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<p>A thin liquid layer with a deformable surface, heated from below and covered by an insoluble surfactant, rests on a horizontal rigid substrate. Using the multi-scale analysis, a system of amplitude equations is obtained that governs the pattern selection above the convection threshold. The coefficients in the equations are calculated for specific values of the problem parameters. The equations describe both rolls and hexagons as possible solutions. Two types of hexagons are considered: regular (equilateral) and non-equilateral ones. Internal stability of hexagons is analyzed, along with the modulational instability of regular hexagons in the longwave limit.</p>

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On the stability of hexagonal patterns in Marangoni convection

  • 期刊论文

  • 发表日期：

    2025年12月8日

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  • Alexander B. Mikishev,
  • Alexander A. Nepomnyashchy

摘要

A thin liquid layer with a deformable surface, heated from below and covered by an insoluble surfactant, rests on a horizontal rigid substrate. Using the multi-scale analysis, a system of amplitude equations is obtained that governs the pattern selection above the convection threshold. The coefficients in the equations are calculated for specific values of the problem parameters. The equations describe both rolls and hexagons as possible solutions. Two types of hexagons are considered: regular (equilateral) and non-equilateral ones. Internal stability of hexagons is analyzed, along with the modulational instability of regular hexagons in the longwave limit.