We discuss the linear stability of a cross-doubly-diffusive
fluid layer with surface
tension variation along the free surface. Two limiting cases of the mass
flux basic state
are considered in the presence of non-zero Soret and Dufour diffusivities.
The first case,
which has remained largely unexplored, is one where a temperature difference,
ΔT¯, and
a concentration difference, ΔC¯, are both imposed
across the layer. The second case,
which has greater significance to thermosolutal systems, is that where
the imposed
ΔT¯
across the layer induces a ΔC¯. We rescale the
problem in the absence of buoyancy,
which leads to a more concise representation of neutral stability results
in and near the
limit of zero gravity. We obtain exact solutions for stationary stability
in both cases.
One important consequence of the exact solutions is the validation of recently
published numerical results in the limit of zero gravity. Moreover, the
precise location
of asymptotes in relevant parameter
(Smc, Mac)
space are computed from exact
solutions. Both numerical and exact solutions are used to further examine
stability
behaviour. We also derive algebraic expressions for stationary stability,
oscillatory
stability, frequency, and codimension two point from a one-term Galerkin
approximation. The one-term solutions qualitatively reflect the stability
behaviour of the
system over the parameter ranges in our investigation. A practical consequence
is that
the nature of the stability (oscillatory or stationary) for a given set
of parameter values
can be determined approximately, without solving the numerical eigenvalue
problem.
Effect of Interface Momentum Distribution on the Stability in a
Porous-Fluid System
