The internal circulations on internal mass transfer rate of a single drop in nonlinear uniaxial extensional flow

doi:10.1016/j.cjche.2022.12.003

中国化学工程学报 ›› 2023, Vol. 59 ›› Issue (7): 51-60.DOI: 10.1016/j.cjche.2022.12.003

• Full Length Article • 上一篇下一篇

The internal circulations on internal mass transfer rate of a single drop in nonlinear uniaxial extensional flow

Anjun Liu¹, Jie Chen², Meng Guo^1,3, Chengmin Chen³, Meihong Yang¹, Chao Yang²

1. Qilu University of Technology (Shandong Academy of Sciences), Shandong Computer Science Center (National Supercomputer Center in Jinan), Jinan 250101, China;
2. CAS Key Laboratory of Green Process and Engineering, Institute of Process Engineering, Chinese Academy of Sciences, Beijing 100190, China;
3. Jinan Key Laboratory of High Performance Industrial Software, Jinan Institute of Supercomputer Technology, Jinan 251013, China

收稿日期:2022-08-24 修回日期:2022-11-24 出版日期:2023-07-28 发布日期:2023-10-14
通讯作者: Jie Chen,E-mail:jchen@ipe.ac.cn;Meng Guo,E-mail:guomeng@sdas.org;Chao Yang,E-mail:chaoyang@ipe.ac.cn
基金资助:
This work was supported by the National Key Research and Development Program of China (2021YFC2902502); the National Natural Science Foundation of China (22078320, 22035007), the NSFC-EU project (31961133018); the Shandong Provincial Key Research and Development Program (2022CXGC020106); the Shandong Key Research and Development Program (International Cooperation Office) (2019GHZ018); the Shandong Province Postdoctoral Innovative Talents Support Plan (SDBX2020018) and the External Cooperation Program of BIC, Chinese Academy of Sciences (122111KYSB20190032). We would like to thank Professor M. Favelukis for helpful discussions regarding the application of velocity field.

The internal circulations on internal mass transfer rate of a single drop in nonlinear uniaxial extensional flow

Anjun Liu¹, Jie Chen², Meng Guo^1,3, Chengmin Chen³, Meihong Yang¹, Chao Yang²

1. Qilu University of Technology (Shandong Academy of Sciences), Shandong Computer Science Center (National Supercomputer Center in Jinan), Jinan 250101, China;
2. CAS Key Laboratory of Green Process and Engineering, Institute of Process Engineering, Chinese Academy of Sciences, Beijing 100190, China;
3. Jinan Key Laboratory of High Performance Industrial Software, Jinan Institute of Supercomputer Technology, Jinan 251013, China

Received:2022-08-24 Revised:2022-11-24 Online:2023-07-28 Published:2023-10-14
Contact: Jie Chen,E-mail:jchen@ipe.ac.cn;Meng Guo,E-mail:guomeng@sdas.org;Chao Yang,E-mail:chaoyang@ipe.ac.cn
Supported by:
This work was supported by the National Key Research and Development Program of China (2021YFC2902502); the National Natural Science Foundation of China (22078320, 22035007), the NSFC-EU project (31961133018); the Shandong Provincial Key Research and Development Program (2022CXGC020106); the Shandong Key Research and Development Program (International Cooperation Office) (2019GHZ018); the Shandong Province Postdoctoral Innovative Talents Support Plan (SDBX2020018) and the External Cooperation Program of BIC, Chinese Academy of Sciences (122111KYSB20190032). We would like to thank Professor M. Favelukis for helpful discussions regarding the application of velocity field.

摘要/Abstract

摘要： The internal flow of a droplet in the nonlinear extensional flow field will exhibit more than two internal circulations with the variation of nonlinear intensity (E). In this paper, the effect of positions and sizes of internal circulations on internal mass transfer rate of a single spherical droplet in a nonlinear extensional flow field is studied and compared with that in a linear extensional flow field. The simulation results show that when E ≥ 0, there are two symmetrical internal circulations in the droplet, which is the same with that in a linear extensional flow. The limit value of mass transfer rate Sh is 15, which is equal to that in a linear extensional flow, no matter how large E is. When E ≤ -3/7, the number of internal flow circulation of a droplet increase to four and the transfer rate Sh increases. When E = -1, the maximum internal transfer rate Sh equals 30 which is twice of that in a linear extensional flow. The generation of new flow circulations in droplets and the circulation positions will enhance mass transfer when E ≤ -3/7, which provides a new idea for enhancing the internal mass transfer rate of droplets.

关键词: Internal mass transfer, Nonlinear extensional flow field, Spherical droplet, Internal circulations

Abstract: The internal flow of a droplet in the nonlinear extensional flow field will exhibit more than two internal circulations with the variation of nonlinear intensity (E). In this paper, the effect of positions and sizes of internal circulations on internal mass transfer rate of a single spherical droplet in a nonlinear extensional flow field is studied and compared with that in a linear extensional flow field. The simulation results show that when E ≥ 0, there are two symmetrical internal circulations in the droplet, which is the same with that in a linear extensional flow. The limit value of mass transfer rate Sh is 15, which is equal to that in a linear extensional flow, no matter how large E is. When E ≤ -3/7, the number of internal flow circulation of a droplet increase to four and the transfer rate Sh increases. When E = -1, the maximum internal transfer rate Sh equals 30 which is twice of that in a linear extensional flow. The generation of new flow circulations in droplets and the circulation positions will enhance mass transfer when E ≤ -3/7, which provides a new idea for enhancing the internal mass transfer rate of droplets.

Key words: Internal mass transfer, Nonlinear extensional flow field, Spherical droplet, Internal circulations

Anjun Liu, Jie Chen, Meng Guo, Chengmin Chen, Meihong Yang, Chao Yang. The internal circulations on internal mass transfer rate of a single drop in nonlinear uniaxial extensional flow[J]. 中国化学工程学报, 2023, 59(7): 51-60.

参考文献

[1] V.A. Vlasov, On a theory of mass transfer during the evaporation of a spherical droplet, Int. J. Heat Mass Transf. 178 (2021) 121597. http://dx.doi.org/10.1016/j.ijheatmasstransfer.2021.121597
[2] Z. Cao, D.K. Tafti, Convective heat transfer in suspensions of prolate ellipsoids, Int. J. Heat Mass Transf. 177 (2021) 121575. http://dx.doi.org/10.1016/j.ijheatmasstransfer.2021.121575
[3] S. Wroński, V. Vladimirov, A. Adach, Modelling of mass transfer from multiple emulsions, Int. J. Heat Mass Transf. 55 (15-16) (2012) 4241-4245. http://dx.doi.org/10.1016/j.ijheatmasstransfer.2012.03.065
[4] Y.H. Zhang, A. Prosperetti, Dynamics, heat and mass transfer of a plasmonic bubble on a solid surface, Int. J. Heat Mass Transf. 167 (2021) 120814. http://dx.doi.org/10.1016/j.ijheatmasstransfer.2020.120814
[5] T.T.B. Lan, A.C.A. Sun, Evaporation model of aqueous non-spherical nanoparticle in lab scale: A theoretical approach, Int. J. Multiph. Flow 147 (2022) 103884. http://dx.doi.org/10.1016/j.ijmultiphaseflow.2021.103884
[6] Z.J. Ni, C. Hespel, K. Han, F. Foucher, Numerical simulation of heat and mass transient behavior of single hexadecane droplet under forced convective conditions, Int. J. Heat Mass Transf. 167 (2021) 120736. http://dx.doi.org/10.1016/j.ijheatmasstransfer.2020.120736
[7] Q.B. Liu, S. Xu, Z.J. Chen, J.T. Wang, Analysis of rheological behaviors of two-dimensional emulsion globules with asymmetric internal structures in modest extensional flows, Phys. Fluids 31 (4) (2019) 042003. http://dx.doi.org/10.1063/1.5089678
[8] M. Favelukis, Mass transfer around a double emulsion droplet in a uniform flow, Eur. J. Mech. B fluids 89 (2021) 501-508. http://dx.doi.org/10.1016/j.euromechflu.2021.07.005
[9] M. Favelukis, Mass transfer around a compound drop in an extensional flow, Can. J. Chem. Eng. 99 (S1) (2021) 800-808. https://doi.org/10.1002/cjce.23972
[10] A.J. Liu, J. Chen, Z.Z. Wang, Z.S. Mao, C. Yang, Internal mass and heat transfer between a single deformable droplet and simple extensional creeping flow, Int. J. Heat Mass Transf. 127 (2018) 1040-1053. http://dx.doi.org/10.1016/j.ijheatmasstransfer.2018.07.135
[11] D. Krishnamurthy, G. Subramanian, Heat or mass transport from drops in shearing flows. Part 1. The open-streamline regime, J. Fluid Mech. 850 (2018) 439-483. https://doi.org/10.1017/jfm.2018.439
[12] D. Krishnamurthy, G. Subramanian, Heat or mass transport from drops in shearing flows. Part 2. Inertial effects on transport, J. Fluid Mech. 850 (2018) 484-524. https://doi.org/10.1017/jfm.2018.481
[13] Y.R. Lu, D. Pashchenko, P.A. Nikrityuk, A new semiempirical model for the heat and mass transfer inside a spherical catalyst in a stream of hot CH₄/H₂O gases, Chem. Eng. Sci. 238 (2021) 116565. http://dx.doi.org/10.1016/j.ces.2021.116565
[14] G. Juncu, A numerical study of the unsteady heat/mass transfer inside a circulating sphere, Int. J. Heat Mass Transf. 53 (15-16) (2010) 3006-3012. http://dx.doi.org/10.1016/j.ijheatmasstransfer.2010.03.030
[15] Z.W. Jiang, Y.H. Gan, Y.L. Shi, Numerical analysis on the heat/mass transfer to a deformed droplet under a steady electric field, Int. J. Heat Mass Transf. 188 (2022) 122617. http://dx.doi.org/10.1016/j.ijheatmasstransfer.2022.122617
[16] D.L.R. Oliver, T.E. Carleson, J.N. Chung, Transient heat transfer to a fluid sphere suspended in an electric field, Int. J. Heat Mass Transf. 28 (5) (1985) 1005-1009. http://dx.doi.org/10.1016/0017-9310(85)90282-0
[17] D.L.R. Oliver, K.J. DeWitt, Heat transfer in bubbles and droplets at moderate Reynolds numbers: Interior problem, AIChE Symp. Ser. 91(306) (1995) 87-92.
[18] A.J. Liu, J. Chen, M. Favelukis, M. Guo, M.H. Yang, C. Yang, T. Zhang, M. Wang, H.Y. Quan, External mass transfer from/to a single sphere in a nonlinear uniaxial extensional creeping flow, Chin. J. Chem. Eng. 41 (2022) 230-245. http://dx.doi.org/10.1016/j.cjche.2021.11.017
[19] M. Favelukis, Mass transfer around a slender drop in a nonlinear extensional flow, Nonlinear Eng. 8 (1) (2019) 117-126. https://doi.org/10.1515/nleng-2018-0019
[20] S.J. Geng, Z.S. Mao, Q.S. Huang, C. Yang, Process intensification in pneumatically agitated slurry reactors, Engineering 7 (3) (2021) 304-325. http://dx.doi.org/10.1016/j.eng.2021.03.002
[21] A.N. Manzano Martínez, M. Assirelli, J. van der Schaaf, Droplet size and liquid-liquid mass transfer with reaction in a rotor-stator Spinning Disk Reactor, Chem. Eng. Sci. 242 (2021) 116706. http://dx.doi.org/10.1016/j.ces.2021.116706
[22] Z.Z. Wang, J. Chen, X. Feng, Z.S. Mao, C. Yang, Visual dynamical measurement of the solute-induced Marangoni effect of a growing drop with a PLIF method, Chem. Eng. Sci. 233 (2021) 116401. http://dx.doi.org/10.1016/j.ces.2020.116401
[23] H.H. Zhang, Y.L. Wang, A. Sayyar, T.F. Wang, Experimental study on breakup of a single bubble in a stirred tank: Effect of gas density and liquid properties, AIChE J. (2021) e17511. https://www.semanticscholar.org/paper/5882ea745ab4def9d3adbcaaaa4b1416248a09b6
[24] H.H. Zhang, Y.L. Wang, A. Sayyar, T.F. Wang, A CFD-PBM coupled model under entire turbulent spectrum for simulating a bubble column with highly viscous media, AIChE J. (2021) e17473. https://www.semanticscholar.org/paper/48f44f68b430720967e1d684ca42b5452de2ad7f
[25] H.H. Zhang, A. Sayyar, Y.L. Wang, T.F. Wang, Generality of the CFD-PBM coupled model for bubble column simulation, Chem. Eng. Sci. 219 (2020) 115514. http://dx.doi.org/10.1016/j.ces.2020.115514
[26] A.J. Liu, J. Chen, Z.Z. Wang, J.T. Wang, Z.S. Mao, C. Yang, Unsteady conjugate mass transfer of a 2D deformable droplet in a modest extensional flow in across-slot, Can. J. Chem. Eng. 98 (3) (2020) 804-817. https://doi.org/10.1002/cjce.23645
[27] A.J. Liu, J. Chen, Z.Z. Wang, Z.S. Mao, C. Yang, Unsteady conjugate mass and heat transfer from/to a prolate spheroidal droplet in uniaxial extensional creeping flow, Int. J. Heat Mass Transf. 134 (2019) 1180-1190. http://dx.doi.org/10.1016/j.ijheatmasstransfer.2019.02.055
[28] V.S. Cabeza, S. Kuhn, A.A. Kulkarni, K.F. Jensen, Size-controlled flow synthesis of gold nanoparticles using a segmented flow microfluidic platform, Langmuir 28 (17) (2012) 7007-7013. https://pubmed.ncbi.nlm.nih.gov/22475028/
[29] N.A. Frankel, A. Acrivos, Heat and mass transfer from small spheres and cylinders freely suspended in shear flow, Phys. Fluids 11 (9) (1968) 1913-1918. http://dx.doi.org/10.1063/1.1692218
[30] A. Acrivos, Heat transfer at high Péclet number from a small sphere freely rotating in a simple shear field, J. Fluid Mech. 46 (2) (1971) 233-240. https://doi.org/10.1017/s0022112071000508
[31] J.S. Zhang, C. Yang, Z.S. Mao, Mass and heat transfer from or to a single sphere in simple extensional creeping flow, AIChE J. 58 (10) (2012) 3214-3223. https://doi.org/10.1002/aic.12811
[32] Z.B. Zhang, K. Wang, C.B. Xu, Y. Zhang, W.T. Wu, C.H. Lu, W.G. Liu, Y.L. Rao, C. Jiang, C.L. Xu, S.L. Song, Ultrasound enhancing the mass transfer of droplet microreactor for the synthesis of AgInS2 nanocrystals, Chem. Eng. J. 435 (2022) 134948. http://dx.doi.org/10.1016/j.cej.2022.134948
[33] C.A. Edelmann, P.C. le Clercq, B. Noll, Numerical investigation of different modes of internal circulation in spherical drops: Fluid dynamics and mass/heat transfer, Int. J. Multiph. Flow 95 (2017) 54-70. http://dx.doi.org/10.1016/j.ijmultiphaseflow.2017.05.005
[34] M. Hill, On a spherical vortex, Philos. Trans. R. Soc. A Math. Phys. Eng. Sci. 185 (1894) 213-245.
[35] Q.J. Yang, Q. Mao, W. Cao, Numerical simulation of the Marangoni flow on mass transfer from single droplet with different Reynolds numbers, Colloids Surf. A Physicochem. Eng. Aspects 639 (2022) 128385. http://dx.doi.org/10.1016/j.colsurfa.2022.128385
[36] J. Chen, J.X. Wang, Z.L. Deng, X.D. Liu, Y.P. Chen, Experimental study on Rayleigh-Bénard-Marangoni convection characteristics in a droplet during mass transfer, Int. J. Heat Mass Transf. 172 (2021) 121214. http://dx.doi.org/10.1016/j.ijheatmasstransfer.2021.121214
[37] G. Yang, A. Terzis, I. Zarikos, S.M. Hassanizadeh, B. Weigand, R. Helmig, Internal flow patterns of a droplet pinned to the hydrophobic surfaces of a confined microchannel using micro-PIV and VOF simulations, Chem. Eng. J. 370 (2019) 444-454. http://dx.doi.org/10.1016/j.cej.2019.03.191
[38] M. Favelukis, A drop in uniaxial and biaxial nonlinear extensional flows, Phys. Fluids 29 (8) (2017) 087102. http://dx.doi.org/10.1063/1.4997078
[39] J. Sherwood, Tip streaming from slender drops in a nonlinear extensional flow, J. Fluid Mech. 144 (1984) 281-295. https://www.semanticscholar.org/paper/45d28eb4114c6c46dd6babe741c3dd46dde5e854
[40] C. Yang, Z.S. Mao, Numerical simulation of interphase mass transfer with the level set approach, Chem. Eng. Sci. 60 (10) (2005) 2643-2660. http://dx.doi.org/10.1016/j.ces.2004.11.054

The internal circulations on internal mass transfer rate of a single drop in nonlinear uniaxial extensional flow

The internal circulations on internal mass transfer rate of a single drop in nonlinear uniaxial extensional flow

PDF (PC)

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 0

编辑推荐

Metrics

本文评价