Hostname: page-component-5c6d5d7d68-xq9c7 Total loading time: 0 Render date: 2024-08-20T11:17:06.451Z Has data issue: false hasContentIssue false
  • English
  • Français

On the influence of gravity on particle accumulation structures in high aspect-ratio liquid bridges

Published online by Cambridge University Press:  10 December 2020

Paolo Capobianchi Open the ORCID record for Paolo Capobianchi [Opens in a new window]  and
Marcello Lappa Open the ORCID record for Marcello Lappa [Opens in a new window]
Paolo Capobianchi*
Affiliation:
Department of Mechanical and Aerospace Engineering, University of Strathclyde, James Weir Building, 75 Montrose street, GlasgowG1 1XJ, UK
Marcello Lappa
Affiliation:
Department of Mechanical and Aerospace Engineering, University of Strathclyde, James Weir Building, 75 Montrose street, GlasgowG1 1XJ, UK
*
†Email address for correspondence: paolo.capobianchi@strath.ac.uk
Get access Rights & Permissions [Opens in a new window]

Abstract

This analysis focuses on the properties of the so-called particle accumulation structures (PAS) in non-cylindrical liquid bridges in normal gravity conditions. In this regard, it follows and integrates the line of inquiry started in Lappa (J. Fluid Mech., vol. 726, 2013, 160) where the main focus was on the effect of high-frequency vibrations. After the discovery (passed almost unnoticed) of a structure (Sasaki et al. Trans. Japan Soc. Mech. Engrs B, vol. 70, 2004) that seems to escape a simple classification on the basis of existing categorizations or paradigms for this type of phenomena, dedicated numerical simulations are carried out in the framework of an integrated Eulerian–Lagrangian approach. Conditions are considered corresponding to isodense and non-isodense particles in a liquid bridge with high aspect ratio, high Prandtl number fluid and hydrostatically deformed interface. Special attention is paid to the very elusive azimuthal wavenumber $m=1$, for which PAS seem to be possible only in a very restricted range of Marangoni numbers. Two distinct families of particle attractors are identified, which coexist in the space of parameters as multiple solutions. We show that the key ingredient needed to unravel the related basins of attraction is the effect of gravity on particles, which may therefore be regarded as an additional mechanism responsible for the formation of these structures in terrestrial liquid bridges.

JFM classification

Convection: Marangoni convection Interfacial Flows (free surface): Liquid bridges Multiphase and Particle-laden Flows: Particle/fluid flow
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 908 , 10 February 2021 , A29
Check for updates
Copyright
© The Author(s), 2020. 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.)

References

REFERENCES

Abe, Y., Ueno, I. & Kawamura, H. 2007 Effect of shape of HZ liquid bridge on particle accumulation structure (PAS). Microgravity Sci. Technol. 19 (3), 84–86.CrossRefGoogle Scholar
Akbar, M. K., Rahman, M. & Ghiaasiaan, S. M. 2009 Particle transport in a small square enclosure in laminar natural convection. J. Aerosol Sci. 40 (9), 747–761.CrossRefGoogle Scholar
Aksouh, M., Chemini, R., Mataoui, A. & Poncet, S. 2020 Buoyancy-driven instabilities and particle deposition in a Taylor–Couette apparatus. Intl Commun. Heat Mass Transfer 113, 104518.CrossRefGoogle Scholar
Babiano, A., Cartwright, J. H. E., Piro, O. & Provenzale, A. 2000 Dynamics of a small neutrally buoyant sphere in a fluid and targeting in hamiltonian systems. Phys. Rev. Lett. 84, 5764–5767.CrossRefGoogle Scholar
Balboa Usabiaga, F. & Delgado-Buscalioni, R. 2011 Particle Hydrodynamics: From Molecular to Colloidal Fluids. Springer Nature.Google Scholar
Bodnár, T., Galdi, G. P. & Nečasová, Š. 2017 Particles in Flows. Birkhäuser.CrossRefGoogle Scholar
Brenner, H. 1961 The slow motion of a sphere through a viscous fluid towards a plane surface. Chem. Engng Sci. 16 (3), 242–251.CrossRefGoogle Scholar
Capobianchi, P. & Lappa, M. 2020 Particle accumulation structures in non-cylindrical liquid bridges under microgravity, conditions (Article under review).CrossRefGoogle Scholar
Do-Quang, M. & Amberg, G. 2009 The splash of a solid sphere impacting on a liquid surface: numerical simulation of the influence of wetting. Phys. Fluids 21 (2), 022102.CrossRefGoogle Scholar
Ehsan, S., Abbasi, S, Ohringer, K. F. B & Parviz, B. A. 2006 Molten-alloy driven self-assembly for nano and micro scale system integration. Fluid Dyn. Mater. Process. 2 (4), 221–246.Google Scholar
Elghobashi, S. 1994 On predicting particle-laden turbulent flows. Appl. Sci. Res. 52, 309–329.CrossRefGoogle Scholar
Faxén, H. 1959 About T. Bohlin's paper: on the drag on rigid spheres, moving in a viscous liquid inside cylindrical tubes. Kolloidn. Z. 167 (2), 146–146.CrossRefGoogle Scholar
Gotoda, M., Melnikov, D. E., Ueno, I. & Shevtsova, V. 2016 Experimental study on dynamics of coherent structures formed by inertial solid particles in three-dimensional periodic flows. Chaos 26 (7), 073106.CrossRefGoogle Scholar
Gotoda, M., Sano, T., Kaneko, T. & Ueno, I. 2015 Evaluation of existence region and formation time of particle accumulation structure (PAS) in half-zone liquid bridge. Eur. Phys. J. 224 (2), 299–307.Google Scholar
Gotoda, M., Toyama, A., Ishimura, M., Sano, T., Suzuki, M., Kaneko, T. & Ueno, I. 2019 Experimental study of coherent structures of finite-size particles in thermocapillary liquid bridges. Phys. Rev. Fluids 4, 094301.CrossRefGoogle Scholar
Gresho, P. M. & Sani, R. L. 1987 On pressure boundary conditions for the incompressible Navier–Stokes equations. Intl J. Numer. Meth. Fluids 7 (10), 1111–1145.CrossRefGoogle Scholar
Happel, J. & Brenner, H. 1991 Low Reynolds Number Hydrodynamics: With Special Applications to Particulate Media. Kluwer Academic.Google Scholar
Hofmann, E. & Kuhlmann, H. C. 2011 Particle accumulation on periodic orbits by repeated free surface collisions. Phys. Fluids 23 (7), 072106.CrossRefGoogle Scholar
Issa, R. I. 1986 Solution of the implicitly discretised fluid flow equations by operator-splitting. J. Comput. Phys. 62 (1), 40–65.CrossRefGoogle Scholar
Kang, Q., Wu, D., Duan, L., Hu, L., Wang, J., Zhang, P. & Hu, W. 2019 The effects of geometry and heating rate on thermocapillary convection in the liquid bridge. J. Fluid Mech. 881, 951–982.CrossRefGoogle Scholar
Kuhlmann, H. C., Lappa, M., Melnikov, D., Mukin, R., Muldoon, F. H., Pushkin, D., Shevtsova, V. & Ueno, I. 2014 The Jeremi-project on thermocapillary convection in liquid bridges. Part A: Overview of particle accumulation structures. Fluid Dyn. Mater. Process. 10 (1), 1–10.Google Scholar
Lappa, M. 2004 Combined effect of volume and gravity on the three-dimensional flow instability in noncylindrical floating zones heated by an equatorial ring. Phys. Fluids 16 (2), 331–343.CrossRefGoogle Scholar
Lappa, M. 2009 Thermal Convection: Patterns, Evolution and Stability. John Wiley and Sons.CrossRefGoogle Scholar
Lappa, M. 2013 a Assessment of the role of axial vorticity in the formation of particle accumulation structures in supercritical Marangoni and hybrid thermocapillary-rotation-driven flows. Phys. Fluids 25 (1), 012101.CrossRefGoogle Scholar
Lappa, M. 2013 b On the existence and multiplicity of one-dimensional solid particle attractors in time-dependent Rayleigh–Bénard convection. Chaos 23 (1), 013105.CrossRefGoogle ScholarPubMed
Lappa, M. 2013 c On the variety of particle accumulation structures under the effect of g-jitters. J. Fluid Mech. 726, 160–195.CrossRefGoogle Scholar
Lappa, M. 2014 Stationary solid particle attractors in standing waves. Phys. Fluids 26 (1), 013305.CrossRefGoogle Scholar
Lappa, M. 2016 a Numerical study into the morphology and formation mechanisms of three-dimensional particle structures in vibrated cylindrical cavities with various heating conditions. Phys. Rev. Fluids 1, 064203.CrossRefGoogle Scholar
Lappa, M. 2016 b On the nature, formation and diversity of particulate coherent structures in microgravity conditions and their relevance to materials science and problems of astrophysical interest. Geophys. Astrophys. Fluid Dyn. 110 (4), 348–386.CrossRefGoogle Scholar
Lappa, M. 2018 On the transport, segregation, and dispersion of heavy and light particles interacting with rising thermal plumes. Phys. Fluids 30 (3), 033302.CrossRefGoogle Scholar
Lappa, M. 2019 On the formation and morphology of coherent particulate structures in non-isothermal enclosures subjected to rotating g-jitters. Phys. Fluids 31 (7), 073303.CrossRefGoogle Scholar
Lappa, M., Savino, R. & Monti, R. 2001 Three-dimensional numerical simulation of Marangoni instabilities in non-cylindrical liquid bridges in microgravity. Intl J. Heat Mass Transfer 44 (10), 1983–2003.CrossRefGoogle Scholar
Lashgari, I., Picano, F. & Brandt, L. 2015 Transition and self-sustained turbulence in dilute suspensions of finite-size particles. Theor. Appl. Mech. Lett. 5 (3), 121–125.CrossRefGoogle Scholar
Lyubimov, D. V., Lyubimova, T. P. & Straube, A. V. 2005 Accumulation of solid particles in convective flows. Microgravity Sci. Technol. 16, 210–214.CrossRefGoogle Scholar
Matas, J.-P., Morris, J. F. & Guazzelli, É. 2003 Transition to turbulence in particulate pipe flow. Phys. Rev. Lett. 90, 014501.CrossRefGoogle ScholarPubMed
Melnikov, D. E., Pushkin, D. O. & Shevtsova, D. M. 2011 Accumulation of particles in time-dependent thermocapillary flow in a liquid bridge. Modeling of experiments. Eur. Phys. J. 192, 29–39.Google Scholar
Melnikov, D. E., Pushkin, D. O. & Shevtsova, V. M. 2013 Synchronization of finite-size particles by a traveling wave in a cylindrical flow. Phys. Fluids 25 (9), 092108.CrossRefGoogle Scholar
Melnikov, D. E. & Shevtsova, V. 2017 Different types of lagrangian coherent structures formed by solid particles in three-dimensional time-periodic flows. Eur. Phys. J. 226 (6), 1239–1251.Google Scholar
Melnikov, D. E., Shevtsova, V. M. & Legros, J. C. 2004 Onset of temporal aperiodicity in high Prandtl number liquid bridge under terrestrial conditions. Phys. Fluids 16 (5), 1746–1757.CrossRefGoogle Scholar
Melnikov, D. E., Shevtsova, V. M. & Legros, J. C. 2005 Route to aperiodicity followed by high Prandtl-number liquid bridge. 1-g case. Acta Astronaut. 56 (6), 601–611.CrossRefGoogle Scholar
Mukin, R. V. & Kuhlmann, H. C. 2013 Topology of hydrothermal waves in liquid bridges and dissipative structures of transported particles. Phys. Rev. E 88, 053016.CrossRefGoogle ScholarPubMed
Muldoon, F. H. & Kuhlmann, H. C. 2013 Coherent particulate structures by boundary interaction of small particles in confined periodic flows. Physica D 253, 40–65.CrossRefGoogle Scholar
Niigaki, Y. & Ueno, I. 2012 Formation of particle accumulation structure (PAS) in half-zone liquid bridge under an effect of thermo-fluid flow of ambient gas. Trans. Japan. Soc. Aeronaut. Space Sci. 10, 33–37.Google Scholar
Nishino, K., Yano, T., Kawamura, H, Matsumoto, S., Ueno, I. & Ermakov, M. K. 2015 Instability of thermocapillary convection in long liquid bridges of high Prandtl number fluids in microgravity. J. Cryst. Growth 420, 57–63.CrossRefGoogle Scholar
Oba, T., Toyama, A., Hori, T. & Ueno, I. 2019 Experimental study on behaviors of low-stokes number particles in weakly chaotic structures induced by thermocapillary effect within a closed system with a free surface. Phys. Rev. Fluids 4, 104002.CrossRefGoogle Scholar
Puragliesi, R., Dehbi, A., Leriche, E., Soldati, A. & Deville, M. O. 2011 Dns of buoyancy-driven flows and lagrangian particle tracking in a square cavity at high rayleigh numbers. Intl J. Heat Fluid Flow 32 (5), 915–931.CrossRefGoogle Scholar
Pushkin, D. O., Melnikov, D. E. & Shevtsova, V. M. 2011 Ordering of small particles in one-dimensional coherent structures by time-periodic flows. Phys. Rev. Lett. 106, 234501.CrossRefGoogle ScholarPubMed
Rhie, C. M. & Chow, W. L. 1983 Numerical study of the turbulent flow past an airfoil with trailing edge separation. AIAA J. 21 (11), 1525–1532.CrossRefGoogle Scholar
Romanò, F. & Kuhlmann, H. C. 2018 Finite-size lagrangian coherent structures in thermocapillary liquid bridges. Phys. Rev. Fluids 3, 094302.CrossRefGoogle Scholar
Saghir, Z. & Abdulmajeed, M. 2017 Effectiveness in incorporating Brownian and thermophoresis effects in modelling convective flow of water-Al2O3 nanoparticles. Intl J. Numer. Meth. Heat Fluid Flow 28 (1), 47–63.CrossRefGoogle Scholar
Sapsis, T. & Haller, G. 2008 Instabilities in the dynamics of neutrally buoyant particles. Phys. Fluids 20 (1), 017102.CrossRefGoogle Scholar
Sasaki, Y., Tanaka, S. & Kawamura, H. 2004 Particle accumulation structure in thermocapillary convection of small liquid bridge. Trans. Japan Soc. Mech. Engrs B 70 (692), 831–838.Google Scholar
Schwabe, D., Hintz, P. & Frank, S. 1996 New features of thermocapillary convection in floating zones revealed by tracer particle accumulation structures (PAS). Microgravity Sci. Technol. 9, 163–168.Google Scholar
Schwabe, D. & Mizev, A. I. 2011 Particles of different density in thermocapillary liquid bridges under the action of travelling and standing hydrothermal waves. Eur. Phys. J. 192, 13–27.Google Scholar
Schwabe, D., Mizev, A. I., Udhayasankar, M. & Tanaka, S. 2007 Formation of dynamic particle accumulation structures in oscillatory thermocapillary flow in liquid bridges. Phys. Fluids 19 (7), 072102.CrossRefGoogle Scholar
Shevtsova, V., Mialdun, A., Kawamura, H., Ueno, I., Nishino, K. & Lappa, M. 2011 Onset of hydrothermal instability in liquid bridge. Experimental benchmark. Fluid Dyn. Mater. Process. 7 (1), 1–28.Google Scholar
Stocco, A. & Nobili, M. 2017 A comparison between liquid drops and solid particles in partial wetting. Adv. Colloid Interface Sci. 247, 223–233.CrossRefGoogle ScholarPubMed
Subbotin, S. V. & Kozlov, V. G. 2020 Effect of differential rotation of oscillating inner core on steady flow instability in a rotating sphere. Microgravity Sci. Technol. 32 (5), 825–836.CrossRefGoogle Scholar
Swartenbroux, F. & Schwabe, D. 1997 Temporal and spatial elements of thermocapillary convection in floating zones. Exp. Fluids 23, 234–251.Google Scholar
Szeri, A. J., Wiggins, S. & Leal, L. G. 1991 On the dynamics of suspended microstructure in unsteady, spatially inhomogeneous, two-dimensional fluid flows. J. Fluid Mech. 228, 207–241.Google Scholar
Tanaka, S., Kawamura, H., Ueno, I. & Schwabe, D. 2006 Flow structure and dynamic particle accumulation in thermocapillary convection in a liquid bridge. Phys. Fluids 18 (6), 067103.CrossRefGoogle Scholar
Toyama, A., Gotoda, M., Kaneko, T. & Ueno, I. 2017 Existence conditions and formation process of second type of spiral loop particle accumulation structure (SL-2 PAS) in half-zone liquid bridge. Microgravity Sci. Technol. 29 (4), 263–274.CrossRefGoogle Scholar
Ueno, I., Abe, Y., Noguchi, K. & Kawamura, H. 2008 Dynamic particle accumulation structure (PAS) in half-zone liquid bridge – reconstruction of particle motion by 3-D PTV. Adv. Space Res. 41 (12), 2145–2149.CrossRefGoogle Scholar
Ueno, I., Tanaka, S. & Kawamura, H. 2003 Oscillatory and chaotic thermocapillary convection in a half-zone liquid bridge. Phys. Fluids 15 (2), 408–416.CrossRefGoogle Scholar
Vassileva, N., Van den Ende, D., Mugele, F. & Mellema, J. 2005 Capillary forces between spherical particles floating at a liquid-liquid interface. Langmuir 21, 11190–200.CrossRefGoogle Scholar
Vilela, R. D., de Moura, A. P. S. & Grebogi, C. 2006 Finite-size effects on open chaotic advection. Phys. Rev. E 73, 026302.CrossRefGoogle ScholarPubMed
Vorobev, A & Khlebnikova, E. 2018 Modelling of the rise and absorption of a fluid inclusion. Intl J. Heat Mass Transfer 125, 801–814.CrossRefGoogle Scholar
Vorobev, A., Zagvozkin, T. & Lyubimova, T. 2020 Shapes of a rising miscible droplet. Phys. Fluids 32 (1), 012112.CrossRefGoogle Scholar
Wang, J., Wu, D., Duan, L. & Kang, Q. 2017 Ground experiment on the instability of buoyant-thermocapillary convection in large-scale liquid bridge with large Prandtl number. Intl J. Heat Mass Transfer 108, 2107–2119.CrossRefGoogle Scholar
Yamaguchi, K., Hori, T. & Ueno, I. 2019 Long-term behaviors of a single particle forming a coherent structure in thermocapillary- driven convection in half-zone liquid bridge of high Prandtl-number fluid. Intl J. Microgravity Sci. Appl. 36, 360203.Google Scholar