Main Article Content
A perfect dielectric model was incorporated into the OpenFOAM® software and used for investigation and, possibly, improvements of electrohydrodynamic calculations. Two different sets of numerical simulations were analyzed, in which two different fluids were present. The first set was one-dimensional, while in the second, a drop of one fluid was surrounded by the other fluid. It is shown that oscillations and possible artificial generation of a curl of the electric field strength can be observed at applying certain expressions or calculation strategies, which can be thus abandoned. Usage of dynamic meshes, at least those present in the used software, and of limiters for the gradient of the electric field strength can lead to large numerical errors. It is also shown that usage of certain cell face values could improve the results. An electric Courant number was derived by dimensional analysis, and it could be suggested for future calculations. Conclusions made in this paper are expected to be transferable to other more complicated models.
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.Authors who publish with this journal agree to the following terms:
Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
Authors grant to the Publisher the following rights to the manuscript, including any supplemental material, and any parts, extracts or elements thereof:
- the right to reproduce and distribute the Manuscript in printed form, including print-on-demand;
- the right to produce prepublications, reprints, and special editions of the Manuscript;
- the right to translate the Manuscript into other languages;
- the right to reproduce the Manuscript using photomechanical or similar means including, but not limited to photocopy, and the right to distribute these reproductions;
- the right to reproduce and distribute the Manuscript electronically or optically on any and all data carriers or storage media – especially in machine readable/digitalized form on data carriers such as hard drive, CD-Rom, DVD, Blu-ray Disc (BD), Mini-Disk, data tape – and the right to reproduce and distribute the Article via these data carriers;
- the right to store the Manuscript in databases, including online databases, and the right of transmission of the Manuscript in all technical systems and modes;
- the right to make the Manuscript available to the public or to closed user groups on individual demand, for use on monitors or other readers (including e-books), and in printable form for the user, either via the internet, other online services, or via internal or external networks.
López-Herrera JM, Popinet S, Herrada MA. A charge-conservative approach for simulating electrohydrodynamic two-phase flows using volume-of-fluid. J Comput Phys. 2011; 230: 1939-1955 https://dx.doi.org/10.1016/j.jcp.2010.11.042
Castellanos A, ed. Electrohydrodynamics. Vienna, Austria: Springer-Verlag Wien; 1998 https://dx.doi.org/10.1007/978-3-7091-2522-9
Bošković S, Bugarski B. Review of electrospray observations and theory. J Eng Process Manag. 2018; 10: 41-53 https://dx.doi.org/10.7251/jepm181002041b
Singh R, Bahga SS, Gupta A. Electrohydrodynamics in leaky dielectric fluids using lattice Boltzmann method. Eur J Mech B Fluids. 2019; 74: 167-179 https://dx.doi.org/10.1016/j.euromechflu.2018.11.011
Shin W-T, Yiacoumi S, Tsouris C. Electric-field effects on interfaces: electrospray and electrocoalescence. Curr Opin Colloid Interface Sci. 2004; 9: 249-255 https://dx.doi.org/10.1016/j.cocis.2004.06.006
Pongrác B, Kim H-H, Negishi N, Machala Z. Influence of water conductivity on particular electrospray modes with dc corona discharge – optical visualization approach. Eur Phys J D. 2014; 68: 224 https://dx.doi.org/10.1140/epjd/e2014-50052-4
Fernandez de la Mora J, Van Berkel GJ, Enke CG, Cole RB, Martinez-Sanchez M, Fenn JB. Electrochemical processes in electrospray ionization mass spectrometry. J Mass Spectrom. 2000; 35: 939-952 https://dx.doi.org/10.1002/1096-9888(200008)35:8<939::aid-jms36>3.0.co;2-v
Notz PK, Basaran OA. Dynamics of Drop Formation in an Electric Field. J Colloid Interface Sci. 1999; 213: 218-237 https://dx.doi.org/10.1006/jcis.1999.6136
Xie J, Wang C-H. Encapsulation of Proteins in Biodegradable Polymeric Microparticles Using Electrospray in the Taylor Cone-Jet Mode. Biotechnol Bioeng. 2007; 97: 1278-1290 https://dx.doi.org/10.1002/bit.21334
Thirumalaisamy R, Natarajan G, Dalal A. Towards an improved conservative approach for simulating electrohydrodynamic two-phase flows using volume-of-fluid. J Comput Phys. 2018; 367: 391-398 https://dx.doi.org/10.1016/j.jcp.2018.04.024
Bugarski B, Smith J, Wu J, Goosen MFA. Methods for animal cell immobilization using electrostatic droplet generation. Biotechnol Techn. 1993; 7: 677-682 https://dx.doi.org/10.1007/BF00151869
Bugarski B, Li Q, Goosen MFA, Poncelet D, Neufeld RJ, Vunjak G. Electrostatic Droplet Generation: Mechanism of Polymer Droplet Formation. AIChE J. 1994: 40: 1026-1031 https://dx.doi.org/10.1002/aic.690400613
Poncelet D, Bugarski B, Amsden BG, Zhu J, Neufeld R, Goosen MFA. A Parallel plate electrostatic droplet generator: parameters affecting microbead size. Appl Microbiol Biotechnol. 1994; 42: 251-255 https://dx.doi.org/10.1007/BF00902725
Poncelet D, Neufeld RJ, Goosen MFA, Burgarski B, Babak V. Formation of microgel beads by electric dispersion of polymer solutions. AIChE J. 1999; 45: 2018-2023 https://dx.doi.org/10.1002/aic.690450918
Manojlovic V, Djonlagic J, Obradovic B, Nedovic V, Bugarski B. Immobilization of cells by electrostatic droplet generation: a model system for potential application in medicine. Int J Nanomed. 2006; 1: 163-171 https://dx.doi.org/10.2147/nano.2006.1.2.163
Poncelet D, Babak VG, Neufeld RJ, Goosen MFA, Burgarski B. Theory of electrostatic dispersion of polymer solutions in the production of microgel beads containing biocatalyst. Adv Colloid Interface Sci. 1999; 79: 213-228 https://dx.doi.org/10.1016/S0001-8686(97)00037-7
Supeene G, Koch CR, Bhattacharjee S. Deformation of a droplet in an electric field: Nonlinear transient response in perfect and leaky dielectric media. J Colloid Interface Sci. 2008; 318: 463-476 https://dx.doi.org/10.1016/j.jcis.2007.10.022
Munoz CN. Computational modelling of electrohydrodynamic atomization. MSc. Thesis, The University of Manchester, Manchester, UK; 2014.
Reddy MN, Esmaeeli A. The EHD-driven fluid flow and deformation of a liquid jet by a transverse electric field. Int J Multiphase Flow. 2009; 35: 1051-1065 https://dx.doi.org/10.1016/j.ijmultiphaseflow.2009.06.008
Taylor GI. Studies in electrohydrodynamics. I. The circulation produced in a drop by an electric field. Proc R Soc London, Ser A. 1966; 291: 159-166 https://dx.doi.org/10.1098/rspa.1966.0086
Moukalled F, Mangani L, Darwish M. The Finite Volume Method in Computational Fluid Dynamics: An Advanced Introduction with OpenFOAM® and Matlab®. Switzerland: Springer International Publishing Switzerland; 2016 https://dx.doi.org/10.1007/978-3-319-16874-6
Andersson B, Andersson R, Håkansson L, Mortensen M, Sudiyo R, Van Wachem B, Hellstrom L. Computational Fluid Dynamics for Engineers. Cambridge, UK: Cambridge University Press; 2012. ISBN: 978-1-107-01895-2
Li X-g, Fritsching U. Spray Transport Fundamentals. In: Henein H, Uhlenwinkel V, Fritsching U, eds. Metal Sprays and Spray Deposition. Cham, Switzerland: Springer International Publishing AG; 2017:89-176 https://dx.doi.org/10.1007/978-3-319-52689-8
Hemida H. OpenFOAM tutorial: Free surface tutorial using interFoam and rasInterFoam. 2008.
Lima NC. Numerical Studies in Electrohydrodynamics. Ph.D. Thesis, School of Mechanical Engineering of the University of Campinas; 2017.
Chen C-H. Electrohydrodynamic Stability. In: Ramos A, ed. Electrokinetics and Electrohydrodynamics in Microsystems. New York, New York, USA: SpringerWienNewYork; 2011:177-220 https://dx.doi.org/10.1007/978-3-7091-0900-7
Lastow O, Balachandran W. Numerical simulation of electrohydrodynamic (EHD) atomization. J Electrostat. 2006; 64: 850-859 https://dx.doi.org/10.1016/j.elstat.2006.02.006
Greenshields CJ. OpenFOAM The Open Source CFD Toolbox: Programmer’s Guide Version 3.0.1. OpenFOAM Foundation Ltd.; 2015.
Davidson PA. Turbulence: An Introduction for Scientists and Engineers. New York, USA: Oxford University Press; 2004. ISBN: 0198529481
Aguerre HJ, Pairetti CI, Venier CM, Márquez Damián S, Nigro NM. An oscillation-free flow solver based on flux reconstruction. J Comput Phys. 2018; 365: 135-148 https://dx.doi.org/10.1016/j.jcp.2018.03.033
Sander S, Gawor S, Fritsching U. Separating polydisperse particles using electrostatic precipitators with wire and spiked-wire discharge electrode design. Particuology. 2018; 38: 10-17 https://dx.doi.org/10.1016/j.partic.2017.05.014
Weber N, Galindo V, Stefani F, Weier T, Wondrak T. Numerical simulation of the Tayler instability in liquid metals. New J Phys. 2013; 15: 043034 https://dx.doi.org/10.1088/1367-2630/15/4/043034