Levich Institute Seminar Announcement, 12/04/2012
Steinman Hall, Room #312
(Chemical Engineering Conference Room)
Professor Ganesh Subramanian
Jewaharlal Nehru Centre for Advanced Scientific Research (JNCASR)
"Orientation Dynamics of Particles in Sedimentation and Shearing Flows"
The talk will focus on the orientation dynamics of spheroidal particles in Newtonian and viscoelastic fluids; a problem relevant to suspensions of anisotropic particles. A novel spheroidal harmonics formalism allows one to obtain analytical results for arbitrary aspect ratios (particles examined range from slender fibers to disks). I will begin with the simpler sedimentation problem where the Stokes equations allow for all possible steady orientations, leading to an indeterminate orientation distribution. The opposing torques due to weak inertia and elasticity break this degeneracy, and determine a neutral curve in the De/Re-aspect ratio parameter plane that separates broadside-on and longside-on equilibria. Earlier simulations also motivate the analytical examination of the two-dimensional scenario, that of an elliptic cylinder, which allows for the possibility of stable intermediate orientations even for small De.
Next, we consider the orientation behaviour in simple shear flow where the Newtonian inertialess scenario leads to an indeterminate orientation distribution across Jeffery orbits. Small but finite inertia drives an irreversible drift across Jeffery orbits, and the direction of this drift is determined as a function of particle aspect ratio. Interestingly, apart from the expected reversal in drift in going from prolate to oblate particles, there is an additional reversal that occurs below a critical aspect ratio of about 0.14.
Finally, I will comment on the nature of the large De problem, again in two dimensions, where the balance of inertia and elasticity at large distances, even for small Re, leads to the possibility of a sonic transition (with respect to elastic shear waves). The resulting predictions should allow one to examine speculations based on earlier experiments and simulations by Dan Joseph and co-workers.
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