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CATEGORIES:DAMTP info aggregator
SUMMARY:On a toroidal method to solve the sessile drop osc
illation problem - Saksham Sharma\, University of
Cambridge\, UK
DTSTART;TZID=Europe/London:20210430T163000
DTEND;TZID=Europe/London:20210430T170000
UID:TALK160225AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/160225
DESCRIPTION:The natural oscillation of a drop is a classical f
luid mechanics problem. Analytical expressions for
the simple case of free\, spherical drops were ob
tained by Rayleigh\, Lamb\, Chandrasekhar and othe
rs using spherical coordinate system. In recent ti
mes\, the focus on this problem has shifted toward
s a sessile drop supported on a flat substrate\, a
s evident through some recent works. The majority
of these are computational in nature. In this talk
\, I will present an alternative new mathematical
framework\, the toroidal coordinate system\, to so
lve this long-standing problem analytically for sm
all drops (Bond number << 1) with pinned contact l
ines. I start with the governing hydrodynamic equa
tions and boundary conditions\, write them in term
s of the toroidal coordinate system and then obtai
n solutions by reducing them to an eigenmode probl
em. Resonant frequencies are identified for zonal\
, sectoral and tesseral vibration modes and compar
ed with results presented in the literature and by
other models. The impact of viscous dissipation i
n the bulk liquid\, at the contact line\, and cont
act line mobility is discussed qualitatively. I co
nclude with a discussion of the importance of conf
ormal mapping for solving axisymmetric physical pr
oblems with complicated geometries.
LOCATION:GKB 100 Fluid Mechanics Webinar Series
CONTACT:Deryck Thake
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