(425d) Stability of the Inertial Flow of Thin Liquid Film inside a Uniformly Heated Rotating Horizontal Cylinder
AIChE Annual Meeting
2017
2017 Annual Meeting
Engineering Sciences and Fundamentals
Fundamentals of Interfacial Phenomena II
Tuesday, October 31, 2017 - 4:00pm to 4:15pm
The stability behavior is investigated for a thin film of viscous
liquid flowing inside a uniformly heated horizontal cylinder
rotating about its longitudinal axis. An approximate evolution
equation for the film thickness is obtained by simplifying the
Navier-Stokes and energy equations within the lubrication
approximation. The model includes the effect of gravity, viscous
drag, inertia, surface tension, and thermocapillary stress. The
film thickness evolution equation is solved numerically to obtain
two-dimensional solutions neglecting axial variations. Dynamics of
this 2D profile shows interesting features such as formation of a
localized liquid ridge and recirculation zones. These 2D profiles
have been shown to be unstable for some suitable parameter ranges,
leading to the formation of the so called 'shark-teeth' patterns
in the axial direction. Linear stability analysis is carried out
by imposing an infintesimally small axial perturbation to the
obtained two-dimensional solutions. It is found that the inertia
and capillary pressure destabilize whereas the gravity and
thermocapillary stress stabilize the 2D profile. Thicker films are
shown to be more susceptible to become unstable due to inertia. It
is shown that the oscillations in the 2D profile appear in the
presence of inertia, whereas the presence of the thermocapillary
stress dampens these oscillations. Parametric regions are computed
in which the film becomes unstable leading to the formation of
shark-teeth patterns.
liquid flowing inside a uniformly heated horizontal cylinder
rotating about its longitudinal axis. An approximate evolution
equation for the film thickness is obtained by simplifying the
Navier-Stokes and energy equations within the lubrication
approximation. The model includes the effect of gravity, viscous
drag, inertia, surface tension, and thermocapillary stress. The
film thickness evolution equation is solved numerically to obtain
two-dimensional solutions neglecting axial variations. Dynamics of
this 2D profile shows interesting features such as formation of a
localized liquid ridge and recirculation zones. These 2D profiles
have been shown to be unstable for some suitable parameter ranges,
leading to the formation of the so called 'shark-teeth' patterns
in the axial direction. Linear stability analysis is carried out
by imposing an infintesimally small axial perturbation to the
obtained two-dimensional solutions. It is found that the inertia
and capillary pressure destabilize whereas the gravity and
thermocapillary stress stabilize the 2D profile. Thicker films are
shown to be more susceptible to become unstable due to inertia. It
is shown that the oscillations in the 2D profile appear in the
presence of inertia, whereas the presence of the thermocapillary
stress dampens these oscillations. Parametric regions are computed
in which the film becomes unstable leading to the formation of
shark-teeth patterns.