Math Modeling Seminar - Thin Film Flow Along a Partially Immersed Rotating Cylinder

Thin Film Flow Along a Partially Immersed Rotating Cylinder

Dr. Mohamed Samaha
Associate Professor
Department of Mechanical and Industrial Engineering
RIT Dubai

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Abstract:
The steady-state withdrawal of a two-dimensional liquid film from a horizontal and partially immersed rotating cylinder in a pool is examined theoretically.  As such flows are an essential element of more sophisticated roll-coating operations, its study is warranted.  A boundary layer form of the Navier-Stokes equations is coupled with essentially-hydrostatic pressure variations induced by the interface under conditions of negligible capillarity.  Following the approach of von-Karman and Polhausen, these simplified equations are integrated to obtain an integro-differential equation; subsequently, an assumed parabolic velocity profile is inserted to obtain an approximate first-order nonlinear-ordinary differential equation (the film equation) that governs the film thickness.  A removable critical point singularity (Weinstein & Ruschak 1999, Chem. Eng. Sci. 54 (8)) arises in the film equation at the location where inertia and gravitational effects balance, and removal of this singularity sets the volumetric flow rate and the height of the film as a function of azimuthal location along the cylinder.  The interface location can be determined by integrating the equation upstream and downstream starting from the critical point. The azimuthal location of the critical point location is linked to the submerged depth of the roller. Whereas the film equation is designed to enable the film equation to approach a horizontal pool away from the roller, it is unable to do so.  This is an unexpected result, as film equations developed using parabolic velocity profiles that describe flows along stationary surfaces meet this horizontal condition (Ruschak 1978 AIChE J. 24 (4)).  We find that the deficiency in the film equation is a result of parabolic profile used in its development.  In this study, we utilize full numerical solutions of the Navier-Stokes equations to guide the choice of velocity profile that enables an accurate approximate solution of the interface shape along the roller.  Interface predictions from the resulting film equation are in good agreement with numerical solutions evaluated at different Reynolds numbers, cylinder radii and static pool height.

Speaker Bio:
Dr. Mohamed A. Samaha is currently an associate professor and graduate program advisor, Mechanical Engineering, at RIT’s campus in Dubai. He joined RIT-Dubai in 2014 as an assistant professor, then, promoted to the associate rank in 2019. His research focuses on experimental, numerical and theoretical approaches in thermofluids with applications in active and passive flow control for saving energy and promoting convection heat transfer. In addition, his research spans methods of harvesting renewable energy including wind turbines and solar panels. Mohamed also worked in advancing relatively low-cost micro/nanofabrication of slippery superhydrophobic and omniphobic surfaces for drag-reduction purposes. He also contributed to other areas such as turbulence modeling of the flow through hydraulic capsule pipelines. See more details here.

Intended Audience:
Undergraduates, graduates, and experts. Those with interest in the topic.

The Math Modeling Seminar will recur each week throughout the semester on the same day and time. Find out more about upcoming speakers on the Mathematical Modeling Seminar Series webpage.