A review of fluid instabilities and control strategies with applications in microgravity

J. Porter^1, 2 ; P. Salgado Sánchez^1, 2 ; V. Shevtsova^3, 4 ; V. Yasnou³

¹ E-USOC, Center for Computational Simulation, Universidad Politécnica de Madrid, Campus de Montegancedo, Boadilla del Monte, 28660 Madrid, Spain.
² Escuela Técnica Superior de Ingeniería Aeronáutica y del Espacio, Universidad Politécnica de Madrid, Plaza Cardenal Cisneros 3, 28040 Madrid, Spain.
³ Microgravity Research Centre, CP-165/62, Université libre de Bruxelles (ULB), av. F. D. Roosevelt, 50, 1050 Brussels, Belgium.
⁴ Mechanical and Manufacturing Department, Mondragon Goi Eskola Politeknikoa (MGEP), Loramendi 4, Apdo. 23, 20500 Mondragon, Spain.

Mathematical modelling of natural phenomena, Tome 16 (2021), article no. 24.

Résumé

We give a brief review of several prominent fluid instabilities representing transitions driven by gravity, surface tension, thermal energy, and applied motion/acceleration. Strategies for controlling these instabilities, including their pattern formation properties, are discussed. The importance of gravity for many common fluid instabilities is emphasized and used to understand the sometimes dramatically different behavior of fluids in microgravity environments. This is illustrated in greater detail, using recent results, for the case of the frozen wave instability, which leads to large columnar structures in the absence of gravity. The development of these highly nonlinear states is often complex, but can be manipulated through an appropriate choice of forcing amplitude, container length and height, initial inclination of the surface, and other parameters affecting the nonlinear and inhomogeneous growth process. The increased opportunity for controlling fluids and their instabilities via small forcing or parameter changes in microgravity is noted.

Détail

DOI : 10.1051/mmnp/2021020

Bibliographie

[1] G. Ahlers, F.F. Araujo, D. Funfschilling, S. Grossmann, D. Lohse Non-Oberbeck-Boussinesq Effects in Gaseous Rayleigh-Bénard Convection Phys. Rev. Lett 2007 054501

[2] A.V. Anilkumar, R.N. Grugel, X.F. Shen, C.P. Lee, T.G. Wang Control of thermocapillary convection in a liquid bridge by vibration J. Appl. Phys 1993 4165 4170

[3] H. Arbell, J. Fineberg Pattern formation in two-frequency forced parametric waves Phys. Rev. E 2002 036224

[4] P. Ashwin, A. Zaikin Pattern selection: the importance of “how you get there” Biophys. J 2015 1307 1308

[5] H. Ayanle, A.J. Bernoff, S. Lichter. Spanwise modal competition in cross-waves Physica D 1990 87 104

[6] T. Azami, S. Nakamura, T. Hibiya Effect of oxygen on thermocapillary convection in a molten silicon column under microgravity J. Electrochem. Soc 2001 G185

[7] L. Bárcena, J. Shiomi, G. Amberg. Control of oscillatory thermocapillary convection with local heating J. Cryst. Growth 2006 502 511

[8] B.J.S. Barnard, W.G. Pritchard Cross-waves. Part 2. Experiments. J. Fluid Mech. 1972 245 255

[9] O.A. Basaran, H. Gao, P.P. Bhat. Nonstandard inkjets Annu. Rev. Fluid Mech 2013 85 113

[10] J.M. Becker, J.W. Miles. Standing radial cross-waves J. Fluid Mech 1991 471 499

[11] G. Beintema, A. Corbetta, L. Biferale, F. Toschi. Controlling Rayleigh-Bénard convection via reinforcement learning J. Turbul 2020 1 21

[12] R. Bellman, R.H. Pennington Effects of surface tension and viscosity on Taylor instability Quart. Appl. Math 1954 151 162

[13] H. Bénard Les tourbillons cellulaires dans une nappe liquide Rev. Gén. Sciences Pure Appl. 1900 1261 1271

[14] T.B. Benjamin, F. Ursell. The stability of a plane free surface of a liquid in vertical periodic motion Proc. Roy. Soc. Lond. A 1954 505 515

[15] J. Berg, A. Acrivos. The effect of surface active agents on convection cells induced by surface tension Chem. Eng. Sci 1965 737 745

[16] K. Beyer, I. Gawriljuk, M. Günther, I. Lukovsky, A. Timokha. Compressible potential flows with free boundaries. Part I: Vibrocapillary equilibria. Z. Angew. Math. Mech. 2001 261 271

[17] K. Beyer, M. Günther, A. Timokha Variational and finite element analysis of vibroequilibria Comput. Methods Appl. Math 2004 290 323

[18] D. Beysens Vibrations in space as an artificial gravity? Europhysics News 2006 22 25

[19] N.K. Bezdenezhnykh, V.A. Briskman, D.V. Lyubimov, A.A. Cherepanov, M.T. Sharov. Control of stability of a fluid interface by means of vibrations, electric and magnetic fields Third All-Union Seminar on Hydromechanics and Heat and Mass Transfer in Zero Gravity, Abstracts of Papers (in Russian) 1984 18 20

[20] T. Bickel Effect of surface-active contaminants on radial thermocapillary flows Eur. Phys. J. E 2019 131

[21] E. Bodenschatz, W. Pesch, G. Ahlers Recent developments in Rayleigh-Bénard convection Annu. Rev. Fluid Mech 2000 709 778

[22] J.C. Brice, Crystal growth. Blackie and Son (1986).

[23] A. Burkert, D.N.C. Lin Thermal instability and the formation of clumpy gas clouds Astrophys. J 2000 270 282

[24] V. Bychkov, M. Modestov, V. Akkerman, L.-E. Eriksson The Rayleigh-Taylor instability in inertial fusion, astrophysical plasma and flames Plasma Phys. Controlled Fusion 2007 B513 B520

[25] R.V. Cakmur, D.A. Egolf, B.B. Plapp, E. Bodenschatz. Bistability and competition of spatiotemporal chaotic and fixed point attractors in Rayleigh–Bénard convection Phys. Rev. Lett 1997 1853 1856

[26] J.R. Carpenter, E.W. Tedford, M. Rahmani, G.A. Lawrence Holmboe wave fields in simulation and experiment J. Fluid Mech 2010 205 223

[27] J.K. Castelino, D.J. Ratliff, A.M. Rucklidge, P. Subramanian, C.M. Topaz. Spatiotemporal chaos and quasipatterns in coupled reaction-diffusion systems Physica D 2020 132475

[28] Y.-J. Chen, R. Abbaschian, P.H. Steen. Thermocapillary suppression of the Plateau–Rayleigh instability: a model for long encapsulated liquid zones J. Fluid Mech 2003 97 113

[29] C.-H. Chun, W. Wuest Experiments on the transition from the steady to the oscillatory Marangoni-convection of a floating zone under reduced gravity effect Acta Astronaut 1979 1073 1082

[30] I. Cisse, G. Bardan, A. Mojtabi Rayleigh Bénard convective instability of a fluid under high-frequency vibration Int. J. Heat Mass Transf 2004 4101 4112

[31] S.H. Davis. The stability of time-periodic flows Annu. Rev. Fluid Mech 1976 57 74

[32] Y. Ding, P. Umbanhowar Enhanced Faraday pattern stability with three-frequency driving Phys. Rev. E 2006 046305

[33] S. Douady Experimental study of the Faraday instability J. Fluid Mech 1990 383 409

[34] P. Drazin, Dynamical Meteorology | Kelvin–Helmholtz Instability, In G.R. North, J. Pyle and F. Zhang, editors, Encyclopedia of Atmospheric Sciences. Academic Press, Oxford, second edition (2015) 343–346.

[35] R. Dressler, N. Sivakumaran. Non-contaminating method to reduce Marangoni convection in microgravity float zones J. Cryst. Growth 1988 148 158

[36] T. Driessen, P. Sleutel, J. Dijksman, R. Jeurissen, D. Lohse. Control of jet breakup by a superposition of two Rayleigh–Plateau-unstable modes J. Fluid Mech 2014 275 296

[37] V. Duclaux, C. Clanet, D. Quéré The effects of gravity on the capillary instability in tubes J. Fluid Mech 2006 217 226

[38] W.S. Edwards, S. Fauve. Parametrically excited quasicrystalline surface waves Phys. Rev. E 1993 R788 R791

[39] W.S. Edwards, S. Fauve Patterns and quasi-patterns in the Faraday experiment J. Fluid Mech 1994 123 148

[40] J.M. Ezquerro, A. Bello, P. Salgado Sanchez, A. Laveron-Simavilla, V. Lapuerta The Thermocapillary Effects in Phase Change Materials in Microgravity experiment: Design, preparation and execution of a parabolic flight experiment Acta Astronaut 2019 185 196

[41] J.M. Ezquerro, P. Salgado Sanchez, A. Bello, J. Rodriguez, V. Lapuerta, A. Laveron-Simavilla Experimental evidence of thermocapillarity in phase change materials in microgravity: measuring the effect of Marangoni convection in solid/liquid phase transitions Int. Commun. Heat Mass Transf 2020 104529

[42] O. Faltinsen and A. Timokha. Sloshing. Cambridge Univ. Press (2009).

[43] M. Faraday On a peculiar class of acoustical figures Phil. Trans. R. Soc. Lond 1831 299 340

[44] J. Fernandez, P. Salgado Sánchez, I. Tinao, J. Porter, J.M. Ezquerro The CFVib experiment: control of fluids in microgravity with vibrations Microgravity Sci. Technol 2017 351 364

[45] J. Fernández, I. Tinao, J. Porter, A. Laverón-Simavilla Instabilities of vibroequilibria in rectangular containers Phys. Fluids 2017 024108

[46] G.B. Field Thermal instability Astrophys. J 1965 531 567

[47] J. Fröhlich, P. Laure, R. Peyret Large departures from Boussinesq approximation in the Rayleigh–Bénard problem Phys. Fluids A 1992 1355 1372

[48] T. Funada, D.D. Joseph Viscous potential flow analysis of Kelvin–Helmholtz instability in a channel J. Fluid Mech 2001 263 283

[49] G. Gandikota, D. Chatain, S. Amiroudine, T. Lyubimova, D. Beysens Frozen-wave instability in near-critical hydrogen subjected to horizontal vibration under various gravity fields Phys. Rev. E 2014 012309

[50] R.F. Ganiev, V.D. Lakiza, A.S. Tsapenko Dynamic behavior of the free liquid surface subject to vibrations under conditions of near-zero gravity Sov. Appl. Mech 1977 499 503

[51] Y. Gaponenko, A. Mialdun, V. Shevtsova Pattern selection in miscible liquids under periodic excitation in microgravity: Effect of interface width Phys. Fluids 2018 062103

[52] Y. Gaponenko, V. Yasnou, A. Mialdun, A. Nepomnyashchy, V. Shevtsova Hydrothermal waves in a liquid bridge subjected to a gas stream along the interface J. Fluid Mech 2021 A34

[53] Y.A. Gaponenko, M.M. Torregrosa, V. Yasnou, A. Mialdun, V. Shevtsova Interfacial pattern selection in miscible liquids under vibration Soft Matter 2015 8221 8224

[54] Y. Garrabos, D. Beysens, C. Lecoutre, A. Dejoan, V. Polezhaev, V. Emelianov Thermoconvectional phenomena induced by vibrations in supercritical SF6 under weightlessness Phys. Rev. E 2007 056317

[55] C.J.R. Garrett On Cross-waves. J. Fluid Mech 1970 837 849

[56] I. Gavrilyuk, I. Lukovsky, A. Timokha Two-dimensional variational vibroequilibria and Faraday’sdrops Z. Angew. Math. Phys 2004 1015 1033

[57] A. Gelfgat, P. Bar-Yoseph, A. Solan Effect of axial magnetic field on three-dimensional instability of natural convection in a vertical Bridgman growth configuration J. Cryst. Growth 2001 63 72

[58] G.Z. Gershuni, E.M. Zhukhovitskii Free thermal convection in a vibrational field under conditions of weightlessness Sov. Phys. Dokl 1979 894 896

[59] A.V. Getling, Rayleigh-Bénard convection, World Scientific (1998).

[60] D. Gligor, P. Salgado Sánchez, J. Porter, V. Shevtsova Influence of gravity on the frozen wave instability in immiscible liquids Phys. Rev. Fluids 2020 084001

[61] P.M. Gresho, R.L. Sani The effects of gravity modulation on the stability of a heated fluid layer J. Fluid Mech 1970 783 806

[62] S. Haefner, M. Benzaquen, O. Bäumchen, T. Salez, R. Peters, J.D. Mcgraw, K. Jacobs, E. Raphaël, K. Dalnoki-Veress Influence of slip on the Plateau–Rayleigh instability on a fibre Nat. Commun 2015 7409

[63] T. Havelock LIX. Forced surface-waves on water Phil. Mag 1929 569 576

[64] M. Haynes, E. Vega, M. Herrada, E. Benilov, J. Montanero Stabilization of axisymmetric liquid bridges through vibration-induced pressure fields J. Colloid Interface Sci 2018 409 417

[65] H. Helmholtz On discontinuous movements of fluids Philos. Mag 1868 337 346

[66] J. Holmboe On the behavior of symmetric waves in stratified shear layers Geofys. Publ 1962 67 113

[67] L.E. Howle Active control of Rayleigh–Bénard convection Phys. Fluids 1997 1861 1863

[68] I. Mutabazi, J. E. Wesfreid and E. Guyon, editors, Dynamics of spatio-temporal cellular structures. Vol. 207 of Springer Tracts in Modern Physics, Springer-Verlag, New York (2006).

[69] S.V. Jalikop, A. Juel Steep capillary-gravity waves in oscillatory shear-driven flows J. Fluid Mech 2009 131 150

[70] D.L. Jassby Evolution and Large-Electric-Field Suppression of the Transverse Kelvin–Helmholtz Instability Phys. Rev. Lett 1970 1567 1570

[71] A.F. Jones The generation of cross-waves in a long deep channel by parametric resonance J. Fluid Mech 1984 53 74

[72] B.L. Jones, P.H. Heins, E.C. Kerrigan, J.F. Morrison, A.S. Sharma Modelling for robust feedback control of fluid flows J. Fluid Mech 2015 687 722

[73] R. Jurado, J. Pallarés, J. Gavaldà, X. Ruiz Effect of reboosting manoeuvres on the determination of the Soret coefficients of DCMIX ternary systems Int. J. Therm. Sci 2019 205 219

[74] M. Jurisch, W. Löser Analysis of periodic non-rotational W striations in Mo single crystals due to nonsteady thermocapillary convection J. Cryst. Growth 1990 214 222

[75] P.L. Kapitza Dynamic stability of a pendulum when its point of suspension vibrates Soviet Phys. JETP 1951 588 597

[76] R.E. Kelly Stabilization of Rayleigh–Bénard convection by means of a slow nonplanar oscillatory flow Phys. Fluids A 1992 647 648

[77] L. Kelvin, Mathematical and physical papers, IV, hydrodynamics and general dynamics. Cambridge Univ. Press (1910).

[78] A. Khait, L. Shemer. Nonlinear wave generation by a wavemaker in deep to intermediate water depth Ocean Eng 2019 222 234

[79] A. Kidess, S. Kenjereš, C.R. Kleijn The influence of surfactants on thermocapillary flow instabilities in low Prandtl melting pools Phys. Fluids 2016 062106

[80] T.S. Krasnopolskaya, G.J.F.V. Heijst Wave pattern formation in a fluid annulus with a radially vibrating inner cylinder J. FluidMech 1996 229 252

[81] M. Kudo, Y. Akiyama, S. Takei, K. Motegi, I. Ueno Effect of ambient air flow on thermocapillary convection in a full-zone liquid bridge Interfacial Phenom. Heat Transf 2015 231 242

[82] A. Kudrolli, J.P. Gollub Patterns and spatio-temporal chaos in parametrically forced surface waves: a systematic survey at large aspect ratio Physica D 1996 133 154

[83] A. Kudrolli, B. Pier, J.P. Gollub Superlattice patterns in surface waves Physica D 1998 99 111

[84] K. Kumar Linear theory of Faraday instability in viscous liquids Proc. R. Soc. A 1996 1113 1126

[85] K. Kumar, L.S. Tuckerman Parametric instability of the interface between two fluids J. Fluid Mech 1994 49 68

[86] L.D. Landau and E.M. Lifshitz, Fluid mechanics. Vol. 6 of Course of Theoretical Physics. Pergamon Books Ltd., second edition, (1987).

[87] M. Lappa. Review: Possible strategies for the control and stabilization of Marangoni flow in laterally heated floating zones Fluid Dyn. Mater. Process 2005 171 188

[88] J. Lindl Development of the indirect-drive approach to inertial confinement fusion and the target physics basis for ignition and gain Phys. Plasmas 1995 3933 4024

[89] B.J. Lowry, P.H. Steen Capillary surfaces: stability from families of equilibria with application to the liquid bridge Proc. R. Soc. A 1995 411 439

[90] B.J. Lowry, P.H. Steen Flow-influenced stabilization of liquid columns J. Colloid Interface Sci 1995 38 43

[91] D. Lyubimov, T. Lyubimova, A. Croell, P. Dold, K. Benz, B. Roux Vibration-induced convective flows Microgravity Sci. Technol 1998 101 106

[92] D. Lyubimov, T. Lyubimova, B. Roux Mechanisms of vibrational control of heat transfer in a liquid bridge Int. J. Heat Mass Transf 1997 4031 4042

[93] D.V. Lyubimov, A.A. Cherepanov Development of a steady relief at the interface of fluids in a vibrational field Fluid Dyn. Res 1986 849 854

[94] D.V. Lyubimov, A.A. Cherepanov, T.P. Lyubimova, B. Roux Deformation of gas or drop inclusion in high frequency vibrational field Microgravity Q 1996 69 73

[95] D.V. Lyubimov, A.A. Cherepanov, T.P. Lyubimova, B. Roux Interface orienting by vibration C. R. Acad. Sci. Paris, Ser. IIb 1997 391 396

[96] D.V. Lyubimov, A.O. Ivantsov, T.P. Lyubimova, G.L. Khilko Numerical modeling of frozen wave instability in fluids with high viscosity contrast Fluid Dyn. Res 2016 061415

[97] D.V. Lyubimov, T.P. Lyubimova, A.A. Cherepanov Dynamics of Interfaces in Vibrational Fields Fizmatlit 2003

[98] T. Lyubimova, A. Ivantsov, Y. Garrabos, C. Lecoutre, D. Beysens Faraday waves on band pattern under zero gravity conditions Phys. Rev. Fluids 2019 064001

[99] T. Lyubimova, A. Ivantsov, Y. Garrabos, C. Lecoutre, G. Gandikota, D. Beysens Band instability in near-critical fluids subjected to vibrationunder weightlessness Phys. Rev. E 2017 013105

[100] T.P. Lyubimova, R.V. Scuridin, A. Cröll, P. Dold Influence of high frequency vibrations on fluid flow and heat transfer in a floating zone Crys. Res. Technol 2003 635 653

[101] S. Madruga, C. Mendoza Heat transfer performance and melting dynamic of a phase change material subjected to thermocapillary effects Int. J. Heat Mass Transf 2017 501 510

[102] A. Manela, I. Frankel On the Rayleigh–Bénard problem: dominant compressibility effects J. Fluid Mech 2006 461 475

[103] C. Marangoni, Sull’espansione delle goccie d’un liquido galleggianti sulla superfice di altro liquido, Fratelli Fusi, (1865).

[104] M.J. Marr-Lyon, D.B. Thiessen, P.L. Marston Stabilization of a cylindrical capillary Rayleigh–Plateau limit using acoustic radiation pressure and active feedback J. Fluid Mech 1997 345 357

[105] G. Martin, S. Hoath, I. Hutchings Inkjet printing – The physics of manipulating liquid jets and drops J. Phys. Conf. Ser 2008 012001

[106] A. Mialdun, I.I. Ryzhkov, D.E. Melnikov, V. Shevtsova Experimental evidence of thermal vibrational convection in a nonuniformly heated fluid in a reduced gravity environment Phys. Rev. Lett 2008 084501

[107] A.B. Mikishev, A.A. Nepomnyashchy Large-scale Marangoni convection in a liquid layer with insoluble surfactant under heat flux modulation J. Adhes. Sci. Technol 2011 1411 1423

[108] J. Miles, D. Henderson. Parametrically forced surface waves Annu. Rev. Fluid Mech 1990 143 165

[109] A.I. Mizev, D. Schwabe Convective instabilities in liquid layers with free upper surface under the action of an inclined temperature gradient Phys. Fluids 2009 112102

[110] J. Moehlis, J. Porter, E. Knobloch Heteroclinic dynamics in a model of Faraday waves in a square container Physica D 2009 846 859

[111] F. Moisy, G.-J. Michon, M. Rabaud, E. Sultan Cross-waves induced by the vertical oscillation of a fully immersed vertical plate Phys. Fluids 2012 022110

[112] F. Muldoon Numerical study of hydrothermal wave suppression in thermocapillary flow using a predictive control method Comput. Math. Math. Phys 2018 493 507

[113] S. Paolucci, D.R. Chenoweth Departures from the Boussinesq approximation in laminar Bénard convection Phys. Fluids 1987 1561 1564

[114] H.M. Park, M.C. Sung, J.S. Chung Stabilization of Rayleigh-Bénard convection by means of mode reduction Proc. R. Soc. A 2004 1807 1830

[115] M. Pastoor, L. Henning, B.R. Noack, R. King, G. Tadmor Feedback shear layer control for bluff body drag reduction J. Fluid Mech 2008 161 196

[116] J.R.A. Pearson On convection cells induced by surface tension J. Fluid Mech 1958 489 500

[117] J.M. Perez-Gracia, J. Porter, F. Varas, J.M. Vega Oblique cross-waves in horizontally vibrated containers Fluid Dyn. Res 2014 041410

[118] J.M. Perez-Gracia, J. Porter, F. Varas, J.M. Vega Subharmonic capillary-gravity waves in large containers subject to horizontal vibrations J. Fluid Mech 2014 196 228

[119] C.-T. Pham, S. Perrard, G. Le Doudic Surface waves along liquid cylinders. Part 1. Stabilising effect of gravity on the Plateau–Rayleigh instability. J. Fluid Mech. 2020 A8

[120] J.A.F. Plateau, Statique experimentale et theorique des liquides soumis aux seules forces moleculaires. 2 (1873). Gauthier-Villars.

[121] J. Porter, I. Tinao, A. Laverón-Simavilla, C.A. Lopez. Pattern selection in a horizontally vibrated container Fluid Dyn. Res 2012 065501

[122] J. Porter, I. Tinao, A. Laverón-Simavilla, J. Rodríguez Onset patterns in a simple model of localized parametric forcing Phys. Rev. E 2013 042913

[123] J. Porter, C.M. Topaz, M. Silber Pattern control via multifrequency parametric forcing Phys. Rev. Lett 2004 034502

[124] O. Pouliquen, J.M. Chomaz, P. Huerre Propagating Holmboe waves at the interface between two immiscible fluids J. Fluid Mech 1994 277 302

[125] D.S. Praturi, S.S. Girimaji Mechanisms of canonical Kelvin–Helmholtz instability suppression in magnetohydrodynamic flows Phys. Fluids 2019 024108

[126] F. Preisser, D. Schwabe, A. Scharmann Steady and oscillatory thermocapillary convection in liquid columns with free cylindrical surface J. Fluid Mech 1983 545 567

[127] B. Protas, T. Sakajo Harnessing the Kelvin–Helmholtz instability: feedback stabilization of an inviscid vortex sheet J. Fluid Mech 2018 146 177

[128] Lord Rayleigh Investigation of the character of the equilibrium of an incompressible heavy fluid of variable density Proc. London Math. Soc 1882 170 177

[129] Lord Rayleigh On convection currents in a horizontal layer of fluid, when the higher temperature is on the under side Phil. Mag., Ser.6 1916 529 546

[130] On the instability of cylindrical fluid surfaces London, Edinburgh Dublin Philos. Mag. J. Sci. 1892 177 180

[131] A.M. Rucklidge, M. Silber, A.C. Skeldon Three-wave interactions and spatiotemporal chaos Phys. Rev. Lett 2012 074504

[132] P. Salgado Sánchez, J. Fernández, I. Tinao, J. Porter Vibroequilibria in microgravity: Comparison of experiments and theory Phys. Rev. E 2019 063103

[133] P. Salgado Sánchez, Y. Gaponenko, V. Yasnou, A. Mialdun, J. Porter, V. Shevtsova Effect of initial interface orientation on patterns produced by vibrational forcing in microgravity J. Fluid Mech 2020 A38

[134] P. Salgado Sánchez, Y.A. Gaponenko, J. Porter, V. Shevtsova Finite-size effects on pattern selection in immiscible fluids subjected to horizontal vibrations in weightlessness Phys. Rev. E 2019 042803

[135] P. Salgado Sánchez, J. Porter, I. Tinao, A. Laverón-Simavilla Dynamics of weakly coupled parametrically forced oscillators Phys. Rev. E 2016 022216

[136] P. Salgado Sánchez, V. Yasnou, Y. Gaponenko, A. Mialdun, J. Porter, V. Shevtsova Interfacial phenomena in immiscible liquids subjected to vibrations in microgravity J. Fluid Mech 2019 850 883

[137] P. Salgado Sánchez, J.M. Ezquerro, J. Fernández, J. Rodriguez Thermocapillary effects during the melting of phase change materials in microgravity: Heat transport enhancement Int. J. Heat Mass Transf 2020 120478

[138] P. Salgado Sánchez, J.M. Ezquerro, J. Fernández, J. Rodríguez Thermocapillary effects during the melting of phase-change materials in microgravity: steady and oscillatory flow regimes J. Fluid Mech 2021 A20

[139] P. Salgado Sánchez, J.M. Ezquerro, J. Porter, J. Fernández, I. Tinao Effect of thermocapillary convection on the melting of phase change materials in microgravity: Experiments and simulations Int. J. Heat Mass Transf 2020 119717

[140] A.E. Samoilova, A. Nepomnyashchy Nonlinear feedback control of Marangoni wave patterns in a thin film heated from below Physica D 2020 132627

[141] R. Sattler, S. Gier, J. Eggers, C. Wagner The final stages of capillary break-up of polymer solutions Phys. Fluids 2012 023101

[142] H.A. Schäffer Second-order wavemaker theory for irregular waves Ocean Eng 1996 47 88

[143] D. Schwabe Thermocapillary liquid bridges and Marangoni convection under microgravity–Results and lessons learned Microgravity Sci. Technol 2014 1 10

[144] D. Schwabe, A. Scharmann Some evidence for the existence and magnitude of a critical Marangoni number for the onset of oscillatory flow in crystal growth melts J. Cryst. Growth 1979 125 131

[145] D. Sharp An overview of Rayleigh–Taylor instability Physica D 1984 3 18

[146] M. Sheldrake, R. Sheldrake Determinants of Faraday wave-patterns in water samples oscillated vertically at a range of frequencies from 50-200 Hz Water 2017 1 27

[147] V. Shevtsova, Y. Gaponenko, H. Kuhlmann, M. Lappa, M. Lukasser, S. Matsumoto, A. Mialdun, J. Montanero, K. Nishino, I. Ueno The JEREMI-project on thermocapillary convection in liquid bridges. Part B: Overview on impact of co-axial gas flow Fluid Dyn. Mater. Process. 2014 197 240

[148] V. Shevtsova, Y. Gaponenko, A. Nepomnyashchy Thermocapillary flow regimes and instability caused by a gas stream along the interface J. Fluid Mech 2013 644 670

[149] V. Shevtsova, Y.A. Gaponenko, V. Yasnou, A. Mialdun, A. Nepomnyashchy Two-scale wave patterns on a periodically excited miscible liquid–liquid interface J. Fluid Mech 2016 409 422

[150] V. Shevtsova, I.I. Ryzhkov, D.E. Melnikov, Y.A. Gaponenko, A. Mialdun Experimental and theoretical study of vibration-induced thermal convection in low gravity J. Fluid Mech 2010 53 82

[151] J. Shiomi, M. Kudo, I. Ueno, H. Kawamura, G. Amberg Feedback control of oscillatory thermocapillary convection in a half-zone liquid bridge J. Fluid Mech 2003 193 211

[152] F. Simonelli, J.P. Gollub Surface wave mode interactions: Effects of symmetry and degeneracy J. Fluid Mech 1989 349 354

[153] W.A. Sirignano, I. Glassman Flame spreading above liquid fuels: Surface tension driven flows Combust. Sci. Technol 1970 307

[154] A.C. Skeldon, J. Porter Scaling properties of weakly nonlinear coefficients in the Faraday problem Phys. Rev. E 2011 016209

[155] L.A. Slobozhanin, J.M. Perales Stability of liquid bridges between equal disks in an axial gravity field Phys. Fluids A 1993 1305 1314

[156] W.D. Smyth, G.P. Klaassen, W.R. Peltier Finite amplitude holmboe waves Geophys. Astrophys. Fluid Dyn 1988 181 222

[157] W.D. Smyth, W.R. Peltier Instability and transition in finite-amplitude Kelvin–Helmholtz and Holmboe waves J. Fluid Mech 1991 387 415

[158] J.W. Strutt VI. On the capillary phenomena of jets. Proc. R. Soc. London 1879 71 97

[159] R.S. Subramanian and R. Balasubramanian, The Motion of Bubbles and Drops in Reduced Gravity. Cambridge University Press, Cambridge (2001).

[160] A. Swaminathan, S. Garrett, M. Poese, R. Smith Dynamic stabilization of the Rayleigh-Bénard instability by acceleration modulation J. Acoust. Soc. Am 2018 2334 2343

[161] S. Taneda Visual observations of the flow around a half-submerged oscillating circular cylinder Fluid Dyn. Res 1994 119 151

[162] G.I. Taylor The instability of liquid surfaces when accelerated in a direction perpendicular to their planes. I Proc. R. Soc. A 1950 192 196

[163] U. Thiele, J.M. Vega, E. Knobloch Long-wave Marangoni instability with vibration J. Fluid Mech 2006 61 87

[164] S.A. Thorpe Experiments on the instability of stratified shear flows: miscible fluids J. Fluid Mech 1971 299 319

[165] I. Tinao, J. Porter, A. Laverón-Simavilla, J. Fernández Cross-waves excited by distributed forcing in the gravity-capillary regime Phys. Fluids 2014 024111

[166] C.M. Topaz, J. Porter, M. Silber Multifrequency control of Faraday wave patterns Phys. Rev. E 2004 066206

[167] C.M. Topaz, M. Silber Resonances and superlattice pattern stabilization in two-frequency forced Faraday waves Physica D 2002 1 29

[168] M. Troitiño, P. Salgado Sánchez, J. Porter, D. Gligor Symmetry breaking in large columnar frozen wave patterns in weightlessness Microgravity Sci. Technol 2020 907 919

[169] A.M. Turing The chemical basis of morphogenesis Phil. Trans. R. Soc. Lond. B 1952 37 72

[170] L. Turyn The damped Mathieu equation Q. Appl. Math 1993 389 398

[171] W.B. Underhill, S. Lichter, A.J. Bernoff Modulated, frequency-locked and chaotic cross-waves J. Fluid Mech 1991 371 394

[172] F. Varas, J.M. Vega Modulated surface waves in large-aspect-ratio horizontally vibrated containers J. Fluid Mech 2007 271 304

[173] J.T. Waddell, C.E. Niederhaus, J.W. Jacobs Experimental study of Rayleigh–Taylor instability: Low Atwood number liquid systems with single-mode initial perturbations Phys. Fluids 2001 1263 1273

[174] J. Walker, L.M. Witkowski, B. Houchens Effects of a rotating magnetic field on the thermocapillary instability in the floating zone process J. Cryst. Growth 2003 413 423

[175] G.H. Wolf The dynamic stabilization of the Rayleigh-Taylor instability and the corresponding dynamic equilibrium Z. Physik 1969 291 300

[176] G.H. Wolf Dynamic stabilization of the interchange instability of a liquid-gas interface Phys. Rev. Lett 1970 444 446

[177] V. Yasnou, Y. Gaponenko, A. Mialdun, V. Shevtsova Influence of a coaxial gas flow on the evolution of oscillatory states in a liquid bridge Int. J. Heat Mass Transf 2018 747 759

[178] S. Zen’Kovskaya, V. Novosyadlyi, A. Shleikel’ The effect of vertical vibration on the onset of thermocapillary convection in a horizontal liquid layer J. Appl. Math. Mech 2007 247 257

[179] W. Zhang, J. Viñals Pattern formation in weakly damped parametric surface waves J. Fluid Mech 1997 301 330