WIAS Preprint No. 720, (2002)

Flow and thermal convection in full-zone liquid bridges of wide-ranging aspect ratio



Authors

  • Davis, Dominic
  • Smith, Frank

2010 Mathematics Subject Classification

  • 35Q30 35B40 65M60 65N06 75D45

Keywords

  • liquid bridges, crystal growth, floating-zone, axisymmetric, Navier-Stokes equations, thermocapillarity, buoyancy, asymptotic, finite-element

Abstract

Flow and thermal effects concerned with liquid crystal growth are studied nonlinearly for low Prandtl numbers, in an axisymmetric steady configuration with endwalls present. Full solutions are obtained by finite element simulation to examine the influences of aspect ratio, Marangoni number and Rayleigh number. In particular a `lemonhead' phenomenon is found in which the velocity profiles acquire a very localised bell-shaped form as jet like flow starts to emerge, when the relative size of the Marangoni number increases above a finite critical value which is identified. Wide-domain and narrow-domain analyses are then presented, showing favourable agreement with the full solutions and explaining the impact of the end walls on the motion, especially through slender flow modelling in the narrow-domain context. Sensitive scalings for the relative effects of the Marangoni and Rayleigh numbers emerge, and the lemonhead phenomenon is also accounted for as a substantial change in the convective flow structure.

Appeared in

  • Theoret. Comput. Fluid Dynamics, No.17(2), 2003, pp. 113-146

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