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SUMMARY:On a toroidal method to solve the sessile drop oscillation problem
  - Saksham Sharma\, University of Cambridge\, UK
DTSTART:20210430T153000Z
DTEND:20210430T160000Z
UID:TALK160225@talks.cam.ac.uk
CONTACT:Deryck Thake
DESCRIPTION:The natural oscillation of a drop is a classical fluid mechani
 cs problem. Analytical expressions for the simple case of free\, spherical
  drops were obtained by Rayleigh\, Lamb\, Chandrasekhar and others using s
 pherical coordinate system. In recent times\, the focus on this problem ha
 s shifted towards a sessile drop supported on a flat substrate\, as eviden
 t through some recent works. The majority of these are computational in na
 ture. In this talk\, I will present an alternative new mathematical framew
 ork\, the toroidal coordinate system\, to solve this long-standing problem
  analytically for small drops (Bond number << 1) with pinned contact lines
 . I start with the governing hydrodynamic equations and boundary condition
 s\, write them in terms of the toroidal coordinate system and then obtain 
 solutions by reducing them to an eigenmode problem. Resonant frequencies a
 re identified for zonal\, sectoral and tesseral vibration modes and compar
 ed with results presented in the literature and by other models. The impac
 t of viscous dissipation in the bulk liquid\, at the contact line\, and co
 ntact line mobility is discussed qualitatively. I conclude with a discussi
 on of the importance of conformal mapping for solving axisymmetric physica
 l problems with complicated geometries.
LOCATION:GKB 100 Fluid Mechanics Webinar Series
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