  A complete explanation of the synthesis of metal-catalyst nanoparticles, and
the subsequent nucleation and growth of bundles of C-SWNTs is introduced using
a novel model. It is shown that the synthesis process leads to the formation of
a liquid layer supersaturated in carbon surrounding each metallic-catalyst
nanoparticle. The onset of a solutal B\'enard-Marangoni instability and the
subsequent formation of patterns of hexagonal convection cells in the liquid
layer is predicted and quantified by linear and weakly nonlinear analyses. The
nucleation and growth of a C-SWNT at the center of convection cell is
explained.
