Prof. Dr. Dieter Bothe

Director of the institute


work +49 6151 16-21463

Work L2|06 400
Peter-Grünberg-Straße 10
64287 Darmstadt

Research Topics

Continuum thermodynamical modeling, numerical simulation and mathematical analysis of transport processes at fluidic interfaces: Multicomponent diffusion, (reactive) mass transfer with surfactant influence, Non-Newtonian flows, Dynamic Contact Lines

Modeling and Analysis of Reaction-Diffusion-Advection Bulk-Surface Systems

University Education

  • 1982 – 1988 Studies in Mathematics at the University of Paderborn, Germany, Minor subject: Computer Science (Informatik), Additional from 1985: Studies in Physics
  • 05/1988 Degree of “Dipl.-Math.” in Mathematics, University of Paderborn
  • 01/1993 Ph.D. (Dr. rer. nat.) in Mathematics, University of Paderborn, Germany
    Thesis: Multivalued Differential Equations on Graphs and Applications
  • 02/2000 Habilitation, Mathematics, University of Paderborn, Germany
    Thesis: Nonlinear Evolutions in Banach Spaces (opens in new tab)

Current Position

  • 2014 – Full Professor, Department of Mathematics, TU Darmstadt

Previous Positions

  • 1988 – 1993 Research associate, Faculty of Mathematics & Computer Science, University of Paderborn
  • 1993 – 1999 Postdoctoral research fellow, Faculty of Mathematics & Computer Science, University of Paderborn
  • 1999 – 2005 Assistant Professor (Privatdozent) / Associate Professor (Hochschuldozent), Chemical Engineering, Faculty of Natural Sciences, University of Paderborn
  • 2005 – 2009 Chair for Mathematics at the Center for Computational Engineering Science, RWTH Aachen
  • 2009 – 2014 Research Professorship “Mathematical Modeling and Analysis”. Center of Smart Interfaces, TU Darmstadt

Honors, Awards and (declined) Offers of Professorships

  • 1993 Doctorate degree with “summa cum laude”
  • 2002 Research Award 2002 of the University of Paderborn
  • 2005 Offer Associate Professorship (W2) Nonlinear Analysisfrom the University of Magdeburg
  • 2009 – 2014 Awarded Research Professorship at the Cluster of Excellence EXC 259 Center of Smart Interfaces,TU Darmstadt
  • 2014 Offer Full professor (W3) Applied Mathematics from the University of Paderborn

Editorial, Advising and Reviewing Activities

  • 2017 – Assigned Member of the Scientific Council of the TU Darmstadt
  • 2013 – 2015 Steering Committee of the GAMM section Partial Differential Equations
  • 2014 – 2015 Steering Committee of the TU Darmstadt Research Center Smart Interfaces”
  • 2012 – 2019 Steering Committee of the Int. Graduate School Mathematical Fluid Dynamics IRTG 1529
  • 2012 – Editorial Board Nonlinear Analysis: Real World Applications
  • 2010 – Editorial Advisory Board International Journal of Multiphase Flows

Advisory Board of the ProcessNet committees Multiphase Flows (2004-), Mixing Processes (2008-13), Computational Fluid Dynamics (2010-). Reviewer for several National Funding Agencies. Reviewer for numerous mathematical and engineering international journals.

Institutional Responsibilities

  • 2006 – 2009 Vice-Director of the Center for Computational Engineering Science (CCES, with W. Marquardt), RWTH Aachen
  • 2007 – 2009 Founding Member of the Jülich Aachen Research Alliance (JARA)
  • 2016 – 2018 Delegate of the Senate of the TU Darmstadt for Hiring Committees
  • 2020 – 2022 Vice Dean Department of Mathematics, TU Darmstadt

Research Coordination Activities

  • 2006 – 2012 Coordinator of DFG-PAK 119 Reactive mass transfer from rising gas bubbles
  • 2010 – 2017 Coordinator of the DFG Priority Program 1506 Transport Processes at Fluidic Interfaces (with A. Reusken, RWTH Aachen)
  • 2013 – Coordinator of the section Modeling and Simulation within the DFG Priority Program 1740 Reactive Bubbly Flows
  • 2016 – Vice-Director of the TU Darmstadt Profile Area Thermo-Fluids & Interfaces
  • 2016 – Vice-Director of CRC 1194 Interaction between Transport and Wetting Processes, Coordinator of the section Modeling, Simulation & Optimization

Organisation of Scientific Meetings

  • 07/2007 6th International Congress on Multiphase Flows (ICMF2007), Leipzig (LOC)
  • 10/2010 Int. Conf. Evolution Equations, Schmitten (chair)
  • 10/2011 1st Int. Symposium Multiscale Multiphase Process Engineering, Kanazawa (vice chair)
  • 03/2012 GAMM Annual Conference (organising committee)
  • 06/2012 7th Int. OpenFOAM Workshop, Darmstadt (chair)
  • 06/2013 Summer school Transport Processes at Fluidic Interfaces, Darmstadt (chair)
  • 06/2014 2nd Int. Conf. on Numerical Methods in Multiphase Flow, Darmstadt (chair)
  • 2011, 12, 18 Section Interfacial Flows at GAMM Annual Conferences (section chair)
  • 06/2015 Int. Workshop Transport Processes at Fluidic Interfaces, Darmstadt (chair)
  • 06/2016 9th International Congress on Multiphase Flows (ICMF2016), Florence (Scientific Committee)
  • 09/2021 Droplets in Darmstadt (organizer)

Memberships in Scientific Societies

  • 1993 – Member of the DMV (German Mathematical Society)
  • 1999 – 2006 Member of the AMS (American Mathematical Society)
  • 2003 – Member of the DECHEMA (Society for Chemical Technology and Biotechnology)

Teaching Activities

  • 2000 – 2005 Courses on PDEs, Harmonic Analysis, Mathematical Modeling at Univ. Paderborn
  • 2006 – 2009 Math for Comp. Eng. Sci. (new course, 2 x 130 + 3 x 80 hours), PDEs, Linear & Nonlinear Semigroups at RWTH Aachen
  • 2010 – 2020 Math. Modeling of Fluid Interfaces (2 x 40 hours), PDEs, Functional Analysis, Evolution Equations, Reaction-Diffusion systems, Math. for Electrical Engineers
  • 2005 – Different lecture series on Transport Processes at Fluidic Interfaces; at Oberwolfach Research Center, CISM (Udine), Waseda Univ. (Tokyo), several summerschools
  • 2015 – Annual short course lectures: two-phase numerical methods; Volume of Fluid method for droplet collisions
Numerical wetting benchmarks--advancing the plicRDF-isoAdvector unstructured Volume-of-Fluid (VOF) method. Asghar, M. Hassan; Fricke, Mathis; Bothe, Dieter; Marić, Tomislav (preprint).
Efficient three-material PLIC interface positioning on unstructured polyhedral meshes. Kromer, Johannes; Potyka, Johanna; Schulte, Kathrin & Bothe, Dieter (preprint).
A locally signed-distance preserving level set method (SDPLS) for moving interfaces. Fricke, Mathis; Marić, Tomislav; Vučković, Aleksandar & Bothe, Dieter (preprint).
A collocated unstructured finite volume Level Set / Front Tracking method for two-phase flows with large density-ratios. Liu, Jun; Tolle, Tobias; Bothe, Dieter & Marić, Tomislav (preprint).
Second-order accurate normal reconstruction from volume fractions on unstructured meshes with arbitrary polyhedral cells. Kromer, Johannes; Leotta, Fabio & Bothe, Dieter (preprint).
On the structure of continuum thermodynamical diffusion fluxes -- A novel closure scheme and its relation to the Maxwell-Stefan and the Fick-Onsager approach. Bothe, Dieter & Druet, Pierre-Etienne (2023), Int. Journal of Engineering Science 184, 103818.
Third-order accurate initialization of VOF volume fractions on unstructured meshes with arbitrary polyhedral cells. Kromer, Johannes & Bothe, Dieter (2023), J. Comp. Phys. 475, 111840.
Computing hydrodynamic eigenmodes of channel flow with slip – A highly accurate algorithm. Raju, Suraj; Gründing, Dirk; Marić, Tomislav; Bothe, Dieter & Fricke, Mathis (2022), The Canadian Journal of Chemical Engineering 100 (12), 3531-3547.
Computation of interfacial flows using Continuous Surface Stress method with adaptive mesh refinement in a Quad/Octree grid structure. Liu, Muyuan; Bothe, Dieter; Yang, Yiren & Chen, Hao (2022), Computers & Fluids 245, 105610.
On the molecular mechanism behind the bubble rise velocity jump discontinuity in viscoelastic liquids. Bothe, Dieter; Niethammer, Matthias; Pilz, Christian & Brenn, Günter (2022), J. Non-Newtonian Fluid Mech. 302, 104748.
Multipath Flow Metering of High-Velocity Gas using Ultrasonic Phased-Arrays. Haugwitz, Christoph; Hartmann, Claas; Allevato, Gianni; Rutsch, Matthias; Hinrichs, Jan; Brötz, Johannes; Bothe, Dieter; Pelz, Peter F. & Kupnik, Mario (2022), IEEE Open Journal of Ultrasonics, Ferroelectrics, and Frequency Control 2, 30-39.
triSurfaceImmersion: Computing volume fractions and signed distances from triangulated surfaces immersed in unstructured meshes. Tolle, Tobias; Gründing, Dirk; Bothe, Dieter & Marić, Tomislav (2022), Computer Physics Communications 273, 108249.
Sharp-Interface Continuum Thermodynamics of multicomponent fluid systems with interfacial mass. Bothe, Dieter (2022), Int. Journal of Engineering Science 179, 103731.
Face-based Volume-of-Fluid interface positioning in arbitrary polyhedra. Kromer, Johannes & Bothe, Dieter (2022), J. Comp. Phys. 449, 110776.
Multicomponent incompressible fluids – an asymptotic study. Bothe, Dieter; Dreyer, Wolfgang & Druet, Pierre-Etienne (2021), ZAMM e202100174, WIAS Preprint 2825.
Analysis of some heterogeneous catalysis models with fast sorption and fast surface chemistry. Augner, Björn & Bothe, Dieter (2021), J. Evol. Eqs. 21, 3521-3552.
Well-posedness analysis of multicomponent incompressible flow models. Bothe, Dieter & Druet, Pierre-Etienne (2021), J. Evol. Eqs. 21, 4039-4093, WIAS Preprint 2720.
Mass transport in multicomponent compressible fluids: Local and global well-posedness in classes of strong solutions for general class-one models. Bothe, Dieter & Druet, Pierre-Etienne (2021), Nonlinear Analysis: Theory, Methods & Applications 210, 112389, WIAS Prepring 2658.
Small-scale phenomena in reactive bubbly flows: experiments, numerical modeling, and applications. Schlüter, Michael; Herres-Pawlis, Sonja; Nieken, Ulrich; Tuttlies, Ute & Bothe, Dieter (2021), Annual Review of Chemical and Biomolecular Engineering 12, 625-643.
Breakup dynamics of capillary bridges on hypophobic stripes. Hartmann, Maximilian; Fricke, Mathis; Weimar, Lukas; Gründing, Dirk; Marić, Tomislav; Bothe, Dieter & Hardt, Steffen (2021), Int. J. Multiphase Flow 138.
Computing Mass Transfer at Deformable Bubbles for High Schmidt Numbers. Weiner, Andre; Gründing, Dirk & Bothe, Dieter (2021), Chemie Ingenieur Technik.
The fast-sorption and fast-surface-reaction limit of a heterogeneous catalysis model. Augner, Björn & Bothe, Dieter (2021), Discrete Continuous Dynamical Systems – Series S 14 (2), 533-574.
Numerical simulation of non-isothermal viscoelastic flows at high Weissenberg numbers using a finite volume method on general unstructured meshes. Meburger, Stefanie; Niethammer, Matthias; Bothe, Dieter & Schäfer, Michael (2021), Journal of Non-Newtonian Fluid Mechanics, 287, 104451.
On moving hypersurfaces and the discontinuous ODE-system associated with two-phase flows. Bothe, Dieter (2020), Nonlinearity, 33 (10), 5425–56.
Reflections on the article “Moving contact lines and dynamic contact angles: a ‘litmus test’ for mathematical models and some new challenges” by Yulii D. Shikhmurzaev. Bothe, Dieter (2020), The European Physical Journal Special Topics, 229 (10), 1979–87.
Boundary conditions for dynamic wetting – A mathematical analysis. Fricke, Mathis & Bothe, Dieter (2020), The European Physical Journal Special Topics, 229 (10), 1849–65.
Contact line advection using the geometrical Volume-of-Fluid method. Fricke, Mathis; Marić, Tomislav & Bothe, Dieter (2020), Journal of Computational Physics, 407, 109221.
A comparative study of transient capillary rise using direct numerical simulations. Gründing, Dirk; Smuda, Martin; Antritter, Thomas; Fricke, Mathis; Rettenmaier, Daniel; Kummer, Florian; Stephan, Peter; Marschall, Holger & Bothe, Dieter (2020), Applied Mathematical Modelling, 86, 142–65.
Mass transfer from single carbon-dioxide bubbles in surfactant-electrolyte mixed aqueous solutions in vertical pipes. Hori, Yohei; Bothe, Dieter; Hayashi, Kosuke; Hosokawa, Shigeo & Tomiyama, Akio (2020), International Journal of Multiphase Flow, 124, 103207.
Unstructured un-split geometrical Volume-of-Fluid methods – A review. Marić, Tomislav; Kothe, Douglas B. & Bothe, Dieter (2020), Journal of Computational Physics, 420, 109695.
SAAMPLE: A Segregated Accuracy-driven Algorithm for Multiphase Pressure-Linked Equations. Tolle, Tobias; Bothe, Dieter & Marić, Tomislav (2020), Computers & Fluids, 200, 104450.
Breakup Dynamics of Capillary Bridges on Hydrophobic Stripes. Hartmann, Maximilian; Fricke, Mathis; Weimar, Lukas; Gründing, Dirk; Marić, Tomislav; Bothe, Dieter & Hardt, Steffen (04.10.2019).
A kinematic evolution equation for the dynamic contact angle and some consequences. Fricke, Mathis; Köhne, Matthias & Bothe, Dieter (2019), Physica D: Nonlinear Phenomena, 394, 26–43.
Highly accurate computation of volume fractions using differential geometry. Kromer, Johannes & Bothe, Dieter (2019), Journal of Computational Physics, 396, 761–84.
Toward the predictive simulation of bouncing versus coalescence in binary droplet collisions. Liu, M. & Bothe, D. (2019), Acta Mechanica, 230 (2), 623–44.
An extended volume of fluid method and its application to single bubbles rising in a viscoelastic liquid. Niethammer, Matthias; Brenn, Günter; Marschall, Holger & Bothe, Dieter (2019), Journal of Computational Physics, 387, 326–55.
Robust Direct Numerical Simulation of Viscoelastic Flows. Niethammer, Matthias; Marschall, Holger & Bothe, Dieter (2019), Chemie Ingenieur Technik, 91 (4), 522–28.
Load balanced 2D and 3D adaptive mesh refinement in OpenFOAM. Rettenmaier, Daniel; Deising, Daniel; Ouedraogo, Yun; Gjonaj, Erion; Gersem, Herbert de; Bothe, Dieter; Tropea, Cameron & Marschall, Holger (2019), SoftwareX, 10, 100317.
A continuum model of heterogeneous catalysis: Thermodynamic framework for multicomponent bulk and surface phenomena coupled by sorption. Souček, Ondřej; Orava, Vít; Málek, Josef & Bothe, Dieter (2019), International Journal of Engineering Science, 138, 82–117.
Data‐Driven Subgrid‐Scale Modeling for Convection‐Dominated Concentration Boundary Layers. Weiner, Andre; Hillenbrand, Dennis; Marschall, Holger & Bothe, Dieter (2019), Chemical Engineering & Technology, 42 (7), 1349–56.
Experimental and numerical investigation of reactive species transport around a small rising bubble. Weiner, Andre; Timmermann, Jens; Pesci, Chiara; Grewe, Jana; Hoffmann, Marko; Schlüter, Michael & Bothe, Dieter (2019), Chemical Engineering Science: X, 1, 100007.
Direct numerical simulation of mass transfer in bubbly flows. Deising, Daniel; Bothe, Dieter & Marschall, Holger (2018), Computers & Fluids, 172, 524–37.
3D direct numerical simulations of reactive mass transfer from deformable single bubbles: An analysis of mass transfer coefficients and reaction selectivities. Falcone, Manuel; Bothe, Dieter & Marschall, Holger (2018), Chemical Engineering Science, 177, 523–36.
Boundedness-preserving implicit correction of mesh-induced errors for VOF based heat and mass transfer. Hill, S.; Deising, D.; Acher, T.; Klein, H.; Bothe, D. & Marschall, H. (2018), Journal of Computational Physics, 352, 285–300.
An enhanced un-split face-vertex flux-based VoF method. Marić, Tomislav; Marschall, Holger & Bothe, Dieter (2018), Journal of Computational Physics, 371, 967–93.
A numerical stabilization framework for viscoelastic fluid flow using the finite volume method on general unstructured meshes. Niethammer, M.; Marschall, H.; Kunkelmann, C. & Bothe, D. (2018), International Journal for Numerical Methods in Fluids, 86 (2), 131–66.
Computational analysis of single rising bubbles influenced by soluble surfactant. Pesci, Chiara; Weiner, Andre; Marschall, Holger & Bothe, Dieter (2018), Journal of Fluid Mechanics, 856, 709–63.
Global wellposedness for a class of reaction–advection–anisotropic-diffusion systems. Bothe, Dieter; Fischer, André; Pierre, Michel & Rolland, Guillaume (2017), Journal of Evolution Equations, 17 (1), 101–30.
Strong well-posedness for a class of dynamic outflow boundary conditions for incompressible Newtonian flows. Bothe, Dieter; Kashiwabara, Takahito & Köhne, Matthias (2017), Journal of Evolution Equations, 17 (1), 131–71.
Global strong solutions for a class of heterogeneous catalysis models. Bothe, Dieter; Köhne, Matthias; Maier, Siegfried & Saal, Jürgen (2017), Journal of Mathematical Analysis and Applications, 445 (1), 677–709.
Modeling and analysis of reactive multi-component two-phase flows with mass transfer and phase transition the isothermal incompressible case. Bothe, Dieter & Prüss, Jan (2017), Discrete & Continuous Dynamical Systems – S, 10 (4), 673–96.
Colliding drops as coalescing and fragmenting liquid springs. Planchette, C.; Hinterbichler, H.; Liu, M.; Bothe, D. & Brenn, G. (2017), Journal of Fluid Mechanics, 814, 277–300.
Highly accurate two-phase species transfer based on ALE Interface Tracking. Weber, Paul S.; Marschall, Holger & Bothe, Dieter (2017), International Journal of Heat and Mass Transfer, 104, 759–73.
Advanced subgrid-scale modeling for convection-dominated species transport at fluid interfaces with application to mass transfer from rising bubbles. Weiner, Andre & Bothe, Dieter (2017), Journal of Computational Physics, 347, 261–89.
A unified single-field model framework for Volume-Of-Fluid simulations of interfacial species transfer applied to bubbly flows. Deising, Daniel; Marschall, Holger & Bothe, Dieter (2016), Chemical Engineering Science, 139, 173–95.
Numerical and experimental analysis of local flow phenomena in laminar Taylor flow in a square mini-channel. Falconi, C. J.; Lehrenfeld, C.; Marschall, H.; Meyer, C.; Abiev, R.; Bothe, D.; Reusken, A.; Schlüter, M. & Wörner, M. (2016), Physics of Fluids, 28 (1), 12109.
A subgrid-scale model for reactive concentration boundary layers for 3D mass transfer simulations with deformable fluid interfaces. Gründing, Dirk; Fleckenstein, Stefan & Bothe, Dieter (2016), International Journal of Heat and Mass Transfer, 101, 476–87.
Numerical study of head-on droplet collisions at high Weber numbers. Liu, Muyuan & Bothe, Dieter (2016), Journal of Fluid Mechanics, 789, 785–805.
Applicability of the linearized theory of the Maxwell-Stefan equations. Weber, Paul S. & Bothe, Dieter (2016), AIChE Journal, 62 (8), 2929–46.