DOI: 10.1063/1.869799. Capillary breakup of a viscous thread surrounded by another viscous fluid

Capillary breakup of a viscous thread surrounded by another viscous fluid

10.1063/1.869799

Crossref journal-article

AIP Publishing

Physics of Fluids (317)

Abstract

Previous long-wavelength analyses of capillary breakup of a viscous fluid thread in a perfectly inviscid environment show that the asymptotic self-similar regime immediately prior to breakup is given by a balance between surface tension, inertia, and extensional viscous stresses in the thread. In contrast, it is shown here that if viscosity in the external fluid, however small, is included then the asymptotic balance is between surface tension and viscous stresses in the two fluids while inertia is negligible. Scaling estimates for this new balance suggest that both axial and radial scales decrease linearly with time to breakup, so that the aspect ratio remains O(1) with time but scales with viscosity ratio like (μint/μext)1/2 for μint≫μext, where μint and μext are the internal and external viscosities. Numerical solutions to the full Stokes equations for μint=μext confirm the scalings with time and give self-similar behavior near pinching. However, the self-similar pinching region is embedded in a logarithmically large axial advection driven by the increasing range of scales intermediate between that of the pinching region and that of the macroscopic drop. The interfacial shape in the intermediate region is conical with angles of about 6° on one side and 78° on the other.

Bibliography

Lister, J. R., & Stone, H. A. (1998). Capillary breakup of a viscous thread surrounded by another viscous fluid. Physics of Fluids, 10(11), 2758â2764.

Authors 2

John R. Lister (first)
Howard A. Stone (additional)

References 23 Referenced 265

10.1080/14786449208620301 / Philos. Mag. / On the stability of a cylinder of viscous fluid under a capillary force (1892)
10.1016/0169-5983(95)00028-3 / Fluid Dyn. Res. / On the separation of droplets from a liquid jet (1996)
10.1063/1.869435 / Phys. Fluids / On the pinch-off of a pendant drop of viscous fluid (1997)
10.1103/PhysRevLett.73.3391 / Phys. Rev. Lett. / Iterated instabilities during droplet fission (1994)
10.1147/rd.184.0364 / IBM J. Res. Dev. / Drop formation in a liquid jet (1974)
10.1146/annurev.fl.11.010179.001231 / Annu. Rev. Fluid Mech. / Drop formation in a circular liquid jet (1979)
10.1017/S0022112080002108 / J. Fluid Mech. / The nonlinear capillary instability of a liquid jet. Part 1. Theory (1980)
10.1017/S0022112092002738 / J. Fluid Mech. / Satellite and subsatellite formation in capillary breakup (1992)
{'key': '2024021014414069200_r9', 'first-page': '865', 'article-title': 'Nonlinear dynamics and breakup of free-surface flows', 'volume': '3', 'year': '1997', 'journal-title': 'Rev. Mod. Phys.'} / Rev. Mod. Phys. / Nonlinear dynamics and breakup of free-surface flows (1997)
{'key': '2024021014414069200_r10'}
10.1103/PhysRevLett.70.3043 / Phys. Rev. Lett. / Topology transitions and singularities in viscous flows (1993)
10.1002/(SICI)1097-0312(199807)51:7<733::AID-CPA2>3.0.CO;2-7 / Commun. Pure Appl. Math. / Singularity formation in thin jets with surface tension (1998)
10.1103/PhysRevLett.71.3458 / Phys. Rev. Lett. / Universal pinching of 3D axisymmetric free-surface flow (1993)
10.1063/1.868540 / Phys. Fluids / On the breakup of viscous liquid threads (1995)
10.1063/1.869086 / Phys. Fluids / Pinching threads, singularities and the number 0.0304… (1996)
10.1103/PhysRevLett.80.704 / Phys. Rev. Lett. / Self-similar capillary pinchoff of an inviscid fluid (1998)
{'key': '2024021014414069200_r17', 'first-page': '153', 'article-title': 'Slender jets and thin sheets with surface tension', 'volume': '50', 'year': '1990', 'journal-title': 'SIAM (Soc. Ind. Appl. Math.) J. Appl. Math.'} / SIAM (Soc. Ind. Appl. Math.) J. Appl. Math. / Slender jets and thin sheets with surface tension (1990)
{'key': '2024021014414069200_r18', 'first-page': '2125', 'article-title': 'Analysis of drop breakup in creeping flows,”', 'volume': '42', 'year': '1997', 'journal-title': 'Bull. Am. Phys. Soc.'} / Bull. Am. Phys. Soc. / Analysis of drop breakup in creeping flows,” (1997)
10.1017/S0022112078002530 / J. Fluid Mech. / A numerical study of the deformation and burst of a viscous drop in an extensional flow (1978)
10.1017/S0022112090003226 / J. Fluid Mech. / The effect of surfactants on drop deformation and breakup (1990)
10.1017/S002211207000191X / J. Fluid Mech. / Slender-body theory for particles of arbitrary cross-section (1970)
10.1017/S002211207000215X / J. Fluid Mech. / The motion of long slender bodies in a viscous fluid. Part 1 General theory (1970)
10.1017/S0022112096000754 / J. Fluid Mech. / Time-dependent viscous deformation of a drop in a rapidly rotating denser fluid (1996)

Dates

Type	When
Created	23 years, 1 month ago (July 26, 2002, 8:09 a.m.)
Deposited	1 year, 6 months ago (Feb. 10, 2024, 10:55 a.m.)
Indexed	6 days, 15 hours ago (Aug. 26, 2025, 2:42 a.m.)
Issued	26 years, 10 months ago (Nov. 1, 1998)
Published	26 years, 10 months ago (Nov. 1, 1998)
Published Print	26 years, 10 months ago (Nov. 1, 1998)

Funders 0

None

BibTeX

@article{Lister_1998, title={Capillary breakup of a viscous thread surrounded by another viscous fluid}, volume={10}, ISSN={1089-7666}, url={http://dx.doi.org/10.1063/1.869799}, DOI={10.1063/1.869799}, number={11}, journal={Physics of Fluids}, publisher={AIP Publishing}, author={Lister, John R. and Stone, Howard A.}, year={1998}, month=nov, pages={2758–2764} }

JSON

{
  "indexed": {
    "date-parts": [
      [
        2025,
        8,
        26
      ]
    ],
    "date-time": "2025-08-26T06:42:09Z",
    "timestamp": 1756190529968
  },
  "reference-count": 23,
  "publisher": "AIP Publishing",
  "issue": "11",
  "content-domain": {
    "domain": [
      "pubs.aip.org"
    ],
    "crossmark-restriction": true
  },
  "published-print": {
    "date-parts": [
      [
        1998,
        11,
        1
      ]
    ]
  },
  "abstract": "<jats:p>Previous long-wavelength analyses of capillary breakup of a viscous fluid thread in a perfectly inviscid environment show that the asymptotic self-similar regime immediately prior to breakup is given by a balance between surface tension, inertia, and extensional viscous stresses in the thread. In contrast, it is shown here that if viscosity in the external fluid, however small, is included then the asymptotic balance is between surface tension and viscous stresses in the two fluids while inertia is negligible. Scaling estimates for this new balance suggest that both axial and radial scales decrease linearly with time to breakup, so that the aspect ratio remains O(1) with time but scales with viscosity ratio like (\u03bcint/\u03bcext)1/2 for \u03bcint\u226b\u03bcext, where \u03bcint and \u03bcext are the internal and external viscosities. Numerical solutions to the full Stokes equations for \u03bcint=\u03bcext confirm the scalings with time and give self-similar behavior near pinching. However, the self-similar pinching region is embedded in a logarithmically large axial advection driven by the increasing range of scales intermediate between that of the pinching region and that of the macroscopic drop. The interfacial shape in the intermediate region is conical with angles of about 6\u00b0 on one side and 78\u00b0 on the other.</jats:p>",
  "DOI": "10.1063/1.869799",
  "type": "journal-article",
  "created": {
    "date-parts": [
      [
        2002,
        7,
        26
      ]
    ],
    "date-time": "2002-07-26T12:09:39Z",
    "timestamp": 1027685379000
  },
  "page": "2758-2764",
  "update-policy": "http://dx.doi.org/10.1063/aip-crossmark-policy-page",
  "source": "Crossref",
  "is-referenced-by-count": 265,
  "title": "Capillary breakup of a viscous thread surrounded by another viscous fluid",
  "prefix": "10.1063",
  "volume": "10",
  "author": [
    {
      "given": "John R.",
      "family": "Lister",
      "sequence": "first",
      "affiliation": [
        {
          "name": "Institute of Theoretical Geophysics, DAMTP, Cambridge\u2009CB3\u20099EW, England"
        }
      ]
    },
    {
      "given": "Howard A.",
      "family": "Stone",
      "sequence": "additional",
      "affiliation": [
        {
          "name": "Division of Engineering & Applied Sciences, Harvard University, Cambridge, Massachusetts\u200902138"
        }
      ]
    }
  ],
  "member": "317",
  "reference": [
    {
      "key": "2024021014414069200_r1",
      "doi-asserted-by": "crossref",
      "first-page": "145",
      "DOI": "10.1080/14786449208620301",
      "article-title": "On the stability of a cylinder of viscous fluid under a capillary force",
      "volume": "34",
      "year": "1892",
      "journal-title": "Philos. Mag."
    },
    {
      "key": "2024021014414069200_r2",
      "doi-asserted-by": "crossref",
      "first-page": "121",
      "DOI": "10.1016/0169-5983(95)00028-3",
      "article-title": "On the separation of droplets from a liquid jet",
      "volume": "17",
      "year": "1996",
      "journal-title": "Fluid Dyn. Res."
    },
    {
      "key": "2024021014414069200_r3",
      "doi-asserted-by": "crossref",
      "first-page": "3188",
      "DOI": "10.1063/1.869435",
      "article-title": "On the pinch-off of a pendant drop of viscous fluid",
      "volume": "9",
      "year": "1997",
      "journal-title": "Phys. Fluids"
    },
    {
      "key": "2024021014414069200_r4",
      "doi-asserted-by": "crossref",
      "first-page": "3391",
      "DOI": "10.1103/PhysRevLett.73.3391",
      "article-title": "Iterated instabilities during droplet fission",
      "volume": "73",
      "year": "1994",
      "journal-title": "Phys. Rev. Lett."
    },
    {
      "key": "2024021014414069200_r5",
      "doi-asserted-by": "crossref",
      "first-page": "364",
      "DOI": "10.1147/rd.184.0364",
      "article-title": "Drop formation in a liquid jet",
      "volume": "18",
      "year": "1974",
      "journal-title": "IBM J. Res. Dev."
    },
    {
      "key": "2024021014414069200_r6",
      "doi-asserted-by": "crossref",
      "first-page": "207",
      "DOI": "10.1146/annurev.fl.11.010179.001231",
      "article-title": "Drop formation in a circular liquid jet",
      "volume": "11",
      "year": "1979",
      "journal-title": "Annu. Rev. Fluid Mech."
    },
    {
      "key": "2024021014414069200_r7",
      "doi-asserted-by": "crossref",
      "first-page": "257",
      "DOI": "10.1017/S0022112080002108",
      "article-title": "The nonlinear capillary instability of a liquid jet. Part 1. Theory",
      "volume": "96",
      "year": "1980",
      "journal-title": "J. Fluid Mech."
    },
    {
      "key": "2024021014414069200_r8",
      "doi-asserted-by": "crossref",
      "first-page": "297",
      "DOI": "10.1017/S0022112092002738",
      "article-title": "Satellite and subsatellite formation in capillary breakup",
      "volume": "243",
      "year": "1992",
      "journal-title": "J. Fluid Mech."
    },
    {
      "key": "2024021014414069200_r9",
      "first-page": "865",
      "article-title": "Nonlinear dynamics and breakup of free-surface flows",
      "volume": "3",
      "year": "1997",
      "journal-title": "Rev. Mod. Phys."
    },
    {
      "key": "2024021014414069200_r10"
    },
    {
      "key": "2024021014414069200_r11",
      "doi-asserted-by": "crossref",
      "first-page": "3043",
      "DOI": "10.1103/PhysRevLett.70.3043",
      "article-title": "Topology transitions and singularities in viscous flows",
      "volume": "70",
      "year": "1993",
      "journal-title": "Phys. Rev. Lett."
    },
    {
      "key": "2024021014414069200_r12",
      "doi-asserted-by": "crossref",
      "first-page": "733",
      "DOI": "10.1002/(SICI)1097-0312(199807)51:7<733::AID-CPA2>3.0.CO;2-7",
      "article-title": "Singularity formation in thin jets with surface tension",
      "volume": "51",
      "year": "1998",
      "journal-title": "Commun. Pure Appl. Math."
    },
    {
      "key": "2024021014414069200_r13",
      "doi-asserted-by": "crossref",
      "first-page": "3458",
      "DOI": "10.1103/PhysRevLett.71.3458",
      "article-title": "Universal pinching of 3D axisymmetric free-surface flow",
      "volume": "71",
      "year": "1993",
      "journal-title": "Phys. Rev. Lett."
    },
    {
      "key": "2024021014414069200_r14",
      "doi-asserted-by": "crossref",
      "first-page": "1529",
      "DOI": "10.1063/1.868540",
      "article-title": "On the breakup of viscous liquid threads",
      "volume": "7",
      "year": "1995",
      "journal-title": "Phys. Fluids"
    },
    {
      "key": "2024021014414069200_r15",
      "doi-asserted-by": "crossref",
      "first-page": "2827",
      "DOI": "10.1063/1.869086",
      "article-title": "Pinching threads, singularities and the number 0.0304\u2026",
      "volume": "8",
      "year": "1996",
      "journal-title": "Phys. Fluids"
    },
    {
      "key": "2024021014414069200_r16",
      "doi-asserted-by": "crossref",
      "first-page": "704",
      "DOI": "10.1103/PhysRevLett.80.704",
      "article-title": "Self-similar capillary pinchoff of an inviscid fluid",
      "volume": "80",
      "year": "1998",
      "journal-title": "Phys. Rev. Lett."
    },
    {
      "key": "2024021014414069200_r17",
      "first-page": "153",
      "article-title": "Slender jets and thin sheets with surface tension",
      "volume": "50",
      "year": "1990",
      "journal-title": "SIAM (Soc. Ind. Appl. Math.) J. Appl. Math."
    },
    {
      "key": "2024021014414069200_r18",
      "first-page": "2125",
      "article-title": "Analysis of drop breakup in creeping flows,\u201d",
      "volume": "42",
      "year": "1997",
      "journal-title": "Bull. Am. Phys. Soc."
    },
    {
      "key": "2024021014414069200_r19",
      "doi-asserted-by": "crossref",
      "first-page": "191",
      "DOI": "10.1017/S0022112078002530",
      "article-title": "A numerical study of the deformation and burst of a viscous drop in an extensional flow",
      "volume": "89",
      "year": "1978",
      "journal-title": "J. Fluid Mech."
    },
    {
      "key": "2024021014414069200_r20",
      "doi-asserted-by": "crossref",
      "first-page": "161",
      "DOI": "10.1017/S0022112090003226",
      "article-title": "The effect of surfactants on drop deformation and breakup",
      "volume": "220",
      "year": "1990",
      "journal-title": "J. Fluid Mech."
    },
    {
      "key": "2024021014414069200_r21",
      "doi-asserted-by": "crossref",
      "first-page": "419",
      "DOI": "10.1017/S002211207000191X",
      "article-title": "Slender-body theory for particles of arbitrary cross-section",
      "volume": "44",
      "year": "1970",
      "journal-title": "J. Fluid Mech."
    },
    {
      "key": "2024021014414069200_r22",
      "doi-asserted-by": "crossref",
      "first-page": "791",
      "DOI": "10.1017/S002211207000215X",
      "article-title": "The motion of long slender bodies in a viscous fluid. Part 1 General theory",
      "volume": "44",
      "year": "1970",
      "journal-title": "J. Fluid Mech."
    },
    {
      "key": "2024021014414069200_r23",
      "doi-asserted-by": "crossref",
      "first-page": "275",
      "DOI": "10.1017/S0022112096000754",
      "article-title": "Time-dependent viscous deformation of a drop in a rapidly rotating denser fluid",
      "volume": "317",
      "year": "1996",
      "journal-title": "J. Fluid Mech."
    }
  ],
  "container-title": "Physics of Fluids",
  "original-title": [],
  "language": "en",
  "link": [
    {
      "URL": "https://pubs.aip.org/aip/pof/article-pdf/10/11/2758/19007676/2758_1_online.pdf",
      "content-type": "application/pdf",
      "content-version": "vor",
      "intended-application": "syndication"
    },
    {
      "URL": "https://pubs.aip.org/aip/pof/article-pdf/10/11/2758/19007676/2758_1_online.pdf",
      "content-type": "unspecified",
      "content-version": "vor",
      "intended-application": "similarity-checking"
    }
  ],
  "deposited": {
    "date-parts": [
      [
        2024,
        2,
        10
      ]
    ],
    "date-time": "2024-02-10T15:55:19Z",
    "timestamp": 1707580519000
  },
  "score": 1,
  "resource": {
    "primary": {
      "URL": "https://pubs.aip.org/pof/article/10/11/2758/253986/Capillary-breakup-of-a-viscous-thread-surrounded"
    }
  },
  "subtitle": [],
  "short-title": [],
  "issued": {
    "date-parts": [
      [
        1998,
        11,
        1
      ]
    ]
  },
  "references-count": 23,
  "journal-issue": {
    "issue": "11",
    "published-print": {
      "date-parts": [
        [
          1998,
          11,
          1
        ]
      ]
    }
  },
  "URL": "http://dx.doi.org/10.1063/1.869799",
  "relation": {},
  "ISSN": [
    "1070-6631",
    "1089-7666"
  ],
  "subject": [],
  "published-other": {
    "date-parts": [
      [
        1998,
        11
      ]
    ]
  },
  "published": {
    "date-parts": [
      [
        1998,
        11,
        1
      ]
    ]
  }
}