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SUMMARY:Drop splashing at smooth dry surfaces  - Professor Jose Gordillo\,
  University of Seville
DTSTART:20170525T103000Z
DTEND:20170525T113000Z
UID:TALK72219@talks.cam.ac.uk
CONTACT:Catherine Pearson
DESCRIPTION:When a drop impacts a smooth\, dry surface at a velocity above
  the so-called critical speed for drop splashing\, the initial liquid volu
 me loses its integrity\, fragmenting into tiny droplets that are violently
  ejected radially outwards. Making use of experiments\, potential flow and
  lubrication theories and of numerical simulations\, we first develop a mo
 del to predict the critical velocity for splashing. We find that dewetting
  is a necessary but not sufficient condition for splashing. Splashing only
  occurs when the drop velocity is such that\, the much faster and thinner 
 liquid sheet which is expelled in the direction tangent to the solid as a 
 consequence of the impact\, is accelerated vertically up to velocities lar
 ger than those caused by the capillary retraction of the sheet. The vertic
 al accelerations are imparted to the edge of the spreading liquid sheet by
  the aerodynamic lift force exerted by the surrounding gas on the edge of 
 the radially expanding lamella.   The lift force per unit length results a
 s the addition of: i) the classical term used in aerodynamics (which depen
 ds on the product of gas density\, the squared relative velocity and the t
 hickness of the lamella) plus ii) a term that depends on gas viscosity as 
 the product of four terms: gas viscosity\, the velocity of the liquid shee
 t edge relative to that of the ambient gas\, a constant which is a functio
 n of the angle the advancing lamella forms with the substrate and a logari
 thm which incorporates the ratio between the thickness of the lamella and 
 the mean free path of molecules. The contribution of the logarithm\, and a
 s a result\, of the mean free path\, is essential since\, otherwise\, thes
 e “viscous lift forces” would tend to infinite. The wedge angle is not
  the static contact angle with the substrate\, but it is the angle the adv
 ancing liquid front forms with the solid substrate. Our splash criterion c
 an be summarized as follows: if the vertical velocities imparted to the ed
 ge of the sheet by the aerodynamic lift forces are larger than the radial 
 velocity at which the edge of the sheet grows by capillary retraction\, th
 e edge of the sheet “takes off” and the toroidal rim bordering the she
 et is prone to develop Savart-Plateau-Rayleigh capillary instabilities. If
  the growth time of capillary instabilities is sufficiently small when com
 pared with the time of growth of the toroidal rim\, the edge of the lamell
 a breaks into very tiny drops\, of sizes comparable to that of the thickne
 ss of the rim.  \nFor impact velocities larger than the critical splash ve
 locity and making use of a onedimensional approximation describing the fl
 ow in the ejected liquid sheet and of balances of mass and momentum at the
  border of the sheet\, we predict the mean sizes and velocities of the eje
 cted drops. The predictions of the model are in good agreement with experi
 ments. 
LOCATION:Open Plan Area\, BP Institute\, Madingley Rise CB3 0EZ
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