JournalsifbVol. 5 , No. 4DOI 10.4171/ifb/88

Rigorous lubrication approximation

  • Lorenzo Giacomelli

    Università di Roma La Sapienza, Italy
  • Felix Otto

    für Mathematik in den Naturwissenschaften, Leipzig, Germany
Rigorous lubrication approximation cover

Abstract

We rigorously carry out a lubrication approximation for a liquid thin film which spreads on a solid, driven by surface tension. We consider a two--dimensional Darcy liquid as simple model case. Of particular interest to us is the codimension--two free boundary, i.\ e.\ the triple junctions where solid, liquid and vapor meet. In the considered regime of complete wetting, the contact angle vanishes throughout the evolution. We show in particular that this contact angle condition is preserved in the lubrication approximation.