRG) flow of the two-particle vertex function of a model for X-ray absorption in metals. Concerning the appearance of logarithmic divergences, the model is prototypical for an important class of mostly zero- and one-dimensional systems which includes the Kondo model and the interacting one-dimensional Fermi gas. For our analysis we formulate the FRG in the framework of the real-time zero-temperature formalism, in which the model was studied before with a parquet-based approach. We establish that a reasonably crafted, purely-fermionic one-loop FRG approximation is fully equivalent on a detailed level to the leading-logarithmic parquet approximation. These two approximation schemes are thus found to just represent different perspectives on the same technical steps. This finding also reconfirms the traditional understanding of the capabilities of one-loop RG approximations for such models, which was recently put into question by an investigation of the X-ray-absorption model with multiloop FRG.

cond-mat.str-el↗