Numerical simulation of Marangoni effects of single drops induced by interphase mass transfer in liquid-liquid extraction systems by the level set method

Science in China Series B: Chemistry - Tập 51 - Trang 684-694 - 2008
JianFeng Wang1,2, Chao Yang1, ZaiSha Mao1
1Key Laboratory of Green Process and Engineering, Institute of Process Engineering, Chinese Academy of Sciences, Beijing, China
2Department of Chemical Engineering, Zhengzhou University, Zhengzhou, China

Tóm tắt

The mathematical model of mass transfer-induced Marangoni effect is formulated. The drop surface evolution is captured by the level set method, in which the interface is represented by the embedded set of zero level of a scalar distance function defined in the whole computational domain. Numerical simulation of the Marangoni effect induced by interphase mass transfer to/from deformable single drops in unsteady motion in liquid-liquid extraction systems is performed in a Eulerian axisymmetric reference frame. The occurrence and development of the Marangoni effect are simulated, and the results are in good agreement with the classical theoretical analysis and previous simulation.

Tài liệu tham khảo

Sternling C V, Scriven L E. Interfacial turbulence: Hydrodynamic instability and the Marangoni effect. AIChE J, 1959, 5(4): 514–523 Pearson J R A. On convection cells induced by surface tension. J Fluid Mech, 1958, 4: 489–500 Brian P L T. Effect of Gibbs adsorption on Marangoni instability. AIChE J, 1971, 17(4): 765–772 Scanlon J W, Segel L A J. Finite amplitude cellular convection induced by surface tension. J Fluid Mech, 1967, 30(1): 149–162 Cloot A, Lebon G. A nonlinear stability analysis of the Benard-Marangoni problem. J Fluid Mech, 1984, 145: 447–469 Golovin A A, Nepomnyashchy A A, Pismen L M. Pattern formation in large-scale Marangoni convection with deformable interface. Phys D Nonlinear Phenomena, 1995, 81(1–2): 117–147 Bragard J, Slavtchev S G, Lebon G. Nonlinear solutal Marangoni instability in a liquid layer with an adsorbing upper surface. J Colloid Interface Sci, 1994, 168(2): 402–413 Okano Y, Fukuda T, Hirata A, Takano N, Tsukuda T, Hozawa M, Imaishi N. Numerical study on Czochralski growth of oxide single crystals. J Crystal Growth, 1991, 109(1–4): 94–98 Kobayashi M, Tsukuda T, Hozawa M. Effect of internal radiative heat transfer on the convection in CZ oxide melt. J Crystal Growth. 1997, 180(1): 157–166 Galazka Z, Wilke H. Influence of Marangoni convection on the flow pattern in the melt during growth of Y3Al5O12 single crystals by the Czochralski method. J Crystal Growth, 2000, 216(1–4): 389–398 Kawaji M, Gamache O, Hwang D H, Ichikawa N, Viola J P, Sygusch J. Investigation of Marangoni and natural convection during protein crystal growth. J Crystal Growth, 2003, 258(3–4): 420–430 Bergeron A, Henry D, Benhadid H. Marangoni-Bénard instability in microgravity conditions with Soret effect. Int J Heat Mass Transfer, 1994, 37(11): 1545–1562 Bergeron A, Henry D, Benhadid H, Tuckerman L S. Marangoni convection in binary mixture with Soret effect. J Fluid Mech, 1998, 375: 143–177 Bahloul A, Delahaye R, Vasseur P, Robillard L. Effect of surface tension on convection in a binary fluid layer under a zero gravity environment. Int J Heat Mass Transfer, 2003, 46(10): 1759–1771 Lappa M, Piccolo C, Carotenuto L. Mixed buoyant-Marangoni convection due to dissolution of a droplet in liquid-liquid system with miscilbility gap. Eur J Mech B Fluids, 2004, 23: 781–794 Kang Y T, Kashiwagi T. Heat transfer enhancement by Marangoni convection in the NH3-H2O absorption process. Int J Refrig, 2002, 25(6): 780–788 Kim J, Kang Y T, Choi C K. Effects of gas phase and additive properties on Marangoni instability for absorption process in a horizontal fluid layer. Int J Refrig, 2004, 27(2): 140–149 Kim J, Choi C K, Kang Y T. Instability analysis of Marangoni convection for absorption process accompanied by heat transfer. Int J Heat Mass Transfer, 2004, 47(10-11): 2395–2402 Bassano E. Numerical simulation of thermo-solutal-capillary migration of a dissolving drop in a cavity. Int J Num Meth Fluids, 2003, 41(7): 765–788 Mao Z S, Chen J Y. Numerical simulation of the Marangoni effect on mass transfer to single slowly moving drops in the liquid-liquid system. Chem Eng Sci, 2004, 59(8–9): 1815–1828 Harlow F H, Welch J E. Numerical calculation of time-dependent viscous incompressible flow of fluid with free surface. Phys Fluids, 1965, 8(12): 2182–2189 Hirt C W, Nichols B D. Volume of fluid (VOF) method for the dynamics of free boundaries. J Comput Phys, 1981, 39(1): 201–255 Unverdi O S, Tryggvason G J. A front-tracking method for viscous, incompressible, multi-fluid flows. J Comput Phys, 1992, 100(1): 25–37 Baker G R, Moore D W. The rise and distortion of a two-dimensional gas bubble in an inviscid liquid. Phys Fluids A, 1989, 1(9): 1451–1459 Osher S, Sethian J. Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations. J Comput Phys, 1988, 79(1): 12–49 Brackbill J U, Kothe D B, Zemach C. A continuum method for modeling surface tension. J Comput Phys, 1992, 100(2): 335–354 Sussman M, Smereka P, Osher S. A Level set approach for computing solutions to incompressible two-phase flow. J Comput Phys, 1994, 114(1): 146–159 Yang C, Mao Z S. Numerical simulation of interphase mass transfer with the level set approach. Chem Eng Sci, 2005, 60(10): 2643–2660 Pantankar S V. Numerical Heat Transfer and Fluid Flow. Washington: Hemisphere, 1980 Van Doormaal J P, Raithby G D. Enhancements of the SIMPLE methods for prediction incompressible fluid flows. Num Heat Transfer, 1984, 7(2): 147–163 Fedkiw R P, Aslam T, Merriman B, Osher S. A non-oscillatory Eulerian approach to interfaces in multimaterial flows (the Ghost Fluid Method). J Comput Phys, 1999, 152(2): 457–492 Jiang G S, Shu C W. Efficient implementation of weighted ENO schemes. J Comput Phys, 1996, 126(1): 202–228 Wang J F, Yang C, Mao Z S. A simple weighted integration method for calculating surface tension force to suppress parasitic flow in the Level set approach. Chin J Chem Eng, 2006, 14(6): 740–746