Erschienen:
Cambridge University Press (CUP), 2002
Erschienen in:Journal of Fluid Mechanics
Sprache:
Englisch
DOI:
10.1017/s0022112001006814
ISSN:
0022-1120;
1469-7645
Entstehung:
Anmerkungen:
Beschreibung:
<jats:p>We consider the problem of a thin liquid layer falling down an inclined plate that
is subjected to non-uniform heating. The plate temperature is assumed to be linearly
distributed and both directions of the temperature gradient with respect to the flow
are investigated. The film flow is not only influenced by gravity and mean surface
tension, but in addition by the thermocapillary force acting along the free surface. The
coupling of thermocapillary instability and surface-wave instabilities is studied for
two-dimensional disturbances. Applying the long-wave theory, a nonlinear evolution
equation is derived. When the plate temperature is decreasing in the downstream
direction, linear stability analysis exhibits a film stabilization, compared to a uniformly
heated film. In contrast, for increasing temperature along the plate, the film becomes
less stable. Numerical solution of the evolution equation indicates the existence of
permanent finite-amplitude waves of different kinds. The shape of the waves depends
mainly on the mean flow and the mean surface tension, but their amplitudes and
phase speeds are influenced by thermocapillarity.</jats:p>