Three-dimensional effects in directional solidification in Hele-Shaw cells

Vladimir S. Ajaev*, Stephen H Davis

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

We consider the one-sided model of directional solidification of a binary alloy in a Hele-Shaw cell and study the linear stability and nonlinear evolution of an initially curved solid-liquid interface whose shape is determined by the contact-angle condition at the wall. For the values of the angle close to |TT we use a perturbation expansion to obtain the corrections to the known stability criterion of the planar front under various assumptions about the non-dimensional thickness of the HeleShaw cell and both static and dynamic contact-line conditions. A boundary-integral method is used to find stability criteria for arbitrary contact angle. Weakly nonlinear analysis is also carried out; it is shown that subcritical bifurcation can be promoted and the appearance of three-dimensional structures can be delayed due to the contact-angle conditions.

Original languageEnglish (US)
Pages (from-to)3589-3616
Number of pages28
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume455
Issue number1990
DOIs
StatePublished - Jan 1 1999

Keywords

  • Contact lines
  • Directional solidification
  • Hele-shaw cells
  • Instability

ASJC Scopus subject areas

  • Mathematics(all)
  • Engineering(all)
  • Physics and Astronomy(all)

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