Controlling sliding droplets with optimal contact angle distributions and a phase field model

We consider the optimal control of a droplet on a solid by means of the static contact angle between the contact line and the solid. The droplet is described by a thermodynamically consistent phase field model from [Abels et al., Math. Mod. Meth. Appl. Sc., 22(3), 2012] together with boundary data for the moving contact line from [Qian et al., J. Fluid Mech., 564, 2006]. We state an energy stable time discrete scheme for the forward problem based on known results, and pose an optimal control problem with tracking type objective.TU Berlin, Open-Access-Mittel - 201

Direct Numerical Simulations of Liquids on Microstructured Surfaces: Analysing the Fluid Dynamics on Packing

Structured high performance packing for packing columns have macrostructures, e.g., corrugated or folded sheets, and in many cases microstructures or surface topographies with geometrical dimensions in the same order of magnitude as the film thicknesses. For an optimal design of microstructured surfaces and for the development of novel methodologies to predict the mass transfer, a reliable description of the influence of these microstructures is crucial. To research the influence of these microstructures on the liquid film in detail, and later on optimize the geometry, Direct Numerical Simulations applying the Cahn-Hilliard-Navier-Stokes (CHNS) equations were performed for this study. The model and the implementation were validated against analytical solutions for undisturbed laminar film flows. The influence of two single microstructures (triangle and rectangle) on the gas-liquid interface and the velocity in the liquid were systematically investigated. Thereby, it was observed, that small microstructures in comparison to the film thickness have no influence on the gasliquid interface. In contrast, higher structures could increase the interfacial area. The results indicate, that systematic studies on a wide range of geometries, phase properties and gas velocities can give valuable information on the path to optimal microstructures

Experimental characterization of stable liquid rivulets on inclined surfaces: Influence of surface tension, viscosity and inclination angle on the interfacial area

In this work, liquid rivulets on inclined, smooth surfaces were examined experimentally using light-induced fluorescence. The influence of viscosity, surface tension and inclination angle was studied in terms of the Reynolds and Kapitza numbers. Detailed results on the interfacial area of the rivulets were obtained. Based on the experimental results, a correlation of the interfacial area in dependence on the Reynolds and Kapitza numbers is proposed. It is found, that the correlation can reproduce the experiments very well

Comparison of energy stable simulation of moving contact line problems using a thermodynamically consistent Cahn–Hilliard Navier–Stokes model

Liquid droplets sliding along solid surfaces are a frequently observed phenomenon in nature, e.g., raindrops on a leaf, and in everyday situations, e.g., drops of water in a drinking glass. To model this situation, we use a phase field approach. The bulk model is given by the thermodynamically consistent Cahn– Hilliard Navier–Stokes model from [Abels et al., Math. Mod. Meth. Appl. Sc., 22(3), 2012]. To model the contact line dynamics we apply the generalized Navier boundary condition for the fluid and the dynamically advected boundary contact angle condition for the phase field as derived in [Qian et al., J. Fluid Mech., 564, 2006]. In recent years several schemes were proposed to solve this model numerically. While they widely differ in terms of complexity, they all fulfill certain basic properties when it comes to thermodynamic consistency. However, an accurate comparison of the influence of the schemes on the moving contact line is rarely found. Therefore, we thoughtfully compare the quality of the numerical results obtained with three different schemes and two different bulk energy potentials. Especially, we discuss the influence of the different schemes on the apparent contact angles of a sliding droplet

Influence of Liquid Density and Surface Tension on the Pinning of Sliding Droplets on a Triangular Microstructure

Sliding droplets are crucial in many industrial applications. Examples are coating and separation processes involving multiple phases and liquid films. Often one can observe how a sliding droplet halts midstream on a solid surface. Wetting defects such as topographic structures can lead to a pinning of sliding droplets. In order to assess the influence of liquid density and surface tension on the pinning, direct numerical simulations are performed. After the model and its discretization are introduced, the solution is validated. Simulation results of gravity‐driven droplets on inclined surfaces with structures in the size of the droplets are presented and the observed requirements for pinning a sliding droplet to a surface are discussed.DFG, 188264188, GRK 1754: Optimierung und Numerik für partielle Differentialgleichungen mit nicht glatten Strukture

Resistive double-diffusive instability in the dead-zones of protostellar disks

We outline a novel linear instability that may arise in the dead-zones of protostellar disks, and possibly the fluid interiors of planets and protoplanets. In essence it is an axisymmetric buoyancy instability, but one that would not be present in a purely hydrodynamical gas. The necessary ingredients for growth include a negative radial entropy gradient (of any magnitude), weak magnetic fields, and efficient resistive diffusion (in comparison with thermal diffusion). The character of the instability is local, axisymmetric, and double-diffusive, and it attacks lengths much shorter than the resistive scale. Like the axisymmetric convective instability, it draws its energy from the negative radial entropy gradient; but by utilising the diffusing magnetic field, it can negate the stabilising influence of rotation. Its nonlinear saturated state, while not transporting appreciable angular momentum, could drive radial and vertical mixing, which may influence the temperature structure of the disk, dust dynamics and, potentially, planet formation.Comment: 16 pages, 5 figures. MNRAS Accepted. V2: cosmetic changes to bring in line with MNRAS versio

Spontaneous charging affects the motion of sliding drops

Water drops moving on surfaces are not only an everyday phenomenon seen on windows but also form an essential part of many industrial processes. Previous understanding is that drop motion is dictated by viscous dissipation and activated dynamics at the contact line. Here we demonstrate that these two effects cannot fully explain the complex paths of sliding or impacting drops. To accurately determine the forces experienced by moving drops, we imaged their trajectory when sliding down a tilted surface, and applied the relevant equations of motion. We found that drop motion on low-permittivity substrates is substantially influenced by electrostatic forces. Our findings confirm that electrostatics must be taken into consideration for the description of the motion of water, aqueous electrolytes and ethylene glycol on hydrophobic surfaces. Our results are relevant for improving the control of drop motion in many applications, including printing, microfluidics, water management and triboelectric nanogenerators