{
  "id": "2109.09091",
  "version": "v1",
  "published": "2021-09-19T09:16:47.000Z",
  "updated": "2021-09-19T09:16:47.000Z",
  "title": "Taylor bubble motion in stagnant and flowing liquids in vertical pipes. Part I: Steady-states",
  "authors": [
    "Habib Abubakar",
    "Omar Matar"
  ],
  "comment": "34 pages, 20 figures",
  "categories": [
    "physics.flu-dyn"
  ],
  "abstract": "Taylor bubbles are a feature of the slug flow regime in gas-liquid flows in vertical pipes. Their dynamics exhibits a number of transitions such as symmetry-breaking in the bubble shape and wake when rising in downward-flowing and stagnant liquids, respectively, as well as breakup in sufficiently turbulent environments. Motivated by the need to examine the stability of a Taylor bubble in liquids, a systematic numerical study of a steadily-moving Taylor bubble in stagnant and flowing liquids is carried out, characterised by a dimensionless inverse viscosity ($Nf$), and E\\\"{o}tv\\\"{o}s ($Eo$), and Froude ($Fr$) numbers based on the centreline liquid velocity, using a Galerkin finite-element method. A boundary-fitted domain is used to examine the dependence of the steady bubble shape on a wide range of $Nf$ and $Eo$. Our analysis of the bubble nose and bottom curvatures shows that the intervals $Eo = \\left[ 20,30 \\right)$ and $Nf=\\left[60,80 \\right)$ are the limits below which surface tension and viscosity, respectively, have a strong influence on the bubble shape. In the interval $Eo = \\left(60,100 \\right]$, all bubble features studied are weakly-dependent on surface tension. This is Part I of a two-part publication in which its companion paper (Abubakar & Matar, 2021) reports the results of a linear stability analysis of the steady-states discussed herein.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-09-19T09:16:47.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "taylor bubble motion",
      "flowing liquids",
      "vertical pipes",
      "steady-states",
      "bubble shape"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 34,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}