Author:
BERGEON A.,HENRY D.,BENHADID H.,TUCKERMAN L. S.
Abstract
Marangoni convection in a differentially heated binary mixture
is studied numerically
by continuation. The fluid is subject to the Soret effect and is contained
in a two-dimensional
small-aspect-ratio rectangular cavity with one undeformable free surface.
Either or both of the temperature and concentration gradients may be destabilizing;
all three possibilities are considered. A spectral-element time-stepping
code is adapted
to calculate bifurcation points and solution branches via Newton's
method. Linear
thresholds are compared to those obtained for a pure fluid. It is found
that for large
enough Soret coefficient, convection is initiated predominantly by solutal
effects and
leads to a single large roll. Computed bifurcation diagrams show a marked
transition
from a weakly convective Soret regime to a strongly convective Marangoni
regime
when the threshold for pure fluid thermal convection is passed. The presence
of many
secondary bifurcations means that the mode of convection at the onset of
instability
is often observed only over a small range of Marangoni number. In particular,
two-roll states with up-flow at the centre succeed one-roll states via
a well-defined
sequence of bifurcations. When convection is oscillatory at onset, the
limit cycle is
quickly destroyed by a global (infinite-period) bifurcation leading to
subcritical steady
convection.
Publisher
Cambridge University Press (CUP)
Subject
Mechanical Engineering,Mechanics of Materials,Condensed Matter Physics
Cited by
99 articles.
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