Hostname: page-component-5db58dd55d-f6s65 Total loading time: 0 Render date: 2026-06-02T06:47:23.352Z Has data issue: false hasContentIssue false
  • English
  • Français

A numerical study of gravity-driven instability in strongly coupled dusty plasma. Part 3. Homo-interaction between a pair of rising/falling bubbles/droplets

Published online by Cambridge University Press:  20 September 2024

Vikram S. Dharodi Open the ORCID record for Vikram S. Dharodi [Opens in a new window]
Vikram S. Dharodi*
Affiliation:
Department of Physics and Astronomy, West Virginia University, Morgantown, WV 26506, USA
*
†Email address for correspondence: vikram.ipr@gmail.com
Get access Rights & Permissions [Opens in a new window]

Abstract

A numerical study of the homo-interactions between two falling droplets and between two rising bubbles in a strongly coupled dusty plasma medium is presented in this article. The strongly coupled dusty plasma is considered as a viscoelastic fluid using the generalized hydrodynamic fluid model formalism. Two factors that affect homo-interactions are taken into account: the initial spacing and the coupling strength of the medium. Three different spacings between two droplets are simulated: widely, medium and closely. In each case, the coupling strength has been given as mild–strong and strong. It is shown that the overall dynamic is governed by the competition between the acceleration of two droplets/bubbles due to gravity and the interaction due to the closeness of the droplets/bubbles. Particularly in viscoelastic fluids, apart from the initial separation, shear waves originating from rotating vortices are responsible for the closeness of two droplets or bubbles. Several two-dimensional simulations have been carried out. This work is a continuation of the work done in Parts 1 (Dharodi & Das, J. Plasma Phys., vol. 87, issue 2, 2021, 905870216) and 2 (Dharodi, J. Plasma Phys., vol. 87, issue 4, 2021, 905870402).

Keywords

dusty plasmascomplex plasmasplasma instabilities

Information

Type
Research Article
Information
Journal of Plasma Physics , Volume 90 , Issue 4 , August 2024 , 905900408
Check for updates
Copyright
Copyright © The Author(s), 2024. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

Aliabouzar, M., Kripfgans, O.D., Fowlkes, J.B. & Fabiilli, M.L. 2023 Bubble nucleation and dynamics in acoustic droplet vaporization: a review of concepts, applications, and new directions. Z. Med. Physik. 33 (3), 387–406.10.1016/j.zemedi.2023.01.004CrossRefGoogle ScholarPubMed
Arzhannikov, A.V., Bataev, V.A., Bataev, I.A., Burdakov, A.V., Ivanov, I.A., Ivantsivsky, M.V., Kuklin, K.N., Mekler, K.I., Rovenskikh, A.F., Polosatkin, S.V., et al. 2013 Surface modification and droplet formation of tungsten under hot plasma irradiation at the GOL-3. J. Nucl. Mater. 438, S677–S680.10.1016/j.jnucmat.2013.01.143CrossRefGoogle Scholar
Boris, J.P., Landsberg, A.M., Oran, E.S. & Gardner, J.H. 1993 LCPFCT A flux-corrected transport algorithm for solving generalized continuity equations. Tech. Rep. NRL Memorandum Report 93-7192, Naval Research Laboratory.10.21236/ADA265011CrossRefGoogle Scholar
Bourouiba, L. & Bush, J.W.M. 2012 Drops and bubbles in the environment. In Handbook of Environmental Fluid Dynamics, vol. 1, pp. 445–458. CRC.10.1201/b14241-40CrossRefGoogle Scholar
Chaubey, N. & Goree, J. 2022 a Coulomb expansion of a thin dust cloud observed experimentally under afterglow plasma conditions. Phys. Plasmas 29 (11).10.1063/5.0112680CrossRefGoogle Scholar
Chaubey, N. & Goree, J. 2022 b Preservation of a dust crystal as it falls in an afterglow plasma. Front. Phys. 10, 879092.10.3389/fphy.2022.879092CrossRefGoogle Scholar
Chaubey, N. & Goree, J. 2023 a Controlling the charge of dust particles in a plasma afterglow by timed switching of an electrode voltage. J. Phys. D: Appl. Phys. 56 (37), 375202.10.1088/1361-6463/acd78fCrossRefGoogle Scholar
Chaubey, N. & Goree, J. 2023 b Mitigating dust particle contamination in an afterglow plasma by controlled lifting with a dc electric field. J. Phys. D: Appl. Phys. 57 (10), 105201.10.1088/1361-6463/ad1148CrossRefGoogle Scholar
Chaubey, N. & Goree, J. 2024 Controlling the charge of dust particles in an afterglow by modulating the plasma power. J. Phys. D: Appl. Phys. 57 (20), 205202.10.1088/1361-6463/ad291cCrossRefGoogle Scholar
Chaubey, N., Goree, J., Lanham, S.J. & Kushner, M.J. 2021 Positive charging of grains in an afterglow plasma is enhanced by ions drifting in an electric field. Phys. Plasmas 28 (10).10.1063/5.0069141CrossRefGoogle Scholar
Chen, R.-H., Tan, D.S., Lin, K.-C., Chow, L.C., Griffin, A.R. & Rini, D.P. 2008 Droplet and bubble dynamics in saturated FC-72 spray cooling on a smooth surface. Trans. ASME J. Heat Transfer 130 (10).10.1115/1.2953237CrossRefGoogle Scholar
Chen, Y.-H., Chu, H.-Y. & Lin, I. 2006 Interaction and fragmentation of pulsed laser induced microbubbles in a narrow gap. Phys. Rev. Lett. 96 (3), 034505.10.1103/PhysRevLett.96.034505CrossRefGoogle Scholar
Choudhary, M., Mukherjee, S. & Bandyopadhyay, P. 2016 Propagation characteristics of dust–acoustic waves in presence of a floating cylindrical object in the dc discharge plasma. Phys. Plasmas 23 (8).10.1063/1.4960667CrossRefGoogle Scholar
Choudhary, M., Mukherjee, S. & Bandyopadhyay, P. 2017 Experimental observation of self excited co-rotating multiple vortices in a dusty plasma with inhomogeneous plasma background. Phys. Plasmas 24 (3).10.1063/1.4977454CrossRefGoogle Scholar
Choudhary, M., Mukherjee, S. & Bandyopadhyay, P. 2018 Collective dynamics of large aspect ratio dusty plasma in an inhomogeneous plasma background: formation of the co-rotating vortex series. Phys. Plasmas 25 (2).10.1063/1.5019364CrossRefGoogle Scholar
Chu, H.-Y., Chiu, Y.-K., Chan, C.-L. & Lin, I. 2003 Observation of laser-pulse-induced traveling microbubbles in dusty plasma liquids. Phys. Rev. Lett. 90 (7), 075004.10.1103/PhysRevLett.90.075004CrossRefGoogle ScholarPubMed
Cristini, V. & Tan, Y.-C. 2004 Theory and numerical simulation of droplet dynamics in complex flows—a review. Lab on a Chip 4 (4), 257–264.10.1039/B403226HCrossRefGoogle ScholarPubMed
Das, A., Dharodi, V. & Tiwari, S. 2014 Collective dynamics in strongly coupled dusty plasma medium. J. Plasma Phys. 80 (6), 855–861.10.1017/S0022377814000506CrossRefGoogle Scholar
Dharodi, V. 2016 Collective phenomena in strongly coupled dusty plasma medium. PhD thesis, Homi Bhabha National Institute.Google Scholar
Dharodi, V. 2020 Rotating vortices in two-dimensional inhomogeneous strongly coupled dusty plasmas: shear and spiral density waves. Phys. Rev. E 102 (4), 043216.10.1103/PhysRevE.102.043216CrossRefGoogle ScholarPubMed
Dharodi, V. 2021 A numerical study of gravity-driven instability in strongly coupled dusty plasma. Part 2. Hetero-interactions between a rising bubble and a falling droplet. J. Plasma Phys. 87 (4), 905870402.10.1017/S0022377821000684CrossRefGoogle Scholar
Dharodi, V. & Das, A. 2021 A numerical study of gravity-driven instability in strongly coupled dusty plasma. Part 1. Rayleigh–Taylor instability and buoyancy-driven instability. J. Plasma Phys. 87 (2), 905870216.10.1017/S0022377821000349CrossRefGoogle Scholar
Dharodi, V. & Kostadinova, E. 2023 Ring structural transitions in strongly coupled dusty plasmas. Phys. Rev. E 107 (5), 055208.10.1103/PhysRevE.107.055208CrossRefGoogle ScholarPubMed
Dharodi, V. & Kostadinova, E. 2024 Vortex merging in strongly coupled dusty plasmas using a visco-elastic fluid model. Phys. Plasmas 31 (5), 053702.10.1063/5.0201791CrossRefGoogle Scholar
Dharodi, V., Patel, B. & Das, A. 2022 Kelvin–Helmholtz instability in strongly coupled dusty plasma with rotational shear flows and tracer transport. J. Plasma Phys. 88 (1), 905880103.10.1017/S0022377821001288CrossRefGoogle Scholar
Dharodi, V.S., Das, A., Patel, B.G. & Kaw, P.K. 2016 Sub-and super-luminar propagation of structures satisfying poynting-like theorem for incompressible generalized hydrodynamic fluid model depicting strongly coupled dusty plasma medium. Phys. Plasmas 23 (1), 013707.10.1063/1.4940328CrossRefGoogle Scholar
Dharodi, V.S., Tiwari, S.K. & Das, A. 2014 Visco-elastic fluid simulations of coherent structures in strongly coupled dusty plasma medium. Phys. Plasmas 21 (7), 073705.10.1063/1.4888882CrossRefGoogle Scholar
Dollet, B., Marmottant, P. & Garbin, V. 2019 Bubble dynamics in soft and biological matter. Annu. Rev. Fluid Mech. 51, 331–355.10.1146/annurev-fluid-010518-040352CrossRefGoogle Scholar
Dwyer, H.A. 1989 Calculations of droplet dynamics in high temperature environments. Prog. Energy Combust. Sci. 15 (2), 131–158.10.1016/0360-1285(89)90013-0CrossRefGoogle Scholar
Feng, Y., Goree, J. & Liu, B. 2012 Frequency-dependent shear viscosity of a liquid two-dimensional dusty plasma. Phys. Rev. E 85 (6), 066402.10.1103/PhysRevE.85.066402CrossRefGoogle ScholarPubMed
Frenkel, J. 1955 Kinetic Theory Of Liquids. Dover Publications.Google Scholar
Gaudron, R., Warnez, M.T. & Johnsen, E. 2015 Bubble dynamics in a viscoelastic medium with nonlinear elasticity. J. Fluid Mech. 766.10.1017/jfm.2015.7CrossRefGoogle Scholar
Ikezi, H. 1986 Coulomb solid of small particles in plasmas. Phys. Fluids 29 (6), 1764–1766.10.1063/1.865653CrossRefGoogle Scholar
Jia, W. & Zhu, H. 2015 Dynamics of water droplet impact and spread on soybean leaves. Trans. ASABE 58 (4), 1109–1016.Google Scholar
Kaw, P.K. 2001 Collective modes in a strongly coupled dusty plasma. Phys. Plasmas 8 (5), 1870–1878.10.1063/1.1348335CrossRefGoogle Scholar
Kaw, P.K. & Sen, A. 1998 Low frequency modes in strongly coupled dusty plasmas. Phys. Plasmas 5 (10), 3552–3559.10.1063/1.873073CrossRefGoogle Scholar
Kong, G., Mirsandi, H., Buist, K.A., Peters, E.A.J.F., Baltussen, M.W. & Kuipers, J.A.M 2019 Hydrodynamic interaction of bubbles rising side-by-side in viscous liquids. Exp. Fluids 60 (10), 155.10.1007/s00348-019-2798-yCrossRefGoogle Scholar
Kumar, K., Bandyopadhyay, P., Singh, S., Dharodi, V.S. & Sen, A. 2023 Kelvin–Helmholtz instability in a compressible dust fluid flow. Sci. Rep. 13 (1), 3979.10.1038/s41598-023-30992-3CrossRefGoogle Scholar
Leong, F.Y. & Le, D.-V. 2020 Droplet dynamics on viscoelastic soft substrate: toward coalescence control. Phys. Fluids 32 (6), 062102.10.1063/5.0011151CrossRefGoogle Scholar
Melzer, A., Nunomura, S., Samsonov, D., Ma, Z.W. & Goree, J. 2000 Laser-excited mach cones in a dusty plasma crystal. Phys. Rev. E 62 (3), 4162.10.1103/PhysRevE.62.4162CrossRefGoogle Scholar
Merlino, R.L. & Goree, J.A. 2004 Dusty plasmas in the laboratory, industry, and space. Phys. Today 57 (7), 32–38.10.1063/1.1784300CrossRefGoogle Scholar
Moghtadernejad, S., Lee, C. & Jadidi, M. 2020 An introduction of droplet impact dynamics to engineering students. Fluids 5 (3), 107.10.3390/fluids5030107CrossRefGoogle Scholar
Mokhtarzadeh-Dehghan, M.R. & El-Shirbini, A.A. 1985 Dynamics of two-phase bubble-droplets in immiscible liquids. Wärme-und Stoffübertragung 19 (1), 53–59.10.1007/BF01682547CrossRefGoogle Scholar
Ning, W., Lai, J., Kruszelnicki, J., Foster, J.E., Dai, D. & Kushner, M.J. 2021 Propagation of positive discharges in an air bubble having an embedded water droplet. Plasma Sources Sci. Technol. 30 (1), 015005.10.1088/1361-6595/abc830CrossRefGoogle Scholar
Nunomura, S., Samsonov, D. & Goree, J. 2000 Transverse waves in a two-dimensional screened-coulomb crystal (dusty plasma). Phys. Rev. Lett. 84 (22), 5141.10.1103/PhysRevLett.84.5141CrossRefGoogle Scholar
Oinuma, G., Nayak, G., Du, Y. & Bruggeman, P.J. 2020 Controlled plasma–droplet interactions: a quantitative study of oh transfer in plasma–liquid interaction. Plasma Sources Sci. Technol. 29 (9), 095002.10.1088/1361-6595/aba988CrossRefGoogle Scholar
Ou, W., Brochard, F. & Morgan, T.W. 2021 Bubble formation in liquid Sn under different plasma loading conditions leading to droplet ejection. Nucl. Fusion 61 (6), 066030.10.1088/1741-4326/abf9e0CrossRefGoogle Scholar
Peeters, F.M. & Wu, X. 1987 Wigner crystal of a screened-coulomb-interaction colloidal system in two dimensions. Phys. Rev. A 35 (7), 3109.10.1103/PhysRevA.35.3109CrossRefGoogle ScholarPubMed
Pramanik, J., Prasad, G., Sen, A. & Kaw, P.K. 2002 Experimental observations of transverse shear waves in strongly coupled dusty plasmas. Phys. Rev. Lett. 88 (17), 175001.10.1103/PhysRevLett.88.175001CrossRefGoogle ScholarPubMed
Ramkorun, B., Chandrasekhar, G., Rangari, V., Thakur, S.C., Comes, R.B. & Thomas, E. Jr. 2024 a Comparing growth of titania and carbonaceous dusty nanoparticles in weakly magnetised capacitively coupled plasmas. Plasma Sources Sci. Technol. arXiv:2402.00951.10.1088/1361-6595/ad8ae8CrossRefGoogle Scholar
Ramkorun, B., Jain, S., Taba, A., Mahjouri-Samani, M., Miller, M.E., Thakur, S.C., Thomas, E. & Comes, R.B. 2024 b Introducing dusty plasma particle growth of nanospherical titanium dioxide. Appl. Phys. Lett. 124 (14).10.1063/5.0186797CrossRefGoogle Scholar
Schmidt, P., Zwicknagel, G., Reinhard, P.-G. & Toepffer, C. 1997 Longitudinal and transversal collective modes in strongly correlated plasmas. Phys. Rev. E 56 (6), 7310.10.1103/PhysRevE.56.7310CrossRefGoogle Scholar
Schwabe, M., Rubin-Zuzic, M., Zhdanov, S., Ivlev, A.V., Thomas, H.M. & Morfill, G.E. 2009 Formation of bubbles, blobs, and surface cusps in complex plasmas. Phys. Rev. Lett. 102 (25), 255005.10.1103/PhysRevLett.102.255005CrossRefGoogle ScholarPubMed
Shew, W.L. & Pinton, J.-F. 2006 Viscoelastic effects on the dynamics of a rising bubble. J. Stat. Mech. 2006 (01), P01009.10.1088/1742-5468/2006/01/P01009CrossRefGoogle Scholar
Shukla, P.K. & Mamun, A.A. 2015 Introduction to Dusty Plasma Physics. CRC.10.1201/9781420034103CrossRefGoogle Scholar
Stenzel, R.L. & Urrutia, J.M. 2012 a Oscillating plasma bubbles. I. Basic properties and instabilities. Phys. Plasmas 19 (8).10.1063/1.4743019CrossRefGoogle Scholar
Stenzel, R.L. & Urrutia, J.M. 2012 b Oscillating plasma bubbles. II. Pulsed experiments. Phys. Plasmas 19 (8).10.1063/1.4743020CrossRefGoogle Scholar
Stenzel, R.L. & Urrutia, J.M. 2012 c Oscillating plasma bubbles. III. Internal electron sources and sinks. Phys. Plasmas 19 (8).10.1063/1.4743021CrossRefGoogle Scholar
Stenzel, R.L. & Urrutia, J.M. 2012 d Oscillating plasma bubbles. IV. Grid, gradients and geometry. Phys. Plasmas 19, 082108.CrossRefGoogle Scholar
Swarztrauber, P., Sweet, R. & Adams, J.C. 1999 FISHPACK: Efficient FORTRAN Subprograms for the Solution of Elliptic Partial Differential Equations. UCAR Publication.Google Scholar
Tabor, R.F., Wu, C., Lockie, H., Manica, R., Chan, D.Y.C., Grieser, F. & Dagastine, R.R. 2011 Homo-and hetero-interactions between air bubbles and oil droplets measured by atomic force microscopy. Soft Matt. 7 (19), 8977–8983.10.1039/c1sm06006fCrossRefGoogle Scholar
Tachibana, K., Takekata, Y., Mizumoto, Y., Motomura, H. & Jinno, M. 2011 Analysis of a pulsed discharge within single bubbles in water under synchronized conditions. Plasma Sources Sci. Technol. 20 (3), 034005.10.1088/0963-0252/20/3/034005CrossRefGoogle Scholar
Teng, L.-W., Tsai, C.-Y., Tseng, Y.-P. & Lin, I. 2008 Micro dynamics of pulsed laser induced bubbles in dusty plasma liquids. In AIP Conference Proceedings, vol. 1041, pp. 333–334. American Institute of Physics.10.1063/1.2997259CrossRefGoogle Scholar
Tiwari, S., Dharodi, V., Das, A., Kaw, P. & Sen, A. 2014 a Kelvin–Helmholtz instability in dusty plasma medium: fluid and particle approach. J. Plasma Phys. 80 (6), 817–823.10.1017/S0022377814000397CrossRefGoogle Scholar
Tiwari, S.K., Dharodi, V.S., Das, A., Patel, B.G. & Kaw, P. 2014 b Evolution of sheared flow structure in visco-elastic fluids. In AIP Conference Proceedings, vol. 1582, pp. 55–65. American Institute of Physics.10.1063/1.4865345CrossRefGoogle Scholar
Tiwari, S.K., Dharodi, V.S., Das, A., Patel, B.G. & Kaw, P. 2015 Turbulence in strongly coupled dusty plasmas using generalized hydrodynamic description. Phys. Plasmas 22 (2).10.1063/1.4913581CrossRefGoogle Scholar
Vladimirov, S.V., Shevchenko, P.V. & Cramer, N.F. 1997 Vibrational modes in the dust-plasma crystal. Phys. Rev. E 56 (1), R74.10.1103/PhysRevE.56.R74CrossRefGoogle Scholar
Wang, B., Wang, J., Yu, C., Luo, S., Peng, J., Li, N., Wang, T., Jiang, L., Dong, Z. & Wang, Y. 2023 Sustained agricultural spraying: from leaf wettability to dynamic droplet impact behavior. Global Challenges 7 (9), 2300007.10.1002/gch2.202300007CrossRefGoogle ScholarPubMed
Wang, G.J., Shi, J.K., Reinisch, B.W., Wang, X. & Wang, Z. 2015 Ionospheric plasma bubbles observed concurrently by multi-instruments over low-latitude station hainan. J. Geophys. Res.: Space Phys. 120 (3), 2288–2298.10.1002/2014JA020245CrossRefGoogle Scholar
Wang, X., Bhattacharjee, A. & Hu, S. 2001 Longitudinal and transverse waves in yukawa crystals. Phys. Rev. Lett. 86 (12), 2569.10.1103/PhysRevLett.86.2569CrossRefGoogle ScholarPubMed
Zhang, J., Chen, L. & Ni, M.-J. 2019 Vortex interactions between a pair of bubbles rising side by side in ordinary viscous liquids. Phys. Rev. Fluids 4 (4), 043604.10.1103/PhysRevFluids.4.043604CrossRefGoogle Scholar
Zhao, L., Boufadel, M.C., King, T., Robinson, B., Gao, F., Socolofsky, S.A. & Lee, K. 2017 Droplet and bubble formation of combined oil and gas releases in subsea blowouts. Mar. Pollut. Bull. 120 (1–2), 203–216.10.1016/j.marpolbul.2017.05.010CrossRefGoogle ScholarPubMed
Zhu, X., Sui, P.C. & Djilali, N. 2008 Three-dimensional numerical simulations of water droplet dynamics in a PEMFC gas channel. J. Power Sources 181 (1), 101–115.10.1016/j.jpowsour.2008.03.005CrossRefGoogle Scholar