BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Talks.cam//talks.cam.ac.uk//
X-WR-CALNAME:Talks.cam
BEGIN:VEVENT
SUMMARY:The role of surface tension in hydrodynamics: a new perspective - 
 Dr Rajesh Bhagat\, DAMTP
DTSTART:20241018T150000Z
DTEND:20241018T160000Z
UID:TALK222712@talks.cam.ac.uk
CONTACT:Professor Grae Worster
DESCRIPTION:A liquid's mechanical and surface energies are incontrovertibl
 y interconvertible. The changes in internal energy of a fluid in motion th
 at for simplified situations results in Bernoulli's theorem fails to accou
 nt for the surface energy (see the physical example below). This is due to
  the definition of internal energy used to derive the equation which inher
 ently ignores surface energy [1]. This has wide ranging implications.\n\nI
 n this talk firstly\, I will establish the deficiency of the fluid’s ene
 rgy equation using the existing literature [1\, 2]. Subsequently\, to illu
 strate the implications\, I will examine the exemplar flows of planar (for
  a simpler geometry) and circular hydraulic jump in micro-gravity. In case
  of a \nkitchen sink hydraulic jumps\, in Bhagat et al.(2018) I have shown
  that these jumps occur when the rate of change of the kinetic energy is i
 nsufficient to provide the surface energy and the viscous dissipation. Her
 e\, I will use the Navier-Stokes equations\; I will scale the viscous shal
 low water equation and show that liquid film’s curvature becomes singula
 r at a finite radius when the local We = 1. I will also present experiment
 al and numerical results\, including the experiments conducted in micro-gr
 avity showing kitchen sink hydraulic jumps are created due to surface tens
 ion and gravity does not play a significant role. I will show that the dev
 iatoric component of the normal stress which is often ignored is the key t
 o explaining kitchen sink hydraulic jumps. Finally\, I will show the consi
 stency of the new energy equation that includes the surface energy with th
 e Navier Stokes equations and it’s application in predicting the \ndisin
 tegration of savart sheets.\n\nPhysical example: Consider an inviscid liqu
 id jet impinging onto a flat surface and spreading radially. Ignoring grav
 ity for simplicity\, the approximately flat thin film possess minimal curv
 ature\, and according to Bernoulli's principle\, the kinetic energy of the
  fluid parcels remains constant. Now\, take a small material volume of the
  fluid in the jet\, and track it at a later time 𝑡\, as it spreads to a
  radius 𝑟 in the film. It can be shown that the ratio of the \ninterfac
 ial area at radius 𝑟 to that in the jet is proportional to 𝑟. Accoun
 ting for the total energy \nof this volume\, it now possesses not only its
  kinetic energy but also additional surface energy due to the increased in
 terfacial area.\n\nReferences: \n1. Batchelor\, G. K. An introduction to f
 luid dynamics. Cambridge university press\, 2000.\n2. Lighthill\, M. J. Wa
 ves in fluids. Cambridge university press\, 2001.\n3. Bhagat RK\, Jha NK\,
  Linden PF\, Wilson DI. On the origin of the circular hydraulic jump in a 
 thin liquid film. Journal of Fluid Mechanics. 2018 Sep\;851:R5.\n
LOCATION:MR2
END:VEVENT
END:VCALENDAR