Shear-imposed falling thin Newtonian film over a porous slippery surface

The stability of a Newtonian thin film flow over porous slippery wall approximated by Darcy's law is investigated. modified Orr–Sommerfeld system derived for the frequency-dependent linear analysis and energy-budget analysis. Moreover, in longwave regime, both weakly nonlinear analyses are conducted small aspect ratios. In addition, multiple scale approach performed directly deformation equation free surface to predict extraordinary behavior amplitude speed disturbance subcritical supercritical regimes. study finds that larger slip-velocity externally imposed shear on increase total kinetic energy infinitesimal perturbations. critical conditions primary instability described as function stress destabilizes low Reynolds number. Furthermore, stable zone, wave phase with an induced direction velocity slip, reverse trend observed applying opposite direction. On other hand, unstable zone increases decreases, corresponding values slip parameters, respectively.