Effect of Thermocapillary stress on the Stability of a Non-isothermal Thin Liquid Film Flowing Inside a Heated Rotating Horizontal Cylinder

The stability analysis has been carried out for a thin film flowing inside a uniformly heated rotating horizontal cylinder. Mass, momentum, and energy equations are simplified under lubrication approximation to obtain film thickness evolution equation. The mathematical model includes effects of gravity, viscous drag, inertia, surface tension and thermocapillary force. The film thickness evolution equation is solved numerically to obtain two-dimensional solutions neglecting
axial variations. Due to non-uniform film thickness, the temperature varies at the free surface which enables surface tension gradient which in turn generates flow which is called Marangoni flow. It is observed that thermocapillary stress has no significant effect on steady solutions. The two-dimensional solutions show oscillations at higher inertia and the thermocapillary stress enhances the amplitudes of these oscillations. Linear stability analysis is carried out by imposing an infinitesimally small axial perturbation to the obtained two-dimensional solutions. These two-dimensional profiles have been shown to be unstable with thermocapillary stress, leading to the formation of the so-called 'shark teeth' patterns in the axial direction.