Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Effect of imposed shear on the dynamics of a contaminated two-layer film
  flow down a slippery incline   The linear instability of a surfactant-laden two-layer falling film over an
inclined slippery wall is analyzed under an influence of external shear which
is imposed on the top surface of the flow. The free surface of the flow as well
as the interface among the fluids are contaminated by insoluble surfactants.
Dynamics of both the layers are governed by the Navier--Stokes equations, and
the surfactant transport equation regulates the motion of the insoluble
surfactants at the interface and free surface. Instability mechanisms are
compared by imposing the external shear along and opposite to the flow
direction. A coupled Orr--Sommerfeld system of equations for the considered
problem is derived using the perturbation technique and normal mode analysis.
The eigenmodes corresponding to the Orr--Sommerfeld eigenvalue problem are
obtained by employing the spectral collocation method. The numerical results
imply that the stronger external shear destabilizes the interface mode
instability. However, a stabilizing impact of the external shear on the surface
mode is noticed if the shear is imposed in the flow direction, which is in
contrast to the role of imposed external shear on the surface mode for a
surfactant laden single layer falling film. Moreover, the impression of shear
mode on the primary instability is analyzed in the high Reynolds number regime
with sufficiently low inclination angle. Under such configuration, dominance of
the shear mode over the surface mode is observed due to the weaker impact of
the gravitation force on the surface instability. The shear mode can also be
stabilized by applying the external shear in the counter direction of the
streamwise flow. Conclusively, the extra imposed shear on the stratified
two-layer falling film plays an active role to control the attitude of the
instabilities.

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The categories of this paper are: cmp-lg
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The categories of this paper are: adap-org
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The categories of this paper are: econ
4
The categories of this paper are: cond-mat
1
The categories of this paper are: cs
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The categories of this paper are: plasm-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: math-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-th
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The categories of this paper are: comp-gas
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The categories of this paper are: solv-int
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-lat
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The categories of this paper are: dg-ga