شبیه سازی عددی سه بعدی رفتار قطره و عکس العمل قطره و دیوار در میدان الکتریکی

نوع مقاله : مقاله پژوهشی

نویسندگان

دانشکده مهندسی مکانیک، دانشگاه صنعتی اصفهان، اصفهان، ایران

چکیده

در این پژوهش، رفتار قطره و نیز عکس العمل قطره و دیوار در میدان الکتریکی یکنواخت خارجی به صورت کاملا سه بعدی شبیه سازی شده است. میدان الکتریکی با اعمال اختلاف پتانسیل ایجاد و سپس با استفاده از مدل نشت عایق تیلور، نیروی الکتریکی ناشی از این میدان، محاسبه و به معادلات نویر-استوکس اضافه شده است. این نیرو، بسته به خصوصیات الکتریکی قطره و سیال پیرامون، باعث تغییر شکل آن به صورت آبلیت )راستای عمود بر میدان الکتریکی( و یا پرولیت )در راستای میدان الکتریکی( و همچنین ایجاد جریان های القایی داخل و خارج قطره می‌شود. ابتدا تغییر شکل یک قطره‌ی تنها در میدان الکتریکی شبیه سازی و نتیجه با نتایج تجربی موجود، مقایسه و صحت سنجی شده است. سپس رفتار قطره در میدان الکتریکی از نظر نوع تغییر شکل و نوع جریان‌های القایی بررسی شده است. عکس العمل قطره و دیوار، برای قطره‌های آبلیت و پرولیت مورد بررسی قرار گرفته است. اثر عدد مویینگی الکتریکی بر چگونگی عکس العمل قطره و دیوار و نیز حالت نهایی آنها، مطالعه شده است. هم قطرات آبلیت و هم پرولیت به دیوار جذب می‌شوند. افزایش عدد مویینگی الکتریکی این اثر را تقویت می‌کند و تحت شرایطی می‌تواند باعث اعوجاج سطوح قطرات نیز بشود.

کلیدواژه‌ها

موضوعات


عنوان مقاله [English]

Three Dimensional Numerical Simulation of a Drop and Drop-to-Wall Interaction under Uniform Electric Field

نویسندگان [English]

  • M. Akbari
  • S.S. Mortazavi
  • H. Shahin Varnoosfaderani
Department of Mechanical Engineering, Isfahan University of Technology, Isfahan, Iran
چکیده [English]

The behavior of a drop and drop-to-wall interaction under a uniform electric field is studied by numerical simulations in three dimensions. The electric field is created by imposing an electric-potential difference. The Taylor Leaky Dielectric Model, is used to compute electric force. This force is added to Navier-Stokes equations as a body force. The drop can obtain an Oblate shape (deformation perpendicular to direction of electric field) or a Prolate shape (deformation in the direction of electric field) depending on the electric properties of drop and ambient fluid. It found that the deformation of the drop is in agreement with experimental results finding in literature. The interaction of the drop with the existing walls of the channel is investigated for both Oblate and Prolate drops. This is done at various capillary numbers. Attraction of both Oblate and Prolate drops to the wall, are the results. Increasing the electric capillary number reduces the time of attraction for both drops. For Oblate and Prolate drops with similar flows, higher electric capillary number causes distortion of drop surface near the wall. For another type of Prolate drops, increasing the electric capillary number eventuates to more distance between drop center and the wall.

کلیدواژه‌ها [English]

  • Front-tracking method
  • Electric Capillary Number
  • Ohnesorge Number
  • Oblate/Prolate Deformation
  • Electric conductivity/permittivity ratio
[1] J. Zeng, T. Korsmeyer, Principles of droplet electrohydrodynamics for lab-on-a-chip, Lab on a Chip, 4(4) (2004) 265-277.
[2] S.K. Cho, H. Moon, C.-J. Kim, Creating, transporting, cutting, and merging liquid droplets by electrowetting-based actuation for digital microfluidic circuits, Journal of Microelectromechanical Systems, 12(1) (2003) 70-80.
[3] H.T. Yudistira, V.D. Nguyen, P. Dutta, D. Byun, Flight behavior of charged droplets in electrohydrodynamic inkjet printing, Applied Physics Letters, 96(2) (2010) 023503.
[4] J. Shrimpton, A. Yule, Characterisation of charged hydrocarbon sprays for application in combustion systems, Experiments in fluids, 26(5) (1999) 460-469.
[5] C.T. O'Konski, H.C. Thacher Jr, The distortion of aerosol droplets by an electric field, The Journal of Physical Chemistry, 57(9) (1953) 955-958.
[6] G. Taylor, Disintegration of water drops in an electric field, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 280(1382) (1964) 383-397.
[7] R. Allan, S. Mason, Particle behaviour in shear and electric fields. I. Deformation and burst of fluid drops, Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, 267(1328) (1962) 45-61.
[8] G. Taylor, Studies in electrohydrodynamics. I. The circulation produced in a drop by electrical field, Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, 291(1425) (1966) 159-166.
[9] D. Saville, Electrohydrodynamics: the Taylor-Melcher leaky dielectric model, Annual review of fluid mechanics, 29(1) (1997) 27-64.
[10] T. Tsukada, T. Katayama, Y. Ito, M. Hozawa, Theoretical and Experimental Studies of Circulations Inside and Outside a Deformed Drop under a Uniform Electric Field, Journal of chemical engineering of Japan, 26(6) (1993) 698-703.
[11] H. Paknemat, A. Pishevar, P. Pournaderi, Numerical simulation of drop deformations and breakup modes caused by direct current electric fields, Physics of Fluids (1994-present), 24(10) (2012) 102101.
[12] W.-F. Hu, M.-C. Lai, Y.-N. Young, A hybrid immersed boundary and immersed interface method for electrohydrodynamic simulations, Journal of Computational Physics, 282 (2015) 47-61.
[13] A. Fernández, G. Tryggvason, J. Che, S.L. Ceccio, The effects of electrostatic forces on the distribution of drops in a channel flow: Two-dimensional oblate drops, Physics of Fluids (1994-present), 17(9) (2005) 093302.
[14] M.A. Halim, A. Esmaeeli, Computational studies on the transient electrohydrodynamics of a liquid drop, FDMP: Fluid Dynamics & Materials Processing, 9(4) (2013) 435-460.
[15] T. Wang, H.-X. Li, J.-F. Zhao, Three-Dimensional Numerical Simulation of Bubble Dynamics in Microgravity under the Influence of Nonuniform Electric Fields, Microgravity Science and Technology, (2016) 1-10.
[16] J. Melcher, G. Taylor, Electrohydrodynamics: a review of the role of interfacial shear stresses, Annual Review of Fluid Mechanics, 1(1) (1969) 111-146.
[17] G. Tryggvason, B. Bunner, A. Esmaeeli, D. Juric, N. Al-Rawahi, W. Tauber, J. Han, S. Nas, Y.-J. Jan, A front-tracking method for the computations of multiphase flow, Journal of Computational Physics, 169(2) (2001) 708-759.
[18] S.O. Unverdi, G. Tryggvason, A front-tracking method for viscous, incompressible, multi-fluid flows, Journal of computational physics, 100(1) (1992) 25-37.
[19] P.H. Rhodes, R.S. Snyder, G.O. Roberts, Electrohydrodynamic distortion of sample streams in continuous flow electrophoresis, Journal of Colloid and interface Science, 129(1) (1989) 78-90.
[20] P.F. Salipante, P.M. Vlahovska, Electrohydrodynamics of drops in strong uniform dc electric fields, Physics of Fluids (1994-present), 22(11) (2010) 112110.
[21] S. Torza, R. Cox, S. Mason, Electrohydrodynamic deformation and burst of liquid drops, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences, 269(1198) (1971) 295-319.