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Study of non-isothermal liquid evaporation in synthetic micro-pore structures with hybrid lattice Boltzmann model

Published online by Cambridge University Press:  08 March 2019

Feifei Qin
Affiliation:
Chair of Building Physics, Department of Mechanical and Process Engineering, ETH Zürich (Swiss Federal Institute of Technology in Zürich), Zürich 8093, Switzerland Laboratory of Multiscale Studies in Building Physics, Empa (Swiss Federal Laboratories for Materials Science and Technology), Dübendorf 8600, Switzerland
Luca Del Carro
Affiliation:
Smart System Integration, IBM Research – Zurich, Saumerstrasse 4, Rüschlikon 8803, Switzerland
Ali Mazloomi Moqaddam
Affiliation:
Laboratory of Multiscale Studies in Building Physics, Empa (Swiss Federal Laboratories for Materials Science and Technology), Dübendorf 8600, Switzerland
Qinjun Kang
Affiliation:
Earth and Environment Sciences Division (EES-16), Los Alamos National Laboratory (LANL), Los Alamos, NM 87545, USA
Thomas Brunschwiler
Affiliation:
Smart System Integration, IBM Research – Zurich, Saumerstrasse 4, Rüschlikon 8803, Switzerland
Dominique Derome
Affiliation:
Laboratory of Multiscale Studies in Building Physics, Empa (Swiss Federal Laboratories for Materials Science and Technology), Dübendorf 8600, Switzerland
Jan Carmeliet
Affiliation:
Chair of Building Physics, Department of Mechanical and Process Engineering, ETH Zürich (Swiss Federal Institute of Technology in Zürich), Zürich 8093, Switzerland
Corresponding
E-mail address:

Abstract

Non-isothermal liquid evaporation in micro-pore structures is studied experimentally and numerically using the lattice Boltzmann method. A hybrid thermal entropic multiple-relaxation-time multiphase lattice Boltzmann model (T-EMRT-MP LBM) is implemented and validated with experiments of droplet evaporation on a heated hydrophobic substrate. Then liquid evaporation is investigated in two specific pore structures, i.e. spiral-shaped and gradient-shaped micro-pillar cavities, referred to as SMS and GMS, respectively. In SMS, the liquid receding front follows the spiral pattern; while in GMS, the receding front moves layer by layer from the pillar rows with large pitch to the rows with small one. Both simulations agree well with experiments. Moreover, evaporative cooling effects in liquid and vapour are observed and explained with simulation results. Quantitatively, in both SMS and GMS, the change of liquid mass with time coincides with experimental measurements. The evaporation rate generally decreases slightly with time mainly because of the reduction of liquid–vapour interface. Isolated liquid films in SMS increase the evaporation rate temporarily resulting in local peaks in evaporation rate. Reynolds and capillary numbers show that the liquid internal flow is laminar and that the capillary forces are dominant resulting in menisci pinned to the pillars. Similar Péclet number is found in simulations and experiments, indicating a diffusive type of heat, liquid and vapour transport. Our numerical and experimental studies indicate a method for controlling liquid evaporation paths in micro-pore structures and maintaining high evaporation rate by specific geometry designs.

Type
JFM Papers
Copyright
© 2019 Cambridge University Press 

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References

Anderson, D. M., McFadden, G. B. & Wheeler, A. A. 1998 Diffuse-interface methods in fluid mechanics. Annu. Rev. Fluid Mech. 30 (1), 139165.CrossRefGoogle Scholar
Blunt, M. J., Bijeljic, B., Dong, H., Gharbi, O., Iglauer, S., Mostaghimi, P., Paluszny, A. & Pentland, C. 2013 Advances in water resources pore-scale imaging and modelling. Adv. Water Resour. 51, 197216.10.1016/j.advwatres.2012.03.003CrossRefGoogle Scholar
Boek, E. S. & Venturoli, M. 2010 Lattice-Boltzmann studies of fluid flow in porous media with realistic rock geometries. Comput. Maths Applics. 59 (7), 23052314.10.1016/j.camwa.2009.08.063CrossRefGoogle Scholar
Boles, M. A., Engel, M. & Talapin, D. V. 2016 Self-assembly of colloidal nanocrystals: from intricate structures to functional materials. Chem. Rev. 116 (18), 1122011289.CrossRefGoogle ScholarPubMed
Bösch, F., Chikatamarla, S. S. & Karlin, I. V. 2015 Entropic multirelaxation lattice Boltzmann models for turbulent flows. Phys. Rev. E 92 (4), 043309.CrossRefGoogle ScholarPubMed
Brunschwiler, T., Zürcher, J., Del Carro, L., Schlottig, G., Burg, B., Zimmermann, S., Zschenderlein, U., Wunderle, B., Schindler-Saefkow, F. & Stässle, R. 2016 Review on percolating and neck-based underfills for three-dimensional chip stacks. J. Electronic Packaging 138 (4), 041009.CrossRefGoogle Scholar
Chen, C., Duru, P., Joseph, P., Geoffroy, S. & Prat, M. 2017 Control of evaporation by geometry in capillary structures. From confined pillar arrays in a gap radial gradient to phyllotaxy-inspired geometry. Sci. Rep. 7 (1), 15110.Google Scholar
Chen, C., Joseph, P., Geoffroy, S., Prat, M. & Duru, P. 2018 Evaporation with the formation of chains of liquid bridges. J. Fluid Mech. 837, 703728.CrossRefGoogle Scholar
Chen, L., Kang, Q., Mu, Y., He, Y. L. & Tao, W. Q. 2014 A critical review of the pseudopotential multiphase lattice Boltzmann model: methods and applications. Intl J. Heat Mass Transfer 76, 210236.CrossRefGoogle Scholar
Chen, L., Luan, H.-B., He, Y.-L. & Tao, W.-Q. 2012 Pore-scale flow and mass transport in gas diffusion layer of proton exchange membrane fuel cell with interdigitated flow fields. Intl J. Therm. Sci. 51, 132144.CrossRefGoogle Scholar
Chikatamarla, S. S., Ansumali, S. & Karlin, I. V. 2006 Entropic lattice Boltzmann models for hydrodynamics in three dimensions. Phys. Rev. Lett. 97 (1), 010201.10.1103/PhysRevLett.97.010201CrossRefGoogle ScholarPubMed
Cueto-felgueroso, L., Fu, X. & Juanes, R. 2018 Pore-scale modeling of phase change in porous media. Phys. Rev. Fluids 3, 084302.10.1103/PhysRevFluids.3.084302CrossRefGoogle Scholar
Dash, S. & Garimella, S. V. 2013 Droplet evaporation dynamics on a superhydrophobic surface with negligible hysteresis. Langmuir 29 (34), 1078510795.CrossRefGoogle ScholarPubMed
Dash, S. & Garimella, S. V. 2014 Droplet evaporation on heated hydrophobic and superhydrophobic surfaces. Phys. Rev. E 89 (4), 042402.CrossRefGoogle ScholarPubMed
Defraeye, T. 2014 Advanced computational modelling for drying processes – a review. Appl. Energy 131, 323344.CrossRefGoogle Scholar
Defraeye, T., Aregawi, W., Saneinejad, S., Vontobel, P., Lehmann, E., Carmeliet, J., Verboven, P., Derome, D. & Nicolaï, B. 2013 Novel application of neutron radiography to forced convective drying of fruit tissue. Food Bioprocess Technol. 6 (12), 33533367.CrossRefGoogle Scholar
Defraeye, T., Houvenaghel, G., Carmeliet, J. & Derome, D. 2012 Numerical analysis of convective drying of gypsum boards. Intl J. Heat Mass Transfer 55 (9–10), 25902600.CrossRefGoogle Scholar
Dunn, G. J., Wilson, S. K., Duffy, B. R., David, S. & Sefiane, K. 2009 The strong influence of substrate conductivity on droplet evaporation. J. Fluid Mech. 623, 329351.CrossRefGoogle Scholar
Fantinel, P., Borgman, O., Holtzman, R. & Goehring, L. 2017 Drying in a microfluidic chip: experiments and simulations. Sci. Rep. 7 (1), 15572.CrossRefGoogle Scholar
Fatt, I. 1956 The network model of porous media. Petrol. Trans. AIME 207, 144181.Google Scholar
Ghassemi, A. & Pak, A. 2011 Numerical study of factors influencing relative permeabilities of two immiscible fluids flowing through porous media using lattice Boltzmann method. J. Petrol. Sci. Engng 77 (1), 135145.CrossRefGoogle Scholar
Gong, W., Yan, Y. Y., Chen, S. & Wright, E. 2018 A modified phase change pseudopotential lattice Boltzmann model. Intl J. Heat Mass Transfer 125, 323329.CrossRefGoogle Scholar
Hamon, C., Postic, M., Mazari, E., Bizien, T., Dupuis, C., Even-Hernandez, P., Jimenez, A., Courbin, L., Gosse, C., Artzner, F. & Marchi-Artzner, V. 2012 Three-dimensional self-assembling of gold nanorods with controlled macroscopic shape and local smectic B order. ACS Nano 6 (5), 41374146.CrossRefGoogle ScholarPubMed
Hirt, C. W. & Nichols, B. D. 1981 Volume of fluid (VOF) method for the dynamics of free boundaries. J. Comput. Phys. 39 (1), 201225.CrossRefGoogle Scholar
Huang, H., Li, Z., Liu, S. & Lu, X.-Y. 2009 Shan-and-Chen-type multiphase lattice Boltzmann study of viscous coupling effects for two-phase flow in porous media. Intl J. Numer. Meth. Fluids 61, 341354.CrossRefGoogle Scholar
Irawan, A.2006 Isothermal drying of pore networks: influence of pore structure on drying kinetics. PhD thesis, Otto-von-Guericke-University of Magdeburg.Google Scholar
Kang, Q., Zhang, D. & Chen, S. 2002 Displacement of a two-dimensional immiscible droplet in a channel. Phys. Fluids 14 (9), 32033214.CrossRefGoogle Scholar
Karlin, I. V., Bösch, F. & Chikatamarla, S. S. 2014 Gibbs’ principle for the lattice-kinetic theory of fluid dynamics. Phys. Rev. E 90 (3), 031302(R).CrossRefGoogle ScholarPubMed
Karlin, I. V., Ferrante, A. & Öttinger, H. C. 1999 Perfect entropy functions of the lattice Boltzmann method. Europhys. Lett. 47 (2), 182188.CrossRefGoogle Scholar
Laurindo, J. B. & Prat, M. 1998 Numerical and experimental network study of evaporation in capillary porous media. Drying rates. Chem. Engng Sci. 51 (23), 51715185.CrossRefGoogle Scholar
Law, C. K. 1982 Recent advances in droplet vaporization and combustion. Prog. Energy Combust. Sci. 8 (3), 171201.CrossRefGoogle Scholar
Lee, T. & Lin, C. L. 2005 A stable discretization of the lattice Boltzmann equation for simulation of incompressible two-phase flows at high density ratio. J. Comput. Phys. 206 (1), 1647.10.1016/j.jcp.2004.12.001CrossRefGoogle Scholar
Li, H., Pan, C. & Miller, C. T. 2005 Pore-scale investigation of viscous coupling effects for two-phase flow in porous media. Phys. Rev. E 72 (2), 026705.10.1103/PhysRevE.72.026705CrossRefGoogle ScholarPubMed
Li, Q., Kang, Q. J., Francois, M. M., He, Y. L. & Luo, K. H. 2015 Lattice Boltzmann modeling of boiling heat transfer: the boiling curve and the effects of wettability. Intl J. Heat Mass Transfer 85, 787796.CrossRefGoogle Scholar
Li, Q., Luo, K. H., Kang, Q., He, Y. L., Chen, Q. & Liu, Q. 2016a Lattice Boltzmann methods for multiphase flow and phase-change heat transfer. Prog. Energy Combust. Sci. 52 (0), 62105.CrossRefGoogle Scholar
Li, Q., Zhou, P. & Yan, H. J. 2016b Pinning-depinning mechanism of the contact line during evaporation on chemically patterned surfaces: a lattice Boltzmann study. Langmuir 32 (37), 93899396.10.1021/acs.langmuir.6b01490CrossRefGoogle Scholar
Li, Q., Zhou, P. & Yan, H. J. 2017 Improved thermal lattice Boltzmann model for simulation of liquid-vapor phase change. Phys. Rev. E 96 (6), 063303.Google ScholarPubMed
Liu, H., Kang, Q., Leonardi, C. R., Schmieschek, S., Narváez, A., Jones, B. D., Williams, J. R., Valocchi, A. J. & Harting, J. 2016 Multiphase lattice Boltzmann simulations for porous media applications – a review. Comput. Geosci. 20, 777805.CrossRefGoogle Scholar
Liu, H., Valocchi, A. J., Zhang, Y. & Kang, Q. 2013 Phase-field-based lattice Boltzmann finite-difference model for simulating thermocapillary flows. Phys. Rev. E 87 (1), 013010.10.1103/PhysRevE.87.013010CrossRefGoogle ScholarPubMed
Liu, H., Valocchi, A. J., Zhang, Y. & Kang, Q. 2014 Lattice Boltzmann phase-field modeling of thermocapillary flows in a confined microchannel. J. Comput. Phys. 256, 334356.CrossRefGoogle Scholar
Liu, H., Zhang, Y. & Valocchi, A. J. 2015 Lattice Boltzmann simulation of immiscible fluid displacement in porous media: homogeneous versus heterogeneous pore network. Phys. Fluids 27 (5), 052103.CrossRefGoogle Scholar
Metzger, T. & Tsotsas, E. 2008 Viscous stabilization of drying front: three-dimensional pore network simulations. Chem. Engng Res. Des. 86 (7), 739744.CrossRefGoogle Scholar
Osher, S. & Fedkiw, R. P. 2001 Level set methods: an overview and some recent results. J. Comput. Phys. 169 (2), 463502.CrossRefGoogle Scholar
Pillai, K. M., Prat, M. & Marcoux, M. 2009 A study on slow evaporation of liquids in a dual-porosity porous medium using square network model. Intl J. Heat Mass Transfer 52 (7–8), 16431656.CrossRefGoogle Scholar
Prat, M. 2007 On the influence of pore shape, contact angle and film flows on drying of capillary porous media. Intl J. Heat Mass Transfer 50 (7–8), 14551468.CrossRefGoogle Scholar
Qin, F., Moqaddam, A. M., Kang, Q., Derome, D. & Carmeliet, J. 2018 Entropic multiple-relaxation-time multirange pseudopotential lattice Boltzmann model for two-phase flow. Phys. Fluids 30, 032104.CrossRefGoogle Scholar
Saxton, M. A., Whiteley, J. P., Vella, D. & Oliver, J. M. 2016 On thin evaporating drops: when is the d 2 -law valid?. J. Fluid Mech. 792, 134167.CrossRefGoogle Scholar
Sbragaglia, M., Benzi, R., Biferale, L., Succi, S., Sugiyama, K. & Toschi, F. 2007 Generalized lattice Boltzmann method with multirange pseudopotential. Phys. Rev. E 75 (2), 026702.CrossRefGoogle ScholarPubMed
Shaeri, M. R., Beyhaghi, S. & Pillai, K. M. 2013 On applying an external-flow driven mass transfer boundary condition to simulate drying from a pore-network model. Intl J. Heat Mass Transfer 57 (1), 331344.CrossRefGoogle Scholar
Städler, R. & Carro, L. D.2016 Study of capillary bridging induced self-assembly to improve robustness of neck-based thermal underfill. Master thesis, ETHz.Google Scholar
Städler, R., Carro, L. D., Zurcher, J., Schlottig, G., Studart, A. R. & Brunschwiler, T. 2017 Direct investigation of microparticle self-assembly to improve the robustness of neck formation in thermal underfills. In 16th IEEE Intersociety Conference on Thermal and Thermomechanical Phenomena in Electronic Systems (ITherm). pp. 167173.CrossRefGoogle Scholar
Stalder, A. F., Melchior, T., Müller, M., Sage, D., Blu, T. & Unser, M. 2010 Low-bond axisymmetric drop shape analysis for surface tension and contact angle measurements of sessile drops. Colloids Surf. A 364 (1–3), 7281.10.1016/j.colsurfa.2010.04.040CrossRefGoogle Scholar
Stauber, J. M., Wilson, S. K., Duffy, B. R. & Sefiane, K. 2014 On the lifetimes of evaporating droplets. J. Fluid Mech. 744, R2.CrossRefGoogle Scholar
Sukop, M. C. & Or, D. 2003 Invasion percolation of single component, multiphase fluids with lattice Boltzmann models. Physica B 338 (1–4), 298303.CrossRefGoogle Scholar
Surasani, V. K., Metzger, T. & Tsotsas, E. 2008 Consideration of heat transfer in pore network modelling of convective drying. Intl J. Heat Mass Transfer 51 (9–10), 25062518.CrossRefGoogle Scholar
Surasani, V. K., Metzger, T. & Tsotsas, E. 2009 A non-isothermal pore network drying model with gravity effect. Trans. Porous Med. 80 (3), 431439.CrossRefGoogle Scholar
Surasani, V. K., Metzger, T. & Tsotsas, E. 2010 Drying simulations of various 3D pore structures by a nonisothermal pore network model. Drying Technol. 28 (5), 615623.CrossRefGoogle Scholar
Sussman, M., Smereka, P. & Osher, S. 1994 A level set approach for computing solutions to incompressible two-phase flow. J. Comput. Phys. 114 (1), 146159.CrossRefGoogle Scholar
Taslimi Taleghani, S. & Dadvar, M. 2014 Two dimensional pore network modelling and simulation of non-isothermal drying by the inclusion of viscous effects. Intl J. Multiphase Flow 62, 3744.CrossRefGoogle Scholar
Vorhauer, N., Metzger, T. & Tsotsas, E. 2011 On the influence of temperature gradients on drying of pore networks. In Proceedings of European Drying Conference – EuroDrying’2011, October, pp. 2628.Google Scholar
Vorhauer, N., Tran, Q. T., Metzger, T., Tsotsas, E. & Prat, M. 2013 Experimental investigation of drying in a model porous medium: influence of thermal gradients. Drying Technol. 31 (8), 920929.CrossRefGoogle Scholar
Vorhauer, N., Wang, Y. J., Kharaghani, A., Tsotsas, E. & Prat, M. 2015 Drying with formation of capillary rings in a model porous medium. Trans. Porous Med. 110 (2), 197223.CrossRefGoogle Scholar
Wodlei, F., Sebilleau, J., Magnaudet, J. & Pimienta, V. 2018 Marangoni-driven flower-like patterning of an evaporating drop spreading on a liquid substrate. Nat. Commun. 9 (1), 820.10.1038/s41467-018-03201-3CrossRefGoogle ScholarPubMed
Yiotis, A. G., Boudouvis, A. G., Stubos, A. K., Tsimpanogiannis, I. N. & Yortsos, Y. C. 2004 Effect of liquid films on the drying of porous media. AIChE J. 50, 27212737.CrossRefGoogle Scholar
Yiotis, A. G., Tsimpanogiannis, I. N., Stubos, A. K. & Yortsos, Y. C. 2006 Pore-network study of the characteristic periods in the drying of porous materials. J. Colloid Interface Sci. 297 (2), 738748.CrossRefGoogle ScholarPubMed
Yiotis, A. G., Tsimpanogiannis, I. N., Stubos, A. K. & Yortsos, Y. C. 2007 Coupling between external and internal mass transfer during drying of a porous medium. Water Resour. Res. 43 (6), W06403.CrossRefGoogle Scholar
Yu, Y., Li, Q., Zhou, C. Q., Zhou, P. & Yan, H. J. 2017 Investigation of droplet evaporation on heterogeneous surfaces using a three-dimensional thermal multiphase lattice Boltzmann model. Appl. Therm. Engng 127, 13461354.CrossRefGoogle Scholar
Yuan, P. & Schaefer, L. 2006 Equations of state in a lattice Boltzmann model. Phys. Fluids 18 (4), 042101.CrossRefGoogle Scholar
Zhang, C., Hong, F. & Cheng, P. 2015 Simulation of liquid thin film evaporation and boiling on a heated hydrophilic microstructured surface by Lattice Boltzmann method. Intl J. Heat Mass Transfer 86, 629638.CrossRefGoogle Scholar
Zurcher, J., Chen, X., Burg, B. R., Zimmermann, S., Straessle, R., Studart, A. R. & Brunschwiler, T. 2016 Enhanced percolating thermal underfills achieved by means of nanoparticle bridging necks. IEEE Trans. Compon. Packag. Technol. 6 (12), 17851795.CrossRefGoogle Scholar

Qin et al. supplementary movie 1

Experiment of liquid evaporation in SMS

Video 200 KB

Qin et al. supplementary movie 2

LBM simulation of liquid evaporation in SMS_2D_Density

Video 776 KB

Qin et al. supplementary movie 3

LBM simulation of liquid evaporation in SMS_2D_Temperature

Video 4 MB

Qin et al. supplementary movie 4

Experiment of liquid evaporation in GMS

Video 318 KB

Qin et al. supplementary movie 5

LBM simulation of liquid evaporation in GMS_2D_Density

Video 602 KB

Qin et al. supplementary movie 6

LBM simulation of liquid evaporation in GMS_2D_Temperature

Video 3 MB

Qin et al. supplementary movie 7

LBM simulation of liquid evaporation in SMS_3D_Density

Video 473 KB

Qin et al. supplementary movie 8

LBM simulation of liquid evaporation in SMS_3D_Temperature

Video 1 MB

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