IIT Jodhpur
Congratulations to Dr. Sukhendu Ghosh for the acceptance of his research paper in the journal Physics of Fluids

Title: Effect of imposed shear on the dynamics of a contaminated two-layer film flow down a slippery incline

Authors: Muhammad Sani, Siluvai Antony Selvan, Sukhendu Ghosh*, and Harekrushna
Journal: Physics of Fluids
Volume: 32 (Issue 10)
Year: 2020
DOI: https://doi.org/10.1063/5.0024201
Publisher: American Institute of Physics

Abstract: The linear instability of a surfactant-laden two-layer falling film over an inclined
slippery wall is analyzed under the influence of external shear, which is imposed on the top
surface of the flow. The free surface of the flow and the interface among the fluids are
contaminated by insoluble surfactants. Dynamics of the fluid layers are governed by the
Navier–Stokes equations, and the surfactant transport equations regulate 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 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. Furthermore, in the presence of strong imposed

shear, the overall stabilization of the surface mode by wall velocity slip for the stratified two-
fluid flow is also contrary to that of the single fluid case. The interface mode behaves

differently in the two zones at the moderate Reynolds numbers, and higher external shear
magnifies the interfacial instability in both zones. An opposite trend is observed in the case of
surface instability. 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 gravitational 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 in the control of the attitude of the instabilities.