Cai, Xuan

Deutschmann, Olaf

Marschall, Holger

Wörner, Martin

English

KITopen

KIT – The Research University in the Helmholtz Association9th International Conference on Multiphase Flow, Firenze (Italy), May 22-27, 2016  www.kit.eduNumerical study on the wettability dependent interaction of droplets and bubbles with solid structuresMartin Wörner1, Xuan Cai1, Holger Marschall2, Olaf Deutschmann11 Institute of Catalysis Research and Technology, Karlsruhe Institute of Technology2 Mathematical Modeling and Analysis, Center of Smart Interfaces, Technische Universität DarmstadtInstitute of Catalysis Research and Technology 2 May 24, 2016OutlineMotivationNumerical methodPhase-field methodImplementation in OpenFOAMDroplet applications and validationBubble interaction with solid structuresBubble-cutting by a solid cylinder (validation)Influence of cylinder wettabilityBubble rise through a periodic open cellular structure (POCS)SummaryM. Wörner et al. - Wettability dependent interaction of bubbles with solid structuresInstitute of Catalysis Research and Technology 3 May 24, 2016MotivationManufacturing techniques allow adjustment of wettability properties of solid surfaces (static contact angle e) through roughness (lotus effect) or chemical patterning lab-on-a-chip systemsdrag reduction…   Wettability can have dramatic effect on macroscopic hydrodynamicsM. Wörner et al. - Wettability dependent interaction of bubbles with solid structuresImpact of two spheres differing only in wettability via a nanometriccoating on their surface a) hydrophilic, e =15°b) hydrophobic, e =100° Duez et al., Nature Physics 3 (2007) 180-183a babhttp://www.chemistry-blog.com/2010/06/26/art-on-a-chip/Institute of Catalysis Research and Technology 4 May 24, 2016Motivation (continued)Additive manufacturing allows fabrication of complex solid structuresExample: internals for multiphase chemical reactors (e.g. bubble columns)Goal: Study wettability dependent interaction of gas-liquid flows with solid structures by “direct” numerical simulationMethod of choice: phase-field (PF) methodDo-Quang & Amberg (2009) simulated exp. of Duez using a PF methodM. Wörner et al. - Wettability dependent interaction of bubbles with solid structuresPeriodic Open Cellular Structure (POCS) manufactured at FAU Erlangen-NürnbergMultiphase chemical reactor with structured packingInternal structureSolid sponge (see presentation of X. Cai in session “Interfacial Flows”,Tu 16:20-17:40, Room: Affari-2.A)Question: how should the POCS wettability be designed to enhance mass transfer and reaction? M. Do-Quang, G. Amberg, Phys. Fluids 21 (2009) 022102Institute of Catalysis Research and Technology 5 May 24, 2016Phase distribution is described by order parameter CDiffuse interface representationSmooth transition layer between phasesThickness is characterized by capillary width  > 01D equilibrium profileEvolution of C by convective Cahn-Hilliard equation = chemical potential [J/m3] = mixing energy parameter [J/m] = mobility [m3s/kg]Wetting boundary conditione = equilibrium contact angleDiffusive mechanism for contact line motion at a no slip wallPhase field methodM. Wörner et al. - Wettability dependent interaction of bubbles with solid structures2( ) ( )CC Ct    uC = -1C =12 22( 1)C C Ce 2scos2ˆ (1 )2C Cn ( ) tanh / ( 2 )C x x  J.W. Cahn and J.E. Hilliard, J. Chem. Phys. 28 (1957) 258–2674CL 2 ( )CCt  eInstitute of Catalysis Research and Technology 6 May 24, 2016Coupling with momentum equationNavier-Stokes equation for two incompressible Newtonian fluidsFixing the PF method specific parameters , , Cahn numberL = characteristic macroscopic length scale (here bubble diameter)Mobility based Peclet numberU = characteristic velocity scale (here U =  /L)Coefficient of surface tensionM. Wörner et al. - Wettability dependent interaction of bubbles with solid structures 0( )( ) TC C C Cpt              uuu u u + ( u) f g1 1 1 1, ,2 2 2 2C CC C C CC               fL G L G8 / 9 / ( )CPe LU  /Cn L2 2 / (3 )  D. Jacqmin, J. Comput. Phys. 155 (1999) 96-127; J. Kim, Commun. Comput. Phys. 12 (2012) 613-661Institute of Catalysis Research and Technology 7 May 24, 2016Implementation in OpenFOAMThe method is implemented in OpenFOAM (foam-extend-1.6 and 3.2) as a novel top-level OpenFOAM solver phaseFieldFoamDetails of numerical method will be published in Marschall et al. (2016)Approximation of spatial derivatives by high-resolution scheme (Gauss Gamma)Time integration by a 2ndorder two-time-level backward scheme (Gear’s method)Relative density flux term in momentum equation for better  volume conservation at high density ratios (similar to Ding et al. and Abels et al.)M. Wörner et al. - Wettability dependent interaction of bubbles with solid structures H. Marschall et al. (2016), in preparation H. Ding et al., J. Comput. Phys. 226 (2007) 2078-2095; H. Abels et al., Math. Mod. Meth. Appl. S. 22 (2012)  1150013θe = 60°Institute of Catalysis Research and Technology 8 May 24, 2016Validation of phaseFieldFoamComprehensive validation for test problems with analytical solution X. Cai et al., Chem. Eng. Technol. 38 (2015) 1985–1992Spreading of a droplet on a chemically patterned substrateExperiments by Léopoldès et al. (inkjet droplets with radius 11µm)PhaseFieldFoam simulations by S. Yadav M. Wörner et al. - Wettability dependent interaction of bubbles with solid structurese = 20e = 64Terminal experimental droplet shapes Léopoldès et al. Langmuir, 19 (2003) 9818–9822e = 5 e = 64Terminal bubble shapesInstitute of Catalysis Research and Technology 9 May 24, 2016Bubble-cutting experiment of SegersAir bubble rising in liquid glycerinVariation of bubble diameter (Eötvös number)Variation of liquid viscosity (Morton number)Head-on and oblique collision between bubble and cylinderParameters and fluid properties for present simulationsOnly head-on collisionsMorton number Mo = 0.064M. Wörner et al. - Wettability dependent interaction of bubbles with solid structures2L G B( ) /Eo gD Q. Segers, Cutting Bubbles using Wire-Mesh Structures - Direct Numerical Simulations, PhD thesis TU Eindhoven 20154 2 3L G L L( ) / ( )Mo g(group of Hans Kuipers)Institute of Catalysis Research and Technology 10 May 24, 2016ProcedureValidate for terminal bubble rise velocityValidate for instantaneous bubble cutting processStudy influence of wettability on bubble cutting process M. Wörner et al. - Wettability dependent interaction of bubbles with solid structures2D axisymmetric simulationsUniform grid with mesh size hInfluence of mesh resolutionB44C CC DL NDN Nh h h CnInstitute of Catalysis Research and Technology 11 May 24, 2016Terminal bubble rise velocityM. Wörner et al. - Wettability dependent interaction of bubbles with solid structuresInfluence of Cahn numberInfluence of Peclet numberComparison with experimentNC=6, Cn=0.02, PeC=2016Institute of Catalysis Research and Technology 12 May 24, 2016Cylinder-induced bubble break upParameters according exp. of SegersBubble diameter DB = 9.1 mmDiameter of solid cylinder Dcyl = 3.1 mmCylinder is made of stainless steelContact angle e was not measured, is estimated to be about 60°Simulation set-up3D simulation, one quarter with  symmetry boundary conditionsCross section 2DB  2DB, height 6DBNC = 4Cn = 0.04PeC = 1000M. Wörner et al. – Wettability dependent interaction of bubbles with solid structures X. Cai, M. Wörner, H. Marschall and O. Deutschmann, Catalysis Today, 2016, in press (available online)3cellsCNNCn    θe = 60°Institute of Catalysis Research and Technology 13 May 24, 2016 M. Wörner et al. - Wettability dependent interaction of bubbles with solid structuresExperiment SegersPresent phase field simulationθe = 60°Numerical simulation of Segers with IBM-VOF method, see also Baltussen et al., Cutting bubbles with a single wire, Chem. Eng. Sci., in press Time in figures is slightly differentInstitute of Catalysis Research and Technology 14 May 24, 2016Influence of cylinder wettabilityM. Wörner et al. - Wettability dependent interaction of bubbles with solid structuresGas-liquid interfacial area AiInstitute of Catalysis Research and Technology 15 May 24, 2016 M. Wörner et al. - Wettability dependent interaction of bubbles with solid structuresPeriodic Open Cellular StructuresPOCS of different geometry are manufactured at FAU Erlangen-Nürnberg (e.g. by SEBM)Here a POCS with cubic cell geometry is consideredGeometric parametersWindow size s = 4 mmStrut diameter ds = 1 mmGrid angle  = 90°Entire POCS is titled by 45°STL geometry for mesh generation provided by C.O. Möller, TUHHSimulation parametersAir bubble in water (stagnant)Bubble diameter DB = 4 mmLocally refined static mesh M. Klumpp et al., Chem. Eng. J., 242 (2014) 364-378Institute of Catalysis Research and Technology 16 May 24, 2016Bubble rise (perspective view)M. Wörner et al. - Wettability dependent interaction of bubbles with solid structuresθe = 0°(hydrophilic)θe = 90° θe = 120°(hydrophobic)Decreasing wettability (increasing contact angle) ×Not suited asreactor internalInstitute of Catalysis Research and Technology 17 May 24, 2016Bubble rise (lateral view)M. Wörner et al. - Wettability dependent interaction of bubbles with solid structuresθe = 0° θe = 90°θe = 60°Bubble is not in contact with strutsBubble is in (slight) contact with strutsBubble is in strong contact with struts and climbs them upInstitute of Catalysis Research and Technology 18 May 24, 2016 M. Wörner et al. - Wettability dependent interaction of bubbles with solid structuresConclusionsImplementation of phase-field method coupled with Navier-Stokes equations in OpenFOAM (phaseFieldFoam)Method can well describe wetting phenomena +Method can handle real density and viscosity ratios +Difficulty to choose appropriate value for mobility parameter -Methods globally conserves C but not bubble volume -The numerical results for the cylinder-induced bubble cutting and bubble rise in POCS indicate that the bubble shape and path do significantly depend on the structure wettabilityIn industrial application of POCS for enhancing mass transfer and as catalytic support structures with high wettability are expected to be beneficial Institute of Catalysis Research and Technology 19 May 24, 2016AcknowledgementsM. Wörner et al. - Wettability dependent interaction of bubbles with solid structuresFunding by Helmholtz Association Energy Alliance “Energy-efficient chemical multiphase processes”Thanks to project partners from FAU Erlangen-Nürnberg (Prof. Freund, Prof. Schwieger) and TU Hamburg-Harburg (Prof. Schlüter, C.O. Möller) Thanks to internship student S. Yadav (IIT Kharagpur)Tu 16:20-17:40 Interfacial FlowsRoom: Affari-2.A; Chairperson: Derksen J.INTERFACE-RESOLVING SIMULATIONS OF GAS-LIQUID FLOWS IN A SOLID SPONGE STRUCTURECai X., Woerner M., Deutschmann O.

Numerical study on the wettability dependent interaction of droplets and bubbles with solid structures

https://publikationen.bibliothek.kit.edu/1000055719/150950736

Numerical study on the wettability dependent interaction of droplets and bubbles with solid structures

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