publications

2021

1. Optimal Control of Sliding Droplets Using the Contact Angle Distribution

   Bonart, Henning, and Kahle, Christian

   SIAM Journal on Control and Optimization 2021

   Abs DOI

   Controlling the shape and position of moving and pinned droplets on a solid surface is an important feature often found in microfluidic applications. In this work, we consider a well investigated phase field model including contact line dynamics as the state system for an (open-loop) optimal control problem. Here the spatially and temporally changeable contact angles between droplet and solid are considered as the control variables. We consider a suitable, energy stable, time discrete version of the state equation in our optimal control problem. We discuss regularity of the solution to the time discrete state equation and its continuity and differentiability properties. Furthermore, we show existence of solutions and state first order optimality conditions to the optimal control problem. We illustrate our results by actively pushing a droplet uphill against gravity in an optimal way.

2. Simulation and control of droplets and films on surfaces

   Bonart, Henning

   Doctoral Thesis 2021

   Abs DOI

   Liquid droplets sliding along solid surfaces are frequently observed phenomena in nature, e.g., raindrops on a leaf, and in everyday situations, e.g., drops of water in a drinking glass. Furthermore, sliding droplets (and consequently the suppression of those) are crucial in many applications such as the deicing of planes, coating and separation processes or lab-on-a-chip devices. To simulate the droplet dynamics with high accuracy, we utilize a thermodynamically consistent phase field model for large density ratios. The dynamics of the two-phase flow are described by the coupling between the Cahn-Hilliard (CH) and Navier-Stokes (NS) equations. Especially, the model allows the contact line to slide naturally along the solid surfaces and greatly reduces spurious currents even for low Capillary numbers. In addition, boundary conditions which allow for non-equilibrium contact angles and slip between the moving contact lines and the solid surface are applied. The resulting model forms a very tightly coupled and nonlinear system of equations. Therefore we carefully select the solution strategy to enable efficient and accurate large-scale simulations with millions of degrees of freedom. This includes the linearization and decoupling of the equations, preconditioned Krylov methods for the solution of the arising linear systems as well as anisotropic mesh adaption to guarantee high mesh resolutions. To show the capabilities of our approach we discuss numerous results of flows with or without a moving contact line. In particular, we investigate the influence of single microstructures with sharp corners on the instability onset of overflowing liquid films and the pinning mechanism of sliding droplets on sharp corners. Finally, we introduce the control of both the shape and position of droplets on solid surfaces through optimal contact angle distributions. We demonstrate our approach by pinning a sliding droplet at a specific position on an inclined plate with a desired shape using temporally and spatially varying contact angles.

2020

1. Stability of gravity-driven liquid films overflowing microstructures with sharp corners

   Bonart, Henning, Rajes, Sangitha, Jung, Johannes, and Repke, Jens-Uwe

   Physical Review Fluids 2020

   DOI
2. Optimal Control of Droplets on a Solid Surface Using Distributed Contact Angles

   Bonart, Henning, Kahle, Christian, and Repke, Jens-Uwe

   Langmuir 2020

   Abs DOI

   Controlling the shape and position of moving and pinned droplets on a solid surface is an important feature often found in microfluidic applications. However, automating them, e.g., for high-throughput applications, rarely involves model-based optimal control strategies. In this work, we demonstrate the optimal control of both the shape and position of a droplet sliding on an inclined surface. This basic test case is a fundamental building block in plenty of microfluidic designs. The static contact angle between the solid surface, the surrounding gas, and the liquid droplet serves as the control variable. By using several control patches, e.g., like that performed in electrowetting, the contact angles are allowed to vary in space and time. In computer experiments, we are able to calculate mathematically optimal contact angle distributions using gradient-based optimization. The dynamics of the droplet are described by the Cahn-Hilliard-Navier-Stokes equations. We anticipate our demonstration to be the starting point for more sophisticated optimal design and control concepts.

2019

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

   Bonart, Henning, Kahle, Christian, and Repke, Jens-Uwe

   Journal of Computational Physics 2019

   Abs DOI

   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. (2012) [8]. 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. (2006) [7]. 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.

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

   Bonart, Henning, Kahle, Christian, and Repke, Jens-Uwe

   Proceedings in Applied Mathematics and Mechanics 2019

   Abs DOI

   Abstract 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.

3. Influence of liquid density and surface tension on the pinning of sliding droplets on a triangular microstructure

   Bonart, Henning, Jung, Johannes, Kahle, Christian, and Repke, Jens-Uwe

   Chemical Engineering & Technology 2019

   Abs DOI

   Abstract 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.

2018

1. Direct numerical simulations of liquids on microstructured surfaces: Analysing the fluid dynamics on packing

   Bonart, Henning, and Repke, Jens-Uwe

   Chemical Engineering Transactions 2018

   Abs DOI

   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.

2017

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

   Bonart, Henning, Marek, André, and Repke, Jens-Uwe

   Chemical Engineering Research and Design 2017

   Abs DOI

   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.

2. MOSAIC - enabling large-scale equation-based flow sheet optimization

   Esche, Erik, Hoffmann, Christian, Illner, Markus, Müller, David, Fillinger, Sandra, Tolksdorf, Gregor, Bonart, Henning, Wozny, Günter, and Repke, Jens-Uwe

   Chemie Ingenieur Technik 2017

   Abs DOI

   Abstract Dedicated software exists for both process simulation and optimization. Given the advantages of simultaneous optimization schemes, engineers are frequently tasked with reimplementing their simulation models in optimization languages or environments. In this contribution, a workflow is introduced to model chemical engineering models in MathML and to have an automatic code generation for both specialized simulation and optimization tools. Two examples are given to highlight the performance of this workflow implemented in the modeling, simulation, and optimization environment MOSAIC.

2015

1. Numerical simulation of a structured catalytic methane reformer by DUO: The new computational interface for OpenFOAM&#0174 and DETCHEM™

   Hettel, Matthias, Diehm, Claudia, Bonart, Henning, and Deutschmann, Olaf

   Catalysis Today 2015

   Abs DOI

   The catalytic partial oxidation of methane over a honeycomb-structured Rh/Al2O3 coated catalyst is studied at a molar C/O ratio of unity and short-contact times experimentally and numerically. Axial species and temperature profiles inside the catalytic monolith are measured by a capillary sampling technique. A detailed numerical analysis of the flow, temperature and species concentration profiles is conducted using the new software tool DUO, which is an interface for the coupling of the computational tools OpenFOAM&#0174 and DETCHEM™. This interface enables the integration of detailed surface chemistry into OpenFOAM&#0174 and allows the time-efficient calculation of structured catalysts and other catalytic reactors with multiple combined fluid and solid regions including heterogeneous reactions. In comparison with experimental data, spatial profiles of species and temperature are analyzed. The thermal boundary conditions are shown to have a strong impact on reliable predictions. Even though the characteristics of the influence of radial heat loss on the conversion can be governed, the use of a radiation model is recommended.

2. Direct numerical simulation of chemically reacting flows with the public domain code OpenFOAM

   Zhang, Feichi, Bonart, Henning, Zirwes, Thorsten, Habisreuther, Peter, Bockhorn, Henning, and Zarzalis, Nikolaos

   2015

   Abs DOI

   \copyright Springer International Publishing Switzerland 2015.A new solver for direct numerical simulation (DNS) of chemically reacting flow is introduced, which is developed within the framework of the opensource program OpenFOAM. The code is capable of solving numerically the compressible reactive flow equations employing unstructured grids. Therewith a detailed description of the chemistry, e.g. the reaction rates, and transport, e.g. the diffusion coefficients, has been accomplished by coupling the free chemical kinetics program Cantera. The solver implies a fully implicit scheme of second order for the time derivative and a fourth order interpolation scheme for the discretization of the convective term. An operator-split approach is used by the solver which allows solutions of the flow and chemistry with time scales that differ by orders of magnitude, leading to a significantly improved performance. In addition, the solver has proved to exhibit a good parallel scalability. The implementation of the code has first been validated by means of one-dimensional premixed flames, where the calculated flame profiles are compared with results from the commercially Chemkin code. To demonstrate the applicability of the code for three-dimensional problems, it has been applied to simulate the flame propagation in an explosion vessel of laboratory-scale. A computational grid with 144 million finite volumes has been used for this case. The simulation has been performed parallel on 8192 processors from the HERMIT cluster of HLRS. The calculated burning velocity agrees well with the experimental data.

2014

1. Direct Numerical Simulation of Chemically Reacting Flows with the Public Domain Code OpenFOAM

   Bonart, Henning, Zhang, Feichi, Bonart, Henning, Zirwes, Thorsten, Habisreuther, Peter, Bockhorn, Henning, and Zarzalis, Nikolaos

   2014

   DOI