{
  "id": "1410.2427",
  "version": "v1",
  "published": "2014-10-09T11:27:47.000Z",
  "updated": "2014-10-09T11:27:47.000Z",
  "title": "Arbitrary Lagrangian-Eulerian method for computation of impinging droplet with soluble surfactants and dynamic contact angle",
  "authors": [
    "Sashikumaar Ganesan"
  ],
  "comment": "26 pages, 9 figures and 5 tables",
  "categories": [
    "physics.flu-dyn",
    "math-ph",
    "math.MP"
  ],
  "abstract": "An arbitrary Lagrangian--Eulerian (ALE) finite element scheme for computations of soluble surfactant droplet impingement on a horizontal surface is presented. The numerical scheme solves the time-dependent Navier--Stokes equations for the fluid flow, scalar convection-diffusion equation for the surfactant transport in the bulk phase, and simultaneously, surface evolution equations for the surfactants on the free surface and on the liquid-solid interface. The effects of surfactants on the flow dynamics are included into the model through the surfactant-dependent surface tension and dynamic contact angle. In particular, the dynamic contact angle of the droplet is defined as a function of surfactants using the nonlinear equation of state for surface tension. Further, the surface forces are included in the model using the Boussinesq-Scriven law that allows to incorporate the Marangoni effects without evaluating the gradients of surfactant concentration on the free surface. In addition to a mesh convergence study and a validation of the numerical results with experiments, the effects of adsorption and desorption surfactant coefficients on the flow dynamics in wetting, partially wetting and non-wetting droplets are studied in detail. It is observed that the effect of surfactants are more in wetting droplets than in the non-wetting droplets. Further, the surfactant reduces the equilibrium contact angle further when it is less than $90^\\circ$, and increases further when it is more than $90^\\circ$. The surfactants has no effect on the contact angle, when its value is $90^\\circ$. The numerical study clearly demonstrates that the surfactant-dependent contact angle has to be considered, in addition to the Marangoni effect, in order to study the flow dynamics and the equilibrium states of surfactant droplet impingement accurately.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-10-09T11:27:47.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "dynamic contact angle",
      "arbitrary lagrangian-eulerian method",
      "soluble surfactant",
      "impinging droplet",
      "flow dynamics"
    ],
    "publication": {
      "doi": "10.1016/j.jcp.2015.08.026",
      "journal": "Journal of Computational Physics",
      "year": 2015,
      "month": "Nov",
      "volume": 301,
      "pages": 178
    },
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015JCoPh.301..178G"
    }
  }
}