External mass transfer from/to a single sphere in a nonlinear uniaxial extensional creeping flow

doi:10.1016/j.cjche.2021.11.017

Chinese Journal of Chemical Engineering ›› 2022, Vol. 41 ›› Issue (1): 230-245.DOI: 10.1016/j.cjche.2021.11.017

• Fluid Dynamics and Transport Phenomena • Previous Articles Next Articles

External mass transfer from/to a single sphere in a nonlinear uniaxial extensional creeping flow

Anjun Liu¹, Jie Chen^2,3, Moshe Favelukis⁴, Meng Guo¹, Meihong Yang¹, Chao Yang^2,3, Tao Zhang⁵, Min Wang⁵, Hao-yue Quan⁵

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 School of Chemical Engineering, University of Chinese Academy of Sciences, Beijing 100049, China;
4 Department of Chemical Engineering, Shenkar College of Engineering and Design, Ramat-Gan, 5252626, Israel;
5 Dynamic Machinery Institute of Inner Mongolia, Inner Mongolia, Hohhot 010010, China

Received:2021-06-22 Revised:2021-11-09 Online:2022-02-25 Published:2022-01-28
Contact: Jie Chen,E-mail address:jchen@ipe.ac.cn;Meng Guo,E-mail address:guomeng@sdas.org;Chao Yang,E-mail address:chaoyang@ipe.ac.cn
Supported by:
This paper is dedicated to Prof. Jiayong Chen at Institute of Process Engineering, Chinese Academy of Sciences. The authors are very grateful to Prof. Jiayong Chen for his support and helpful insight. This work was supported by the National Key Research and Development Program (2021YFC2902502), the National Natural Science Foundation of China (21938009, 91934301, 22078320), the Major Scientific and Technological Innovation Projects in Shandong Province (2019JZZY010302), the Shandong Key Research and Development Program (International Cooperation Office) (2019GHZ018), the Shandong Province Postdoctoral Innovative Talents Support Plan (SDBX2020018), the External Cooperation Program of BIC, Chinese Academy of Sciences (122111KYSB20190032), Chemistry and Chemical Engineering Guangdong Laboratory (1922006), and GHfund B(202107021062).

External mass transfer from/to a single sphere in a nonlinear uniaxial extensional creeping flow

Anjun Liu¹, Jie Chen^2,3, Moshe Favelukis⁴, Meng Guo¹, Meihong Yang¹, Chao Yang^2,3, Tao Zhang⁵, Min Wang⁵, Hao-yue Quan⁵

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 School of Chemical Engineering, University of Chinese Academy of Sciences, Beijing 100049, China;
4 Department of Chemical Engineering, Shenkar College of Engineering and Design, Ramat-Gan, 5252626, Israel;
5 Dynamic Machinery Institute of Inner Mongolia, Inner Mongolia, Hohhot 010010, China

通讯作者: Jie Chen,E-mail address:jchen@ipe.ac.cn;Meng Guo,E-mail address:guomeng@sdas.org;Chao Yang,E-mail address:chaoyang@ipe.ac.cn
基金资助:
This paper is dedicated to Prof. Jiayong Chen at Institute of Process Engineering, Chinese Academy of Sciences. The authors are very grateful to Prof. Jiayong Chen for his support and helpful insight. This work was supported by the National Key Research and Development Program (2021YFC2902502), the National Natural Science Foundation of China (21938009, 91934301, 22078320), the Major Scientific and Technological Innovation Projects in Shandong Province (2019JZZY010302), the Shandong Key Research and Development Program (International Cooperation Office) (2019GHZ018), the Shandong Province Postdoctoral Innovative Talents Support Plan (SDBX2020018), the External Cooperation Program of BIC, Chinese Academy of Sciences (122111KYSB20190032), Chemistry and Chemical Engineering Guangdong Laboratory (1922006), and GHfund B(202107021062).

Abstract

Abstract: This work systematically simulates the external mass transfer from/to a spherical drop and solid particle suspended in a nonlinear uniaxial extensional creeping flow. The mass transfer problem is governed by three dimensionless parameters: the viscosity ratio (λ), the Peclet number (^Pe), and the nonlinear intensity of the flow (E). The existing mass transfer theory, valid for very large Peclet numbers only, is expanded, by numerical simulations, to include a much larger range of Peclet numbers (1 ≤ Pe ≤ 10⁵). The simulation results show that the dimensionless mass transfer rate, expressed as the Sherwood number (Sh), agrees well with the theoretical results at the convection-dominated regime (Pe > 10³). Only when E > 5/4, the simulated Sh for a solid sphere in the nonlinear uniaxial extensional flow is larger than theoretical results because the theory neglects the effect of the vortex formed outside the particle on the rate of mass transfer. Empirical correlations are proposed to predict the influence of the dimensionless governing parameters (λ, Pe, E) on the Sherwood number (Sh). The maximum deviations of all empirical correlations are less than 15% when compared to the numerical simulated results.

Key words: External mass transfer, Nonlinear extensional flow, Sphere, Empirical correlation

摘要： This work systematically simulates the external mass transfer from/to a spherical drop and solid particle suspended in a nonlinear uniaxial extensional creeping flow. The mass transfer problem is governed by three dimensionless parameters: the viscosity ratio (λ), the Peclet number (^Pe), and the nonlinear intensity of the flow (E). The existing mass transfer theory, valid for very large Peclet numbers only, is expanded, by numerical simulations, to include a much larger range of Peclet numbers (1 ≤ Pe ≤ 10⁵). The simulation results show that the dimensionless mass transfer rate, expressed as the Sherwood number (Sh), agrees well with the theoretical results at the convection-dominated regime (Pe > 10³). Only when E > 5/4, the simulated Sh for a solid sphere in the nonlinear uniaxial extensional flow is larger than theoretical results because the theory neglects the effect of the vortex formed outside the particle on the rate of mass transfer. Empirical correlations are proposed to predict the influence of the dimensionless governing parameters (λ, Pe, E) on the Sherwood number (Sh). The maximum deviations of all empirical correlations are less than 15% when compared to the numerical simulated results.

关键词: External mass transfer, Nonlinear extensional flow, Sphere, Empirical correlation

Anjun Liu, Jie Chen, Moshe Favelukis, Meng Guo, Meihong Yang, Chao Yang, Tao Zhang, Min Wang, Hao-yue Quan. External mass transfer from/to a single sphere in a nonlinear uniaxial extensional creeping flow[J]. Chinese Journal of Chemical Engineering, 2022, 41(1): 230-245.

References

[1] H.A. Stone, Dynamics of drop deformation and breakup in viscous fluids, Annu. Rev. Fluid Mech. 26(1) (1994) 65–102.
[2] B.J. Briscoe, C.J. Lawrence, W.G.P. Mietus, A review of immiscible fluid mixing, Adv. Colloid Interface Sci. 81(1) (1999) 1–17.
[3] M. Wegener, N. Paul, M. Kraume, Fluid dynamics and mass transfer at single droplets in liquid/liquid systems, Int. J. Heat Mass Transf. 71(2014) 475–495.
[4] J.M. Rallison, The deformation of small viscous drops and bubbles in shear flows, Annu. Rev. Fluid Mech. 16(1) (1984) 45–66.
[5] L.G. Leal, in: Advanced Transport Phenomena, Cambridge University Press, Cambridge, UK, 1999.
[6] G.I. Leal, Laminar Flow and Convective Transport Processes, ButterworthHeineman, Boston, 1992.
[7] R. Clift, J.R. Grace, M.E. Weber, Bubbles, drops, and particles (1978). https://www.researchgate.net/publication/233845152_Bubbles_Drops_and_Particles.
[8] G.K. Batchelor, Mass transfer from a particle suspended in fluid with a steady linear ambient velocity distribution, J. Fluid Mech. 95(2) (1979) 369–400.
[9] I.P. Gupalo, I.S. Riazantsev, Diffusion on a particle in the shear flow of a viscous fluid. Approximation of the diffusion boundary layer, J. Appl. Math. Mech. 36(3) (1972) 447–451.
[10] S.K. Friedlander, A note on transport to spheres in stokes flow, AIChE J. 7(2) (1961) 347–348.
[11] A. Acrivos, T.D. Taylor, Heat and mass transfer from single spheres in stokes flow, Phys. Fluids 5(4) (1962) 387.
[12] E. Ruckenstein, Mass transfer between a single drop and a continuous phase, Int. J. Heat Mass Transf. 10(12) (1967) 1785–1792.
[13] A.C. Lochiel, P.H. Calderbank, Mass transfer in the continuous phase around axisymmetric bodies of revolution, Chem. Eng. Sci. 19(7) (1964) 471–484.
[14] V.N. Kurdyumov, A.D. Polyanin, Mass transfer problem for particles, drops and bubbles in a shear flow, Fluid Dyn. 25(4) (1990) 611–615.
[15] 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.
[16] A. Mustafa, A. Erten, R.M. Ayaz, O. Kayıllıog ?lu, A. Eser, M. Eryürek, M. Irfan, M. Muradoglu, M. Tanyeri, A. Kiraz, Enhanced dissolution of liquid microdroplets in the extensional creeping flow of a hydrodynamic trap, Langmuir 32(37) (2016) 9460–9467.
[17] M. Favelukis, O.M. Lavrenteva, Mass transfer around oblate spheroidal drops in a biaxial stretching motion, Can. J. Chem. Eng. 92(5) (2014) 964–972.
[18] M. Favelukis, O.M. Lavrenteva, Mass transfer around prolate spheroidal drops in an extensional flow, Can. J. Chem. Eng. 91(6) (2013) 1190–1199.
[19] M. Favelukis, A compound drop in a nonlinear extensional flow, Eur. J. Mech.-B/fluids 83(2020) 114–129.
[20] M. Favelukis, Mass transfer around a compound drop in an extensional flow, Can. J. Chem. Eng. 99(s1) (2021) S800–S808.
[21] J. Nuszkowski, J. Schwamb, J. Esposito, A novel gas divider using nonlinear laminar flow, Flow Meas. Instrum. 52(2016) 255–260.
[22] B. Yesilata, C. Clasen, G.H. McKinley, Nonlinear shear and extensional flow dynamics of wormlike surfactant solutions, J. Non-Newton. Fluid Mech. 133(2–3) (2006) 73–90.
[23] M.C. García, S. Sánchez, L.A. Trujillo-Cayado, J. Muñoz, M.C. Alfaro, Tackling slip effects in the nonlinear flow properties of gellan fluid gels, J. Appl. Polym. Sci. 136(1) (2019) 46900.
[24] M.K. Sing, M.J. Glassman, X.T. Vronay-Ruggles, W.R. Burghardt, B.D. Olsen, Structure and rheology of dual-associative protein hydrogels under nonlinear shear flow, Soft Matter 13(45) (2017) 8511–8524.
[25] C. RamReddy, P. Naveen, D. Srinivasacharya, Nonlinear convective flow of nonNewtonian fluid over an inclined plate with convective surface condition: A darcy-forchheimer model, Int. J. Appl. Comput. Math. 4(1) (2018) 1–18.
[26] J. Zhang, M.J. Miksis, S.G. Bankoff, Nonlinear dynamics of a two-dimensional viscous drop under shear flow, Phys. Fluids 18(7) (2006) 072106.
[27] X.X. Chen, Z.H. Wang, Y.L. Yu, Nonlinear shear and heat transfer in hypersonic rarefied flows past flat plates, AIAA J. 53(2) (2014) 413–419.
[28] J.O. Skogestad, E. Keilegavlen, J.M. Nordbotten, Two-scale preconditioning for two-phase nonlinear flows in porous media, Transp. Porous Media 114(2) (2016) 485–503.
[29] B. Pier, P.J. Schmid, Linear and nonlinear dynamics of pulsatile channel flow, J. Fluid Mech. 815(2017) 435–480.
[30] P. Dimitrakopoulos, Dumbbell formation for elastic capsules in nonlinear extensional Stokes flows, Phys. Rev. Fluids 2(6) (2017) 063101.
[31] M. Favelukis, A slender drop in a nonlinear extensional flow, J. Fluid Mech. 808(2016) 337–361.
[32] M. Favelukis, Non-Newtonian slender drops in a nonlinear extensional flow, J. Fluid Mech. 877(2019) 561–581.
[33] M. Favelukis, Mass transfer around a slender drop in a nonlinear extensional flow, Nonlinear Eng. 8(1) (2019) 117–126.
[34] J.D. Sherwood, Tip streaming from slender drops in a nonlinear extensional flow, J. Fluid Mech. 144(1984) 281–295.
[35] M. Favelukis, A drop in uniaxial and biaxial nonlinear extensional flows, Phys. Fluids 29(8) (2017) 087102.
[36] M. Favelukis, Mass transfer around bubbles, drops, and particles in uniaxial and biaxial nonlinear extensional flows, AIChE J. 65(1) (2019) 398–408.
[37] C. Yang, Z.S. Mao, Numerical simulation of interphase mass transfer with the level set approach, Chem. Eng. Sci. 60(10) (2005) 2643–2660.
[38] 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.

External mass transfer from/to a single sphere in a nonlinear uniaxial extensional creeping flow

External mass transfer from/to a single sphere in a nonlinear uniaxial extensional creeping flow

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