DOI: 10.1017/s0022112086000332. The dynamics of the spreading of liquids on a solid surface. Part 1. Viscous flow

The dynamics of the spreading of liquids on a solid surface. Part 1. Viscous flow

10.1017/s0022112086000332

Crossref journal-article

Cambridge University Press (CUP)

Journal of Fluid Mechanics (56)

Abstract

An investigation is made into the dynamics involved in the movement of the contact line when one liquid displaces an immiscible second liquid where both are in contact with a smooth solid surface. In order to remove the stress singularity at the contact line, it has been postulated that slip between the liquid and the solid or some other mechanism must occur very close to the contact line. The general procedure for solution is described for a general model for such slip and also for a general geometry of the system. Using matched asymptotic expansions, it is shown that for small capillary number and for small values of the length over which slip occurs, there are either 2 or 3 regions of expansion necessary depending on the limiting process being considered. For the very important situation where 3 regions occur, solutions are obtained from which it is observed that in general there is a maximum value of the capillary number for which the solutions exist. The results obtained are compared with existing theories and experiments.

Bibliography

Cox, R. G. (1986). The dynamics of the spreading of liquids on a solid surface. Part 1. Viscous flow. Journal of Fluid Mechanics, 168, 169â194.

Authors 1

R. G. Cox (first)

References 23 Referenced 1,187

Dates

Type	When
Created	19 years, 4 months ago (April 21, 2006, 8:25 a.m.)
Deposited	2 months, 1 week ago (June 21, 2025, 3:48 a.m.)
Indexed	20 hours, 11 minutes ago (Aug. 31, 2025, 6:05 a.m.)
Issued	39 years, 2 months ago (July 1, 1986)
Published	39 years, 2 months ago (July 1, 1986)
Published Online	19 years, 4 months ago (April 21, 2006)
Published Print	39 years, 2 months ago (July 1, 1986)

Funders 0

None

BibTeX

@article{Cox_1986, title={The dynamics of the spreading of liquids on a solid surface. Part 1. Viscous flow}, volume={168}, ISSN={1469-7645}, url={http://dx.doi.org/10.1017/s0022112086000332}, DOI={10.1017/s0022112086000332}, journal={Journal of Fluid Mechanics}, publisher={Cambridge University Press (CUP)}, author={Cox, R. G.}, year={1986}, month=jul, pages={169–194} }

JSON

{
  "indexed": {
    "date-parts": [
      [
        2025,
        8,
        31
      ]
    ],
    "date-time": "2025-08-31T10:05:19Z",
    "timestamp": 1756634719395,
    "version": "3.41.0"
  },
  "reference-count": 23,
  "publisher": "Cambridge University Press (CUP)",
  "license": [
    {
      "start": {
        "date-parts": [
          [
            2006,
            4,
            21
          ]
        ],
        "date-time": "2006-04-21T00:00:00Z",
        "timestamp": 1145577600000
      },
      "content-version": "unspecified",
      "delay-in-days": 7234,
      "URL": "https://www.cambridge.org/core/terms"
    }
  ],
  "content-domain": {
    "domain": [],
    "crossmark-restriction": false
  },
  "published-print": {
    "date-parts": [
      [
        1986,
        7
      ]
    ]
  },
  "abstract": "<jats:p>An investigation is made into the dynamics involved in the movement of the contact line when one liquid displaces an immiscible second liquid where both are in contact with a smooth solid surface. In order to remove the stress singularity at the contact line, it has been postulated that slip between the liquid and the solid or some other mechanism must occur very close to the contact line. The general procedure for solution is described for a general model for such slip and also for a general geometry of the system. Using matched asymptotic expansions, it is shown that for small capillary number and for small values of the length over which slip occurs, there are either 2 or 3 regions of expansion necessary depending on the limiting process being considered. For the very important situation where 3 regions occur, solutions are obtained from which it is observed that in general there is a maximum value of the capillary number for which the solutions exist. The results obtained are compared with existing theories and experiments.</jats:p>",
  "DOI": "10.1017/s0022112086000332",
  "type": "journal-article",
  "created": {
    "date-parts": [
      [
        2006,
        4,
        21
      ]
    ],
    "date-time": "2006-04-21T12:25:12Z",
    "timestamp": 1145622312000
  },
  "page": "169-194",
  "source": "Crossref",
  "is-referenced-by-count": 1187,
  "title": "The dynamics of the spreading of liquids on a solid surface. Part 1. Viscous flow",
  "prefix": "10.1017",
  "volume": "168",
  "author": [
    {
      "given": "R. G.",
      "family": "Cox",
      "sequence": "first",
      "affiliation": []
    }
  ],
  "member": "56",
  "published-online": {
    "date-parts": [
      [
        2006,
        4,
        21
      ]
    ]
  },
  "reference": [
    {
      "doi-asserted-by": "crossref",
      "unstructured": "Lowndes J. 1980 J. Fluid Mech. 101,631.",
      "key": "S0022112086000332_ref020",
      "DOI": "10.1017/S0022112080001838"
    },
    {
      "doi-asserted-by": "crossref",
      "unstructured": "Wenzel R. N. 1936 Ind. Engng Chem. 28,988.",
      "key": "S0022112086000332_ref023",
      "DOI": "10.1021/ie50320a024"
    },
    {
      "doi-asserted-by": "crossref",
      "unstructured": "Inverarity G. 1969 Brit. Polymer J. 1,245.",
      "key": "S0022112086000332_ref015",
      "DOI": "10.1002/pi.4980010601"
    },
    {
      "doi-asserted-by": "crossref",
      "unstructured": "Cherry, B. W. & Holmes C. M. 1969 J. Colloid Interface Sci. 29,174.",
      "key": "S0022112086000332_ref004",
      "DOI": "10.1016/0021-9797(69)90367-1"
    },
    {
      "doi-asserted-by": "crossref",
      "unstructured": "Dussan V. , E, B. 1976 J. Fluid Mech. 77,665.",
      "key": "S0022112086000332_ref006",
      "DOI": "10.1017/S0022112076002838"
    },
    {
      "doi-asserted-by": "crossref",
      "unstructured": "Pisman, L. M. & Nir A. 1982 Phys. Fluids 25,3.",
      "key": "S0022112086000332_ref022",
      "DOI": "10.1063/1.863626"
    },
    {
      "doi-asserted-by": "crossref",
      "unstructured": "Hoffman R. L. 1975 J. Colloid Interface Sci. 50,228.",
      "key": "S0022112086000332_ref012",
      "DOI": "10.1016/0021-9797(75)90225-8"
    },
    {
      "doi-asserted-by": "crossref",
      "unstructured": "Huh, C. & Mason S. G. 1977b J. Colloid Interface Sci. 81,401.",
      "key": "S0022112086000332_ref014",
      "DOI": "10.1017/S0022112077002134"
    },
    {
      "doi-asserted-by": "crossref",
      "unstructured": "Burley, R. & Brady P. R. 1973 J. Colloid Interface Sci. 42,131.",
      "key": "S0022112086000332_ref002",
      "DOI": "10.1016/0021-9797(73)90015-5"
    },
    {
      "doi-asserted-by": "crossref",
      "unstructured": "Hocking L. M. 1977 J. Fluid Mech. 79,209.",
      "key": "S0022112086000332_ref010",
      "DOI": "10.1017/S0022112077000123"
    },
    {
      "doi-asserted-by": "crossref",
      "unstructured": "Dussan V. , E, B. 1979 Ann. Rev. Fluid Mech. 11,371.",
      "key": "S0022112086000332_ref008",
      "DOI": "10.1146/annurev.fl.11.010179.002103"
    },
    {
      "doi-asserted-by": "crossref",
      "unstructured": "Cox R. G. 1983 J. Fluid Mech. 131,1.",
      "key": "S0022112086000332_ref005",
      "DOI": "10.1017/S0022112083001214"
    },
    {
      "doi-asserted-by": "crossref",
      "unstructured": "Kennedy, B. S. & Burley R. 1977 J. Colloid Interface Sci. 62,48.",
      "key": "S0022112086000332_ref019",
      "DOI": "10.1016/0021-9797(77)90064-9"
    },
    {
      "doi-asserted-by": "crossref",
      "unstructured": "Huh, C. & Mason S. G. 1977a J. Colloid Interface Sci. 60,11.",
      "key": "S0022112086000332_ref013",
      "DOI": "10.1016/0021-9797(77)90251-X"
    },
    {
      "doi-asserted-by": "crossref",
      "unstructured": "Burley, R. & Kennedy B. S. 1976 Chem. Engrg Sci. 31,901.",
      "key": "S0022112086000332_ref003",
      "DOI": "10.1016/0009-2509(76)87040-6"
    },
    {
      "doi-asserted-by": "crossref",
      "unstructured": "Blake, T. D. & Haynes J. M. 1969 Colloid Interface Sci. 30,421.",
      "key": "S0022112086000332_ref001",
      "DOI": "10.1016/0021-9797(69)90411-1"
    },
    {
      "doi-asserted-by": "crossref",
      "unstructured": "Dussan V. , E, B. 1977 AIChEJ. 23,131.",
      "key": "S0022112086000332_ref007",
      "DOI": "10.1002/aic.690230122"
    },
    {
      "doi-asserted-by": "crossref",
      "unstructured": "Johnson, J. F. & Dettre R. H. 1964 Adv. Chem. 43,112.",
      "key": "S0022112086000332_ref017",
      "DOI": "10.1021/ba-1964-0043.ch007"
    },
    {
      "doi-asserted-by": "crossref",
      "unstructured": "Kafka, F. Y. & Dussan V. , E, B. 1979 J. Fluid Mech. 95,539.",
      "key": "S0022112086000332_ref018",
      "DOI": "10.1017/S0022112079001592"
    },
    {
      "doi-asserted-by": "crossref",
      "unstructured": "Hocking, L. M. & Rivers A. D. 1982 J. Fluid Mech. 121,425.",
      "key": "S0022112086000332_ref011",
      "DOI": "10.1017/S0022112082001979"
    },
    {
      "doi-asserted-by": "crossref",
      "unstructured": "Ngan, C. G. & Dussan V. , E, B. 1982 J. Fluid Mech. 118,27.",
      "key": "S0022112086000332_ref021",
      "DOI": "10.1017/S0022112082000949"
    },
    {
      "doi-asserted-by": "crossref",
      "unstructured": "Jansons K. M. 1985 J. Fluid Mech. 154,1.",
      "key": "S0022112086000332_ref016",
      "DOI": "10.1017/S0022112085001392"
    },
    {
      "doi-asserted-by": "crossref",
      "unstructured": "Greenspan H. P. 1978 J. Fluid Mech. 84,125",
      "key": "S0022112086000332_ref009",
      "DOI": "10.1017/S0022112078000075"
    }
  ],
  "container-title": "Journal of Fluid Mechanics",
  "original-title": [],
  "language": "en",
  "link": [
    {
      "URL": "https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022112086000332",
      "content-type": "unspecified",
      "content-version": "vor",
      "intended-application": "similarity-checking"
    }
  ],
  "deposited": {
    "date-parts": [
      [
        2025,
        6,
        21
      ]
    ],
    "date-time": "2025-06-21T07:48:08Z",
    "timestamp": 1750492088000
  },
  "score": 1,
  "resource": {
    "primary": {
      "URL": "https://www.cambridge.org/core/product/identifier/S0022112086000332/type/journal_article"
    }
  },
  "subtitle": [],
  "short-title": [],
  "issued": {
    "date-parts": [
      [
        1986,
        7
      ]
    ]
  },
  "references-count": 23,
  "alternative-id": [
    "S0022112086000332"
  ],
  "URL": "http://dx.doi.org/10.1017/S0022112086000332",
  "relation": {},
  "ISSN": [
    "0022-1120",
    "1469-7645"
  ],
  "subject": [],
  "container-title-short": "J. Fluid Mech.",
  "published": {
    "date-parts": [
      [
        1986,
        7
      ]
    ]
  }
}