ScienceAsia 28 (2002) :049-054 |doi: 10.2306/scienceasia1513-1874.2002.28.049

Scaling Laws for the Wavelength and the Appearance Time of Cells Resulting from Double-Diffusive Convection

Karsten Kotter^aa and Mario Markus^a,*

ABSTRACT: We investigate the solutions of partial differential equations describing a two-layered fluid system. The lower layer contains a fastly diffusing, stabilizing substance T and a slowly diffusing, destabilizing substance S. The upper layer contains only the solvent. Double-diffusive convection yields cells in agreement with experiments performed with a tenside (S) and glycerine (T) dissolved in water. Approximation of the PDEs renders scaling laws for the appearance time T_em of the cells and their wavelength , as functions of the initial concentrations S₀ and T₀, as well as as a function of time. These approximations agree well with the solutions of the PDEs.

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a Max-Planck-Institut fur molekulare Physiologie, Postfach 500247,
44202 Dortmund, Germany.



* Corresponding author, E-mail: mario.markus@mpi-dortmund.mpg.de

Received 25 May 2001, Accepted 28 Sep 2001