The spin-coating process: Analysis of the free boundary value problem

Robert Denk, Matthias Geissert, Matthias Georg Hieber, Jürgen Saal, Okihiro Sawada

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

In this paper, an accurate model of the spin-coating process is presented and investigated from the analytical point of view. More precisely, the spin-coating process is being described as a one-phase free boundary value problem for Newtonian fluids subject to surface tension and rotational effects. It is proved that for T > 0 there exists a unique, strong solution to this problem in (0, T) belonging to a certain regularity class provided the data and the speed of rotation are small enough in suitable norms. The strategy of the proof is based on a transformation of the free boundary value problem to a quasilinear evolution equation on a fixed domain. The keypoint for solving the latter equation is the so-called maximal regularity approach. In order to pursue in this direction one needs to determine the precise regularity classes for the associated inhomogeneous linearized equations. This is being achieved by applying the Newton polygon method to the boundary symbol.

Original languageEnglish
Pages (from-to)1145-1192
Number of pages48
JournalCommunications in Partial Differential Equations
Volume36
Issue number7
DOIs
Publication statusPublished - 2011 Jul
Externally publishedYes

Fingerprint

Free Boundary Value Problems
Spin coating
Boundary value problems
Coating
Regularity
Newton Polygon
Maximal Regularity
Quasilinear Equations
Newtonian Fluid
Newton-Raphson method
Strong Solution
Surface Tension
Evolution Equation
Surface tension
Norm
Fluids
Class
Model
Strategy

Keywords

  • Free boundary
  • Navier slip
  • Navier-Stokes
  • Newton polygon
  • Spincoating
  • Surface tension

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Cite this

The spin-coating process : Analysis of the free boundary value problem. / Denk, Robert; Geissert, Matthias; Hieber, Matthias Georg; Saal, Jürgen; Sawada, Okihiro.

In: Communications in Partial Differential Equations, Vol. 36, No. 7, 07.2011, p. 1145-1192.

Research output: Contribution to journalArticle

Denk, Robert ; Geissert, Matthias ; Hieber, Matthias Georg ; Saal, Jürgen ; Sawada, Okihiro. / The spin-coating process : Analysis of the free boundary value problem. In: Communications in Partial Differential Equations. 2011 ; Vol. 36, No. 7. pp. 1145-1192.
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