Dieter Bothe

Prof. Dr. Dieter Bothe

+49 6151 16-21463
+49 6151 16-21472

Alarich-Weiss-Straße 10
64287 Darmstadt

Office: L2|06 400

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Research Topics

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

Modeling and Analysis of Reation-Diffusion(-Sorption)-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

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 – Member of the Scientific Council of the TU Darmstad
  • 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
  • 2010 – Editorial Advisory Board International Journal of Multiphase Flows
  • 2012 – Editorial Board Nonlinear Analysis: Real World Applications

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 33 mathematical and 24 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 – 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 of 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

Publications

  • Efficient three-material PLIC interface positioning on unstructured polyhedral meshes.Kromer, Johannes; Potyka, Johanna; Schulte, Kathrin; Bothe, Dieter (2021).
    https://arxiv.org/abs/2105.08972
  • Multicomponent incompressible fluids – an asymptotic study.Bothe, Dieter; Dreyer, Wolfgang; Druet, Pierre-Etienne (2021).
    https://arxiv.org/abs/2104.08628
  • Sharp-interface continuum thermodynamics of multicomponent fluid systems with interfacial mass.Bothe, Dieter (2021).
    https://arxiv.org/abs/2010.05989
  • 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 (2021).
    https://arxiv.org/abs/2008.05327
  • Face-based Volume-of-Fluid interface positioning in arbitrary polyhedra.Kromer, Johannes; Bothe, Dieter (2021).
    https://arxiv.org/abs/2101.03861
  • Well-posedness anaFace-based Volume-of-Fluid interface positioning in arbitrary polyhedralysis of multicomponent incompressible flow models.Bothe, Dieter; Druet, Pierre-Etienne (2021). Journal of Evolution Equations.
    https://link.springer.com/article/10.1007/s00028-021-00712-3
  • Mass transport in multicomponent compressible fluids: local and global well-posedness in classes of strong solutions for general class-one models, Nonlinear Analysis: Theory, Methods & Application.Bothe, Dieter; Druet, Pierre-Etienne (2021).
    https://arxiv.org/abs/2001.08970
  • Analysis of some heterogeneous catalysis models with fast sorption and fast surface chemistry.Augner, Björn; Bothe, Dieter (2021). Journal of Evolution Equations.
    https://link.springer.com/article/10.1007/s00028-021-00692-4
  • 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.
    https://doi.org/10.1146/annurev-chembioeng-092220-100517
  • Breakup dynamics of capillary bridges on hydrophobic stripes.Hartmann, Michael; Fricke, Mathis, Weimar, Lukas; Gründing, Dirk; Maric, Tomislav; Bothe, Dieter; Hardt, Steffen (2021). International Journal of Multiphase Flow 138, 103582.
    https://arxiv.org/abs/1910.01887
  • Computing Mass Transfer at Deformable Bubbles for High Schmidt Numbers. Weiner, Andre; Gründing, Dirk & Bothe, Dieter (2021), Chemie Ingenieur Technik. https://doi.org/10.1002/cite.202000214.
  • 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. https://doi.org/10.1016/j.jnnfm.2020.104451.
  • Sharp-Interface Continuum Thermodynamics of multicomponent fluid systems with interfacial mass. Bothe, Dieter (12.10.2020), https://arxiv.org/pdf/2010.05989.
  • 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 (12.08.2020), https://arxiv.org/pdf/2008.05327.
  • Analysis of some heterogeneous catalysis models with fast sorption and fast surface chemistry. Augner, Björn & Bothe, Dieter (22.06.2020), https://arxiv.org/pdf/2006.12098.
  • Well-posedness analysis of multicomponent incompressible flow models. Bothe, Dieter & Druet, Pierre-Etienne (25.05.2020), https://arxiv.org/pdf/2005.12052.
  • 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 (24.01.2020), https://arxiv.org/pdf/2001.08970.
  • On moving hypersurfaces and the discontinuous ODE-system associated with two-phase flows. Bothe, Dieter (2020), Nonlinearity, 33 (10), 5425–56. https://doi.org/10.1088/1361-6544/ab987d.
  • 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. https://doi.org/10.1140/epjst/e2020-000149-6.
  • Boundary conditions for dynamic wetting – A mathematical analysis. Fricke, Mathis & Bothe, Dieter (2020), The European Physical Journal Special Topics, 229 (10), 1849–65. https://doi.org/10.1140/epjst/e2020-900249-7.
  • Contact line advection using the geometrical Volume-of-Fluid method. Fricke, Mathis; Marić, Tomislav & Bothe, Dieter (2020), Journal of Computational Physics, 407, 109221. https://doi.org/10.1016/j.jcp.2019.109221.
  • A comparative study of transient capillary rise using direct numerical simulations. Gründing, D.; Smuda, M.; Antritter, T.; Fricke, M.; Rettenmaier, D.; Kummer, F.; Stephan, P.; Marschall, H. & Bothe, D. (2020), Applied Mathematical Modelling, 86, 142–65. https://doi.org/10.1016/j.apm.2020.04.020.
  • 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. https://doi.org/10.1016/j.ijmultiphaseflow.2020.103207.
  • Unstructured un-split geometrical Volume-of-Fluid methods – A review. Marić, Tomislav; Kothe, Douglas B. & Bothe, Dieter (2020), Journal of Computational Physics, 420, 109695. https://doi.org/10.1016/j.jcp.2020.109695.
  • SAAMPLE: A Segregated Accuracy-driven Algorithm for Multiphase Pressure-Linked Equations. Tolle, Tobias; Bothe, Dieter & Marić, Tomislav (2020), Computers & Fluids, 200, 104450. https://doi.org/10.1016/j.compfluid.2020.104450.
  • 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), https://arxiv.org/pdf/1910.01887.
  • 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. https://doi.org/10.1016/j.physd.2019.01.008.
  • Highly accurate computation of volume fractions using differential geometry. Kromer, Johannes & Bothe, Dieter (2019), Journal of Computational Physics, 396, 761–84. https://doi.org/10.1016/j.jcp.2019.07.005.
  • Toward the predictive simulation of bouncing versus coalescence in binary droplet collisions. Liu, M. & Bothe, D. (2019), Acta Mechanica, 230 (2), 623–44. https://doi.org/10.1007/s00707-018-2290-4.
  • 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. https://doi.org/10.1016/j.jcp.2019.02.021.
  • Robust Direct Numerical Simulation of Viscoelastic Flows. Niethammer, Matthias; Marschall, Holger & Bothe, Dieter (2019), Chemie Ingenieur Technik, 91 (4), 522–28. https://doi.org/10.1002/cite.201800108.
  • 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, https://doi.org/10, 100317. 10.1016/j.softx.2019.100317.
  • 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. https://doi.org/10.1016/j.ijengsci.2019.01.001.
  • 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. https://doi.org/10.1002/ceat.201900044.
  • 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. https://doi.org/10.1016/j.cesx.2019.100007.
  • The fast-sorption and fast-surface-reaction limit of a heterogeneous catalysis model. Augner, Björn & Bothe, Dieter (2018), Discrete & Continuous Dynamical Systems – S, 0 (0), 0. https://doi.org/10.3934/dcdss.2020406.
  • Direct numerical simulation of mass transfer in bubbly flows. Deising, D.; Bothe, D. & Marschall, H. (2018), Computers & Fluids, 172, 524–37. https://doi.org/10.1016/j.compfluid.2018.03.041.
  • 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. https://doi.org/10.1016/j.ces.2017.11.024.
  • 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. https://doi.org/10.1016/j.jcp.2017.09.027.
  • An enhanced un-split face-vertex flux-based VoF method. Marić, Tomislav; Marschall, Holger & Bothe, Dieter (2018), Journal of Computational Physics, 371, 967–93. https://doi.org/10.1016/j.jcp.2018.03.048.
  • 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. https://doi.org/10.1002/fld.4411.
  • 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. https://doi.org/10.1017/jfm.2018.723.
  • 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. https://doi.org/10.1007/s00028-016-0348-0.
  • 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. https://doi.org/10.1007/s00028-016-0352-4.
  • 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. https://doi.org/10.1016/j.jmaa.2016.08.016.
  • 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. https://doi.org/10.3934/dcdss.2017034.
  • 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. https://doi.org/10.1017/jfm.2016.852.
  • 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. https://doi.org/10.1016/j.ijheatmasstransfer.2016.08.072.
  • 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. https://doi.org/10.1016/j.jcp.2017.06.040.
  • 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. https://doi.org/10.1016/j.ces.2015.06.021.
  • 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. https://doi.org/10.1063/1.4939498.
  • 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. https://doi.org/10.1016/j.ijheatmasstransfer.2016.04.119.
  • Numerical study of head-on droplet collisions at high Weber numbers. Liu, M. & Bothe, D. (2016), Journal of Fluid Mechanics, 789, 785–805. https://doi.org/10.1017/jfm.2015.725.
  • Applicability of the linearized theory of the Maxwell-Stefan equations. Weber, Paul S. & Bothe, Dieter (2016), AIChE Journal, 62 (8), 2929–46. https://doi.org/10.1002/aic.15317.
  • Dynamic behaviour of buoyant high viscosity droplets rising in a quiescent liquid. Albert, C.; Kromer, J.; Robertson, A. M. & Bothe, D. (2015), Journal of Fluid Mechanics, 778, 485–533. https://doi.org/10.1017/jfm.2015.393.
  • Continuum thermodynamics of chemically reacting fluid mixtures. Bothe, Dieter & Dreyer, Wolfgang (2015), Acta Mechanica, 226 (6), 1757–805. https://doi.org/10.1007/s00707-014-1275-1.
  • Global Existence for a Class of Reaction-Diffusion Systems with Mass Action Kinetics and Concentration-Dependent Diffusivities. Bothe, Dieter & Rolland, Guillaume (2015), Acta Applicandae Mathematicae, 139 (1), 25–57. https://doi.org/10.1007/s10440-014-9968-y.
  • Numerical modeling and investigation of viscoelastic fluid–structure interaction applying an implicit partitioned coupling algorithm. Chen, Xingyuan; Schäfer, Michael & Bothe, Dieter (2015), Journal of Fluids and Structures, 54, 390–421. https://doi.org/10.1016/j.jfluidstructs.2014.12.001.
  • Direct Numerical Simulation of droplet formation processes under the influence of soluble surfactant mixtures. Dieter-Kissling, Kathrin; Marschall, Holger & Bothe, Dieter (2015), Computers & Fluids, 113, 93–105. https://doi.org/10.1016/j.compfluid.2015.01.017.
  • Numerical method for coupled interfacial surfactant transport on dynamic surface meshes of general topology. Dieter-Kissling, Kathrin; Marschall, Holger & Bothe, Dieter (2015), Computers & Fluids, 109, 168–84. https://doi.org/10.1016/j.compfluid.2014.12.017.
  • Direct numerical simulations of thermocapillary migration of a droplet attached to a solid wall. Fath, Anja & Bothe, Dieter (2015), International Journal of Multiphase Flow, 77, 209–21. https://doi.org/10.1016/j.ijmultiphaseflow.2015.08.018.
  • Numerical and experimental analysis of short-scale Marangoni convection on heated structured surfaces. Fath, Anja; Horn, Tobias; Gambaryan-Roisman, Tatiana; Stephan, Peter & Bothe, Dieter (2015), International Journal of Heat and Mass Transfer, 86, 764–79. https://doi.org/10.1016/j.ijheatmasstransfer.2015.03.034.
  • A Volume-of-Fluid-based numerical method for multi-component mass transfer with local volume changes. Fleckenstein, Stefan & Bothe, Dieter (2015), Journal of Computational Physics, 301, 35–58. https://doi.org/10.1016/j.jcp.2015.08.011.
  • lentFoam – A hybrid Level Set/Front Tracking method on unstructured meshes. Marić, Tomislav; Marschall, Holger & Bothe, Dieter (2015), Computers & Fluids, 113, 20–31. https://doi.org/10.1016/j.compfluid.2014.12.019.
  • Global linear stability analysis of falling films with inlet and outlet. Albert, C.; Tezuka, A. & Bothe, D. (2014), Journal of Fluid Mechanics, 745, 444–86. https://doi.org/10.1017/jfm.2014.57.
  • Direct Numerical Simulation of interfacial mass transfer into falling films. Albert, Christoph; Marschall, Holger & Bothe, Dieter (2014), International Journal of Heat and Mass Transfer, 69, 343–57. https://doi.org/10.1016/j.ijheatmasstransfer.2013.10.025.
  • Global existence for diffusion–electromigration systems in space dimension three and higher. Bothe, Dieter; Fischer, André; Pierre, Michel & Rolland, Guillaume (2014), Nonlinear Analysis: Theory, Methods & Applications, 99, 152–66. https://doi.org/10.1016/j.na.2013.12.015.
  • Global Well-Posedness and Stability of Electrokinetic Flows. Bothe, Dieter; Fischer, André & Saal, Jürgen (2014), SIAM Journal on Mathematical Analysis, 46 (2), 1263–316. https://doi.org/10.1137/120880926.
  • On the applicability of Drop Profile Analysis Tensiometry at high flow rates using an interface tracking method. Dieter-Kissling, Kathrin; Karbaschi, Mohsen; Marschall, Holger; Javadi, Aliyar; Miller, Reinhard & Bothe, Dieter (2014), Colloids and Surfaces A: Physicochemical and Engineering Aspects, 441, 837–45. https://doi.org/10.1016/j.colsurfa.2012.10.047.
  • Validation of Interface Capturing and Tracking techniques with different surface tension treatments against a Taylor bubble benchmark problem. Marschall, Holger; Boden, Stephan; Lehrenfeld, Christoph; Falconi D., Carlos J.; Hampel, Uwe; Reusken, Arnold; Wörner, Martin & Bothe, Dieter (2014), Computers & Fluids, 102, 336–52. https://doi.org/10.1016/j.compfluid.2014.06.030.
  • Efficient computation of the flow around single fluid particles using an artificial boundary condition. Weirich, D.; Köhne, M. & Bothe, D. (2014), International Journal for Numerical Methods in Fluids, 75 (3), 184–204. https://doi.org/10.1002/fld.3890.

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