1932

Abstract

Rigid or deformable bodies moving through continuously stratified layers or across sharp interfaces are involved in a wide variety of geophysical and engineering applications, with both miscible and immiscible fluids. In most cases, the body moves while pulling a column of fluid, in which density and possibly viscosity differ from those of the neighboring fluid. The presence of this column usually increases the fluid resistance to the relative body motion, frequently slowing down its settling or rise in a dramatic manner. This column also exhibits specific dynamics that depend on the nature of the fluids and on the various physical parameters of the system, especially the strength of the density/viscosity stratification and the relative magnitude of inertia and viscous effects. In the miscible case, as stratification increases, the wake becomes dominated by the presence of a downstream jet, which may undergo a specific instability. In immiscible fluids, the viscosity contrast combined with capillary effects may lead to strikingly different evolutions of the column, including pinch-off followed by the formation of a drop that remains attached to the body, or a massive fragmentation phenomenon. This review discusses the flow organization and its consequences on the body motion under a wide range of conditions, as well as potentialities and limitations of available models aimed at predicting the body and column dynamics.

Loading

Article metrics loading...

/content/journals/10.1146/annurev-fluid-010719-060139
2020-01-05
2024-06-15
Loading full text...

Full text loading...

/deliver/fulltext/fluid/52/1/annurev-fluid-010719-060139.html?itemId=/content/journals/10.1146/annurev-fluid-010719-060139&mimeType=html&fmt=ahah

Literature Cited

  1. Abaid N, Adalsteinsson D, Agyapong A, McLaughlin RM 2004. An internal splash: levitation of falling spheres in stratified fluids. Phys. Fluids 16:1567–80
    [Google Scholar]
  2. Alldredge AL, Cowles TJ, MacIntyre S, Rines JEB, Donaghay PL et al. 2002. Occurrence and mechanisms of formation of a dramatic thin layer of marine snow in a shallow Pacific fjord. Mar. Ecol. Prog. Ser. 233:1–12
    [Google Scholar]
  3. Ardekani AM, Doostmohammadi A, Desai N 2017. Transport of particles, drops, and small organisms in density stratified fluids. Phys. Rev. Fluids 2:100503
    [Google Scholar]
  4. Ardekani AM, Stocker R 2010. Stratlets: low Reynolds number point-force solutions in a stratified fluid. Phys. Rev. Lett. 105:084502
    [Google Scholar]
  5. Aristoff JM, Bush JWM 2009. Water entry of small hydrophobic spheres. J. Fluid Mech. 619:45–78
    [Google Scholar]
  6. Aristoff JM, Truscott TT, Techet AH, Bush JWM 2010. The water entry of decelerating spheres. Phys. Fluids 22:032102
    [Google Scholar]
  7. Batchelor GK 1967. An Introduction to Fluid Dynamics Cambridge, UK: Cambridge Univ. Press
    [Google Scholar]
  8. Bayareh M, Doostmohammadi A, Dabiri S, Ardekani AM 2013. On the rising motion of a drop in stratified fluids. Phys. Fluids 25:103302
    [Google Scholar]
  9. Bearon RN, Grünbaum D 2006. Bioconvection in a stratified environment: experiments and theory. Phys. Fluids 18:127102
    [Google Scholar]
  10. Bearon RN, Grünbaum D, Cattolico RA 2006. Effects of salinity structure on swimming behavior and harmful algal bloom formation in Heterosigma akashiwo, a toxic raphidophyte. Mar. Ecol. Prog. Ser. 306:153–63
    [Google Scholar]
  11. Benjamin TB 1986. Note on added mass and drift. J. Fluid Mech. 169:251–56
    [Google Scholar]
  12. Blanchette F 2013. Mixing and convection driven by particles settling in temperature-stratified ambients. Int. J. Heat Mass Transf. 56:732–40
    [Google Scholar]
  13. Blanchette F, Bush JWM 2005. Particle concentration evolution and sedimentation-induced instabilities in a stably stratified environment. Phys. Fluids 17:073302
    [Google Scholar]
  14. Blanchette F, Shapiro AM 2012. Drops settling in sharp stratification with and without Marangoni effects. Phys. Fluids 24:042104
    [Google Scholar]
  15. Bonhomme R, Magnaudet J, Duval F, Piar B 2012. Inertial dynamics of air bubbles crossing a horizontal fluid–fluid interface. J. Fluid Mech. 707:405–43
    [Google Scholar]
  16. Bush JWM, Thurber BA, Blanchette F 2003. Particle clouds in homogeneous and stratified environments. J. Fluid Mech. 489:29–54
    [Google Scholar]
  17. Camassa R, Falcon C, Lin J, McLaughlin RM, Mykins N 2010. A first-principle predictive theory for a sphere falling through sharply stratified fluid at low Reynolds number. J. Fluid Mech. 664:436–65
    [Google Scholar]
  18. Camassa R, Falcon C, Lin J, McLaughlin RM, Parker R 2009. Prolonged residence times for particles settling through stratified miscible fluids in the Stokes regime. Phys. Fluids 21:031702
    [Google Scholar]
  19. Camassa R, Khatri S, McLaughlin RM, Prairie JC, White BL, Yu S 2013. Retention and entrainment effects: experiments and theory for porous spheres settling in sharply stratified fluids. Phys. Fluids 25:081701
    [Google Scholar]
  20. Camassa R, McLaughlin RM, Moore MNJ, Vaidya A 2008. Brachistochrones in potential flow and the connection to Darwin's theorem. Phys. Lett. A 372:6742–49
    [Google Scholar]
  21. Candelier F, Mehaddi R, Vauquelin O 2014. The history force on a small particle in a linearly stratified fluid. J. Fluid Mech. 749:184–200
    [Google Scholar]
  22. Castrejón-Pita AA, Castrejón-Pita JR, Hutchings IM 2012. Breakup of liquid filaments. Phys. Rev. Lett. 108:074506
    [Google Scholar]
  23. Chemel C, Burns P 2015. Pollutant dispersion in a developing valley cold-air pool. Bound.-Layer Meteor. 154:391–408
    [Google Scholar]
  24. Chen H, Xu Q, Liang S, Li J 2018. Film coating on a small sphere crossing an oil-water interface. Phys. Rev. Fluids 3:124003
    [Google Scholar]
  25. Chi BK, Leal LG 1989. A theoretical study of the motion of a viscous drop toward a fluid interface at low Reynolds number. J. Fluid Mech. 201:123–46
    [Google Scholar]
  26. Chisholm NG, Khair AS 2017. Drift volume in viscous flows. Phys. Rev. Fluids 2:064101
    [Google Scholar]
  27. Condie SA, Bormans M 1997. The influence of density stratification on particle settling, dispersion and population growth. J. Theor. Biol. 187:65–75
    [Google Scholar]
  28. Cooray H, Cicuta P, Vella D 2017. Floating and sinking of a pair of spheres at a liquid–fluid interface. Langmuir 33:1427–36
    [Google Scholar]
  29. Dabiri JO 2005. On the estimation of swimming and flying forces from wake measurements. J. Theor. Biol. 208:3519–32
    [Google Scholar]
  30. Dabiri JO 2006. Note on the induced Lagrangian drift and added-mass of a vortex. J. Fluid Mech. 557:105–13
    [Google Scholar]
  31. Darwin C 1953. Note on hydrodynamics. Math. Proc. Camb. Philos. Soc. 49:342–54
    [Google Scholar]
  32. D'Asaro EA 2003. Performance of autonomous Lagrangian floats. J. Atmos. Ocean. Technol. 20:896–911
    [Google Scholar]
  33. Davies RM, Taylor GI 1950. The mechanics of large bubbles rising through extended liquids and through liquids in tubes. Proc. R. Soc. Lond. A 200:375–90
    [Google Scholar]
  34. De Folter JWJ, De Villeneuve VWA, Aarts DGAL, Lekkerkerker NHW 2010. Rigid sphere transport through a colloidal gas–liquid interface. New J. Phys. 12:023013
    [Google Scholar]
  35. Debrégeas G, De Gennes PG, Brochard-Wyart F 1998. The life and death of ‘bare’ viscous bubbles. Science 279:1704–7
    [Google Scholar]
  36. Denman KL, Gargett AE 1995. Biological-physical interactions in the upper ocean: the role of vertical and small scale transport processes. Annu. Rev. Fluid Mech. 27:225–55
    [Google Scholar]
  37. Díaz-Damacillo L, Ruiz-Angulo A, Zenit R 2016. Drift by air bubbles crossing an interface of a stratified medium at moderate Reynolds number. Int. J. Multiphase Flow 85:258–66
    [Google Scholar]
  38. Dietrich DE, Bowman MJ, Korotenko KA, Bowman MH 2014.Oil Spill Risk Management: Modeling Gulf of Mexico Circulation and Oil Dispersal. Hoboken, NJ: Wiley
  39. Dietrich N, Poncin S, Li HZ 2011. Dynamical deformation of a flat liquid–liquid interface. Exp. Fluids 50:1293–303
    [Google Scholar]
  40. Dietrich N, Poncin S, Pheulpin S, Li HZ 2008. Passage of a bubble through a liquid-liquid interface. AIChE J. 54:594–600
    [Google Scholar]
  41. Doostmohammadi A, Ardekani AM 2014. Reorientation of elongated particles at density interfaces. Phys. Rev. E 90:033013
    [Google Scholar]
  42. Doostmohammadi A, Dabiri S, Ardekani AM 2014. A numerical study of the dynamics of a particle settling at moderate Reynolds numbers in a linearly stratified fluid. J. Fluid Mech. 570:5–32
    [Google Scholar]
  43. Doostmohammadi A, Stocker R, Ardekani AM 2012. Low-Reynolds-number swimming at pycnoclines. PNAS 109:3856–61
    [Google Scholar]
  44. Duclaux V, Caillé F, Duez C, Ybert C, Bocquet L, Clanet C 2007. Dynamics of transient cavities. J. Fluid Mech. 591:1–19
    [Google Scholar]
  45. Eames I 2003. The concept of drift and its application to multiphase and multibody problems. Philos. Trans. R. Soc. Lond. A 361:2951–65
    [Google Scholar]
  46. Eames I, Belcher SE, Hunt JCR 1994. Drift, partial drift and Darwin's proposition. J. Fluid Mech. 275:201–23
    [Google Scholar]
  47. Eames I, Gobby D, Dalziel SB 2003. Fluid displacement by Stokes flow past a spherical droplet. J. Fluid Mech. 485:67–85
    [Google Scholar]
  48. Eames I, Hunt JCR 1997. Inviscid flow around bodies moving in weak density gradients without buoyancy effects. J. Fluid Mech. 353:331–55
    [Google Scholar]
  49. Eggers J, Dupont TF 1994. Drop formation in a one-dimensional approximation of the Navier–Stokes equation. J. Fluid Mech. 262:205–21
    [Google Scholar]
  50. Emery TS, Raghupathi PA, Kandlikar SG 2018. Flow regimes and transition criteria during passage of bubbles through a liquid–liquid interface. Langmuir 34:6766–76
    [Google Scholar]
  51. Ern P, Risso F, Fabre D, Magnaudet J 2012. Wake-induced oscillatory paths of bodies freely rising or falling in fluids. Annu. Rev. Fluid Mech. 44:97–121
    [Google Scholar]
  52. Fabre D, Tchoufag J, Magnaudet J 2012. The steady oblique path of buoyancy-driven disks and spheres. J. Fluid Mech. 707:24–36
    [Google Scholar]
  53. Feng J, Muradoglu M, Kim H, Ault JT, Stone HA 2016. Dynamics of a bubble bouncing at a liquid/liquid/gas interface. J. Fluid Mech. 807:324–52
    [Google Scholar]
  54. Geller AS, Lee SH, Leal LG 1986. The creeping motion of a spherical particle normal to a deformable interface. J. Fluid Mech. 169:27–69
    [Google Scholar]
  55. Greene GA, Chen JC, Conlin MT 1988. Onset of entrainment between immiscible liquid layers due to rising gas bubbles. Int. J. Heat Mass Transf. 31:1309–17
    [Google Scholar]
  56. Han Z, Holappa L 2008. Mechanisms of iron entrainment into slag due to rising gas. ISIJ Int. 43:292–97
    [Google Scholar]
  57. Hanazaki H 2015. Numerical simulation of jets generated by a sphere moving vertically in a stratified fluid. J. Fluid Mech. 765:424–51
    [Google Scholar]
  58. Hanazaki H, Kashimoto K, Okamura T 2009a. Jets generated by a sphere moving vertically in a stratified fluid. J. Fluid Mech. 638:173–97
    [Google Scholar]
  59. Hanazaki H, Konishi K, Okamura T 2009b. Schmidt-number effects on the flow past a sphere moving vertically in a stratified diffusive fluid. Phys. Fluids 21:026602
    [Google Scholar]
  60. Hartland S 1968. The approach of a rigid sphere to a deformable liquid/liquid interface. J. Colloid Interface Sci. 26:383–94
    [Google Scholar]
  61. Hartland S 1969. The profile of the draining film between a rigid sphere and a deformable fluid-liquid interface. J. Colloid Interface Sci. 69:987–95
    [Google Scholar]
  62. Hashimoto H, Kawano S 1990. A study on encapsulated liquid drop formation in liquid–liquid–gas systems: fundamental mechanism of encapsulated drop formation. JSME Int. J. II 33:729–35
    [Google Scholar]
  63. Higginson RC, Dalziel SB, Linden PF 2003. The drag on a vertically moving grid of bars in a linearly stratified fluid. Exp. Fluids 34:678–86
    [Google Scholar]
  64. Hinze JO 1955. Fundamentals of the hydrodynamic mechanism of splitting in dispersion processes. AIChE J. 1:289–95
    [Google Scholar]
  65. Hokenson GJ 1986. Vorticity with variable viscosity. AIAA J. 24:1039–40
    [Google Scholar]
  66. Huh C, Scriven LE 1969. Shapes of axisymmetric fluid interfaces of unbounded extent. J. Colloid Interface Sci. 30:323–37
    [Google Scholar]
  67. Jacquemain D ed 2015. Nuclear Power Reactor Core Melt Accidents Les Ulis, Fr.: EDP Sci.
    [Google Scholar]
  68. Jarvis PA, Mader HM, Huppert HE, Cashman KV, Blundy JD 2019. Experiments on the low-Reynolds-number settling of a sphere through a fluid interface. Phys. Rev. Fluids 4:024003
    [Google Scholar]
  69. Johnson RE 1981. Stokes flow past a sphere coated with a thin fluid film. J. Fluid Mech. 110:217–38
    [Google Scholar]
  70. Jones AF, Wilson SDR 1978. The film drainage problem in droplet coalescence. J. Fluid Mech. 87:263–88
    [Google Scholar]
  71. Kawano S, Hashimoto H, Ihara A, Shin K 1996. Sequential production of mm-sized spherical shells in liquid-liquid gas systems. J. Fluids Eng. 118:614–18
    [Google Scholar]
  72. Keller JB 1998. Surface tension force on a partly submerged body. Phys. Fluids 10:3009–10
    [Google Scholar]
  73. Kindler K, Khalili A, Stocker R 2010. Diffusion-limited retention of porous particles at density interfaces. PNAS 107:22163–68
    [Google Scholar]
  74. King JA, Shair FH, Reible DD 1987. The influence of atmospheric stability on pollutant transport by slope winds. Atmos. Environ. 21:53–59
    [Google Scholar]
  75. Kobayashi S 1993. lron droplet formation due to bubbles passing through molten iron/slag interface. ISIJ Int. 33:577–82
    [Google Scholar]
  76. Kolmogorov AN 1949. On the disintegration of drops in a turbulent flow. Dokl. Akad. Nauk. SSSR 66:825–28
    [Google Scholar]
  77. Kumagai I, Davaille A, Kurita K 2007. On the fate of thermally buoyant mantle plumes at density interfaces. Earth Planet. Sci. Lett. 254:180–93
    [Google Scholar]
  78. Lam T, Vincent L, Kanso E 2018. Passive flight in density-stratified fluids. J. Fluid Mech. 860:200–23
    [Google Scholar]
  79. Landau LD, Lifshitz EM 1987. Fluid Mechanics Oxford: Pergamon. 2nd ed.
    [Google Scholar]
  80. Lande R, Wood AM 1987. Suspension times of particles in the upper ocean. Deep-Sea Res. 34:61–72
    [Google Scholar]
  81. Larsen LH 1969. Oscillations of a neutrally buoyant sphere in a stratified fluid. . Deep-Sea Res. 16587–603
  82. Lawrence CJ, Mei R 1995. Long-time behavior of the drag on a body in impulsive motion. J. Fluid Mech. 283:307–27
    [Google Scholar]
  83. Lee DG, Kim HY 2008. Impact of a superhydrophobic sphere onto water. Langmuir 24:142–45
    [Google Scholar]
  84. Lee DG, Kim HY 2011. Sinking of small sphere at low Reynolds number through interface. Phys. Fluids 23:072104
    [Google Scholar]
  85. Levich VG, Krylov VS 1969. Surface-tension-driven phenomena. Annu. Rev. Fluid Mech. 1:293–316
    [Google Scholar]
  86. Lovalenti PM, Brady JF 1993. The hydrodynamic force on a rigid particle undergoing arbitrary time-dependent motion at small Reynolds number. J. Fluid Mech. 256:561–605
    [Google Scholar]
  87. MacIntyre S, Alldredge AL, Gotschalk CC 1995. Accumulation of marine snow at density discontinuities in the water column. Limnol. Oceanogr. 40:449–68
    [Google Scholar]
  88. Manga M, Stone HA 1995. Low-Reynolds-number motion of bubbles, drops and rigid spheres through fluid–fluid interfaces. J. Fluid Mech. 287:279–98
    [Google Scholar]
  89. Manga M, Stone HA, O'Connell RL 1993. The interaction of plume heads with compositional discontinuities in the Earth's mantle. J. Geophys. Res. 98:19979–90
    [Google Scholar]
  90. Mansfield EH, Sepangui HR, Eastwood EA 1997. Equilibrium and mutual attraction or repulsion of objects supported by surface tension. Philos. Trans. R. Soc. A 355:869–919
    [Google Scholar]
  91. Marmottant P, Villermaux E 2004. On spray formation. J. Fluid Mech. 498:73–111
    [Google Scholar]
  92. Martin DW, Blanchette F 2017. Simulations of surfactant-laden drops rising in a density-stratified medium. Phys. Rev. Fluids 2:023602
    [Google Scholar]
  93. Maru HC, Wasan DT, Kintner RC 1971. Behavior of a rigid sphere at a liquid–liquid interface. Chem. Eng. Sci. 26:1615–28
    [Google Scholar]
  94. Mehaddi R, Candelier F, Mehling B 2018. Inertial drag on a sphere settling in a stratified fluid. J. Fluid Mech. 855:1074–87
    [Google Scholar]
  95. Mercier MJ, Wang S, Péméja J, Ern P, Ardekani AM 2019. Settling disks in a linearly stratified fluid. J. Fluid Mech In press
    [Google Scholar]
  96. Mohamed-Kassim Z, Longmire EK 2004. Drop coalescence through a liquid/liquid interface. Phys. Fluids 16:2170–81
    [Google Scholar]
  97. Mowbray DE, Rarity BSH 1967. The internal wave pattern produced by a sphere moving vertically in a density stratified liquid. J. Fluid Mech. 30:489–95
    [Google Scholar]
  98. Mrokowska MM 2018. Stratification-induced reorientation of disk settling through ambient density transition. Sci. Rep. 8:412
    [Google Scholar]
  99. Noh Y 2000. Sedimentation of a particle cloud across a density interface. Fluid Dyn. Res. 27:129–42
    [Google Scholar]
  100. Notz PK, Basaran OA 2004. Dynamics and breakup of a contracting liquid filament. J. Fluid Mech. 512:223–56
    [Google Scholar]
  101. O'Brien SBG 1996. The meniscus near a small sphere and its relationship to line pinning of contact lines. J. Colloid Interface Sci. 183:51–56
    [Google Scholar]
  102. Okino S, Akiyama S, Hanazaki H 2017. Velocity distribution around a sphere descending in a linearly stratified fluid. J. Fluid Mech. 826:759–80
    [Google Scholar]
  103. Panah M, Blanchette F, Khatri S 2017. Simulations of a porous particle settling in a density-stratified ambient fluid. Phys. Rev. Fluids 2114303
    [Google Scholar]
  104. Peters IR, Madonia M, Lohse D, Van Der Meer D 2016. Volume entrained in the wake of a disc intruding into an oil-water interface. Phys. Rev. Fluids 1:033901
    [Google Scholar]
  105. Pierson JL, Magnaudet J 2018a. Inertial settling of a sphere through an interface. Part 1. From sphere flotation to wake fragmentation. J. Fluid Mech. 835:762–807
    [Google Scholar]
  106. Pierson JL, Magnaudet J 2018b. Inertial settling of a sphere through an interface. Part 2. Sphere and tail dynamics. J. Fluid Mech. 835:808–51
    [Google Scholar]
  107. Pigeonneau F, Sellier A 2011. Low-Reynolds number gravity-driven migration and deformation of bubbles near a free surface. Phys. Fluids 23:092102
    [Google Scholar]
  108. Pitois O, Moucheront P, Weill C 1999. Interface breakthrough and sphere coating. C. R. Acad. Sci. Ser. IIB 327:605–11
    [Google Scholar]
  109. Poggi O, Minto R, Davenport WG 1969. Mechanisms of metal entrapment in slags. JOM 21:40–45
    [Google Scholar]
  110. Powers TR, Zhang D, Goldstein RE, Stone HA 1998. Propagation of a topological transition: the Rayleigh instability. Phys. Fluids 10:1052–57
    [Google Scholar]
  111. Prairie JC, Ziervogel K, Camassa R, McLaughlin RM, White BL et al 2015. Delayed settling of marine snow: effects of density gradient and particle properties and implications for carbon cycling. Mar. Chem. 175:28–38
    [Google Scholar]
  112. Rapacchietta AV, Neumann AW 1977. Force and free-energy analyses of small particles at fluid interfaces. Part II. Spheres. J. Colloid Interface Sci. 59:555–67
    [Google Scholar]
  113. Reiter G, Schwerdtfeger K 1992. Observation of physical phenomena occurring during passage of bubbles through liquid/liquid interfaces. ISIJ Int. 32:50–56
    [Google Scholar]
  114. Renggli CJ, Wiesmaier S, De Campos CP, Hess KU, Dingwell DB 2015. Magma mixing induced by particle settling. Contrib. Mineral. Petrol. 171:96
    [Google Scholar]
  115. Riebesell U 1992. The formation of large marine snow and its sustained residence in surface waters. Limnol. Oceeanogr. 37:63–67
    [Google Scholar]
  116. Rydberg J, Cox M, Musikas C, Choppin GR eds 2004. Solvent Extraction Principles and Practice New York: Marcel Dekker. 2nd ed.
    [Google Scholar]
  117. Scase MM, Dalziel SB 2004. Internal wave fields and drag generated by a translating body in a stratified fluid. J. Fluid Mech. 498:289–311
    [Google Scholar]
  118. Sehgal RB ed 2012. Nuclear Safety in Light Water Reactors Waltham, MA: Academic
    [Google Scholar]
  119. Shah ST, Wasan DT, Kintner RC 1972. Passage of a liquid drop through a liquid–liquid interface. Chem. Eng. Sci. 27:881–93
    [Google Scholar]
  120. Singh KK, Bart HJ 2015. Passage of a single bubble through a liquid–liquid interface. Ind. Eng. Chem. Res. 54:9478–93
    [Google Scholar]
  121. Singh KK, Gebauer F, Bart HJ 2017. Bouncing of a bubble at a liquid–liquid interface. AIChE J. 63:3150–57
    [Google Scholar]
  122. Sinha A, Mollah AK, Hardt S, Ganguly R 2013. Particle dynamics and separation at liquid–liquid interfaces. Soft Matter 9:5438–47
    [Google Scholar]
  123. Shopov PJ, Minev PD 1992. The unsteady motion of a bubble or drop towards a liquid-liquid interface. J. Fluid Mech. 235:123–41
    [Google Scholar]
  124. Shoukry E, Hafez M, Hartland S 1975. Separation of drops from wetted surfaces. J. Colloid Interface Sci. 53:261–70
    [Google Scholar]
  125. Smith PG, Van de Den TGM 1984. The effect of gravity on the drainage of a thin liquid film between a solid sphere and a liquid/fluid interface. J. Colloid Interface Sci. 100:456–64
    [Google Scholar]
  126. Smith PG, Van de Den TGM 1985. The separation of a liquid drop from a stationary solid sphere in a gravitational field. J. Colloid Interface Sci. 105:7–20
    [Google Scholar]
  127. Sparks SRJ, Sigurdsson H, Wilson L 1977. Magma mixing: a mechanism for triggering acid explosive eruptions. Nature 267:315–18
    [Google Scholar]
  128. Srdić-Mitrović AN, Mohamed NA, Fernando HJS 1999. Gravitational settling of particles through density interfaces. J. Fluid Mech. 381:175–98
    [Google Scholar]
  129. Steinberger B, O'Connell RJ 1998. Advection of plumes in mantle flow: implications for hotspot motion, mantle viscosity and plume distribution. Geophys. J. Int. 132:412–34
    [Google Scholar]
  130. Stone HA 1994. Dynamics of drop deformation and breakup in viscous fluids. Annu. Rev. Fluid Mech. 26:65–102
    [Google Scholar]
  131. Stone HA, Bentley BJ, Leal LG 1986. An experimental study of transient effects in the breakup of viscous drops. J. Fluid Mech. 173:131–58
    [Google Scholar]
  132. Stone HA, Leal LG 1989. Relaxation and breakup of an initially extended drop in an otherwise quiescent fluid. J. Fluid Mech. 198:399–427
    [Google Scholar]
  133. Tjahjadi M, Stone HA, Ottino JM 1992. Satellite and subsatellite formation in capillary breakup. J. Fluid Mech. 243:297–317
    [Google Scholar]
  134. Tomotika S 1935. On the instability of a cylindrical thread of a viscous liquid surrounded by another viscous fluid. Proc. R. Soc. Lond. A 150:322–37
    [Google Scholar]
  135. Torres CR, Hanazaki H, Ochoa J, Castillo J, Van Woert M 2000. Flow past a sphere moving vertically in a stratified diffusive fluid. J. Fluid Mech. 417:211–36
    [Google Scholar]
  136. Truscott TT, Epps BP, Belden J 2014. Water entry of projectiles. Annu. Rev. Fluid Mech. 46:355–78
    [Google Scholar]
  137. Tsai SS, Wexler JS, Wan J, Stone HA 2011. Conformal coating of particles in microchannels by magnetic forcing. Appl. Phys. Lett. 99:153509
    [Google Scholar]
  138. Uemura T, Ueda Y, Iguchi M 2010. Ripples on a rising bubble through an immiscible two-liquid interface generate numerous micro droplets. EPL 92:34004
    [Google Scholar]
  139. Vella D 2015. Floating versus sinking. Annu. Rev. Fluid Mech. 47:115–35
    [Google Scholar]
  140. Villermaux E 2007. Fragmentation. Annu. Rev. Fluid Mech. 39:419–46
    [Google Scholar]
  141. Wagner GL, Young WR, Lauga E 2014. Mixing by microorganisms in stratified fluids. J. Mar. Res. 72:47–72
    [Google Scholar]
  142. Warren FWG 1960. Wave resistance to vertical motion in a stratified fluid. J. Fluid Mech. 7:209–29
    [Google Scholar]
  143. Wegener PP, Parlange JY 1973. Spherical-cap bubbles. Annu. Rev. Fluid Mech. 5:79–100
    [Google Scholar]
  144. Widder EA, Johnsen S, Bernstein SA, Case JF, Neilson DJ 1999. Thin layers of bioluminescent copepods found at density discontinuities in the water column. Mar. Biol. 134:429–37
    [Google Scholar]
  145. Winant CD 1974. The descent of neutrally buoyant floats. Deep-Sea Res. 21445–53
    [Google Scholar]
  146. Yiantsios SG, Davis RH 1990. On the buoyancy-driven motion of a drop towards a rigid surface or a deformable interface. J. Fluid Mech. 217:547–73
    [Google Scholar]
  147. Yick KY, Torres CR, Peacock T, Stocker R 2009. Enhanced drag of a sphere settling in a stratified fluid at small Reynolds numbers. J. Fluid Mech. 632:49–68
    [Google Scholar]
  148. Zhang C, Churazov E, Schekochihin AA 2018. Generation of internal waves by buoyant bubbles in galaxy clusters and heating of intracluster medium. Mon. Not. R. Astron. Soc. 478:4785–98
    [Google Scholar]
  149. Zhang J, Mercier MJ, Magnaudet J 2019.Core mechanisms of drag enhancement on bodies settling in a stratified fluid. J. Fluid Mech. 875622–56
  150. Zvirin Y, Chadwick RS 1975. Settling of an axially symmetric body in a viscous stratified fluid. Int. J. Multiphase Flow 1:743–52
    [Google Scholar]
/content/journals/10.1146/annurev-fluid-010719-060139
Loading
/content/journals/10.1146/annurev-fluid-010719-060139
Loading

Data & Media loading...

  • Article Type: Review Article
This is a required field
Please enter a valid email address
Approval was a Success
Invalid data
An Error Occurred
Approval was partially successful, following selected items could not be processed due to error