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CATEGORIES:BPI Seminar Series
SUMMARY:Drop splashing at smooth dry surfaces - Professor
Jose Gordillo\, University of Seville
DTSTART;TZID=Europe/London:20170525T113000
DTEND;TZID=Europe/London:20170525T123000
UID:TALK72219AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/72219
DESCRIPTION:When a drop impacts a smooth\, dry surface at a ve
locity above the so-called critical speed for drop
splashing\, the initial liquid volume loses its i
ntegrity\, fragmenting into tiny droplets that are
violently ejected radially outwards. Making use o
f experiments\, potential flow and lubrication the
ories and of numerical simulations\, we first deve
lop a model to predict the critical velocity for s
plashing. We find that dewetting is a necessary bu
t not sufficient condition for splashing. Splashin
g only occurs when the drop velocity is such that\
, the much faster and thinner liquid sheet which i
s expelled in the direction tangent to the solid a
s a consequence of the impact\, is accelerated ver
tically up to velocities larger than those caused
by the capillary retraction of the sheet. The vert
ical accelerations are imparted to the edge of the
spreading liquid sheet by the aerodynamic lift fo
rce exerted by the surrounding gas on the edge of
the radially expanding lamella. The lift force p
er unit length results as the addition of: i) the
classical term used in aerodynamics (which depends
on the product of gas density\, the squared relat
ive velocity and the thickness of the lamella) plu
s ii) a term that depends on gas viscosity as the
product of four terms: gas viscosity\, the velocit
y of the liquid sheet edge relative to that of the
ambient gas\, a constant which is a function of t
he angle the advancing lamella forms with the subs
trate and a logarithm which incorporates the ratio
between the thickness of the lamella and the mean
free path of molecules. The contribution of the l
ogarithm\, and as a result\, of the mean free path
\, is essential since\, otherwise\, these “viscous
lift forces” would tend to infinite. The wedge an
gle is not the static contact angle with the subst
rate\, but it is the angle the advancing liquid fr
ont forms with the solid substrate. Our splash cri
terion can be summarized as follows: if the vertic
al velocities imparted to the edge of the sheet by
the aerodynamic lift forces are larger than the r
adial velocity at which the edge of the sheet grow
s by capillary retraction\, the edge of the sheet
“takes off” and the toroidal rim bordering the she
et is prone to develop Savart-Plateau-Rayleigh cap
illary instabilities. If the growth time of capill
ary instabilities is sufficiently small when compa
red with the time of growth of the toroidal rim\,
the edge of the lamella breaks into very tiny drop
s\, of sizes comparable to that of the thickness o
f the rim. \nFor impact velocities larger than th
e critical splash velocity and making use of a one
dimensional approximation describing the ﬂow in th
e 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 ejected drops
. The predictions of the model are in good agreeme
nt with experiments.
LOCATION:Open Plan Area\, BP Institute\, Madingley Rise CB3
0EZ
CONTACT:Catherine Pearson
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