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

  • Feifei Qin (a1) (a2), Luca Del Carro (a3), Ali Mazloomi Moqaddam (a2), Qinjun Kang (a4), Thomas Brunschwiler (a3), Dominique Derome (a2) and Jan Carmeliet (a1)...

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.

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Corresponding author

Email addresses for correspondence: fqin@ethz.ch, feifei.qin@empa.ch

References

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Anderson, D. M., McFadden, G. B. & Wheeler, A. A. 1998 Diffuse-interface methods in fluid mechanics. Annu. Rev. Fluid Mech. 30 (1), 139165.
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.2012.03.003
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.2009.08.063
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.
Bösch, F., Chikatamarla, S. S. & Karlin, I. V. 2015 Entropic multirelaxation lattice Boltzmann models for turbulent flows. Phys. Rev. E 92 (4), 043309.
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.
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.
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.
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.
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.
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.97.010201
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.3.084302
Dash, S. & Garimella, S. V. 2013 Droplet evaporation dynamics on a superhydrophobic surface with negligible hysteresis. Langmuir 29 (34), 1078510795.
Dash, S. & Garimella, S. V. 2014 Droplet evaporation on heated hydrophobic and superhydrophobic surfaces. Phys. Rev. E 89 (4), 042402.
Defraeye, T. 2014 Advanced computational modelling for drying processes – a review. Appl. Energy 131, 323344.
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.
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.
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.
Fantinel, P., Borgman, O., Holtzman, R. & Goehring, L. 2017 Drying in a microfluidic chip: experiments and simulations. Sci. Rep. 7 (1), 15572.
Fatt, I. 1956 The network model of porous media. Petrol. Trans. AIME 207, 144181.
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.
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.
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.
Hirt, C. W. & Nichols, B. D. 1981 Volume of fluid (VOF) method for the dynamics of free boundaries. J. Comput. Phys. 39 (1), 201225.
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.
Irawan, A.2006 Isothermal drying of pore networks: influence of pore structure on drying kinetics. PhD thesis, Otto-von-Guericke-University of Magdeburg.
Kang, Q., Zhang, D. & Chen, S. 2002 Displacement of a two-dimensional immiscible droplet in a channel. Phys. Fluids 14 (9), 32033214.
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).
Karlin, I. V., Ferrante, A. & Öttinger, H. C. 1999 Perfect entropy functions of the lattice Boltzmann method. Europhys. Lett. 47 (2), 182188.
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.
Law, C. K. 1982 Recent advances in droplet vaporization and combustion. Prog. Energy Combust. Sci. 8 (3), 171201.
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.2004.12.001
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.72.026705
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.
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.
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.6b01490
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.
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.
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.87.013010
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.
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.
Metzger, T. & Tsotsas, E. 2008 Viscous stabilization of drying front: three-dimensional pore network simulations. Chem. Engng Res. Des. 86 (7), 739744.
Osher, S. & Fedkiw, R. P. 2001 Level set methods: an overview and some recent results. J. Comput. Phys. 169 (2), 463502.
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.
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.
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.
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.
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.
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.
Städler, R. & Carro, L. D.2016 Study of capillary bridging induced self-assembly to improve robustness of neck-based thermal underfill. Master thesis, ETHz.
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.
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.2010.04.040
Stauber, J. M., Wilson, S. K., Duffy, B. R. & Sefiane, K. 2014 On the lifetimes of evaporating droplets. J. Fluid Mech. 744, R2.
Sukop, M. C. & Or, D. 2003 Invasion percolation of single component, multiphase fluids with lattice Boltzmann models. Physica B 338 (1–4), 298303.
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.
Surasani, V. K., Metzger, T. & Tsotsas, E. 2009 A non-isothermal pore network drying model with gravity effect. Trans. Porous Med. 80 (3), 431439.
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.
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.
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.
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.
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.
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.
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/s41467-018-03201-3
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.
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.
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.
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.
Yuan, P. & Schaefer, L. 2006 Equations of state in a lattice Boltzmann model. Phys. Fluids 18 (4), 042101.
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.
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.
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JFM classification

Type Description Title
VIDEO
Movies

Qin et al. supplementary movie 1
Experiment of liquid evaporation in SMS

 Video (200 KB)
200 KB
VIDEO
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Qin et al. supplementary movie 2
LBM simulation of liquid evaporation in SMS_2D_Density

 Video (776 KB)
776 KB
VIDEO
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Qin et al. supplementary movie 3
LBM simulation of liquid evaporation in SMS_2D_Temperature

 Video (4.1 MB)
4.1 MB
VIDEO
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Qin et al. supplementary movie 4
Experiment of liquid evaporation in GMS

 Video (318 KB)
318 KB
VIDEO
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Qin et al. supplementary movie 5
LBM simulation of liquid evaporation in GMS_2D_Density

 Video (602 KB)
602 KB
VIDEO
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Qin et al. supplementary movie 6
LBM simulation of liquid evaporation in GMS_2D_Temperature

 Video (2.8 MB)
2.8 MB
VIDEO
Movies

Qin et al. supplementary movie 7
LBM simulation of liquid evaporation in SMS_3D_Density

 Video (473 KB)
473 KB
VIDEO
Movies

Qin et al. supplementary movie 8
LBM simulation of liquid evaporation in SMS_3D_Temperature

 Video (1.4 MB)
1.4 MB

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