Surface Tension
Spring 2004 BIOEN 301
Extra bonus lecture!
WILL NOT BE ON FINAL!
more bugs that think they’re all that and a bag
of chips: the
Water Strider
Water striders are light (like ants)
thus don’t “break” surface
http://encarta.msn.com/encnet/refpages/RefMedia.aspx?refid=461560390
Even a piece of steel can do this trick
if it is small (steel
~ 8x water)
4 H
2
O
molecules
separated in
space from
each other
have partial
+ and –
charges
what would
they do???
4 H
2
O
molecules
they clump
together
+ and –
charges
snuggle up
close
potential
energy of
system has
Surface Tension
http://hyperphysics.phy-astr.gsu.edu/hbase/surten.html
water in bulk has
many binding partners
water at surface
has less, has
exposed charges left over
potential energy
of water at
surface is higher
deforming
droplet to
Surface Tension
E = FX, energy =
force * distance
dE = F dX
F = dE/dX
e.g. spring
Surface Tension
creating surface
area in 20C water droplet takes
73 ergs/cm^2
droplet thus
seems springy
if mg << l it
Surface Tension
surface area in
20C water costs 73 ergs/cm2
Surface Tension
surface area in
20C water costs 73 ergs/cm2
F = dE/dX
can get from F
in this apparatus
if film is w by w
Surface Tension
Surface Tension
2 W2
(front and back
OK so remember this?
(steel
~ 8x water)
Floating without floating – The SECRET
OF THE STRIDERS REVEALED!!!
= 73 ergs/cm2 = 73 dyne-cm/cm2 = 73 dynes/cm
73 dynes/cm is also like a tear strength
if we stacked poker chips on water it might look like below
area of chip doesn’t matter so much as the edge (vertical
contributions)
lift = perimeter * * sin
Floating without floating
- is constant of water / air interface, so can’t just “choose” to
pull less
surface fails when tension along perimeter of chips exceeds 73
dynes/cm
after that, the water does something else more energetically
Incidentally – Scaling tie-in -
Why droplets are droplet-sized -
mass increases
faster than length or
area, so above
about 1 cm
diameter, water
droplet mg >
l, so
Floating without floating
- anyway so if the outlines of your feet are long enough for L to
“and your contact angle is high”?
need to push off water, not have it wick up onto you
Contact Angles
-Contact
Angle
here’s a slice of
it –
tangent to
droplet edge is
“contact angle”
why is theta
Contact
Angle
balance of
forces
surface tension
pulls up
gravity &
adhesion pulls
down
what are the
Remember this?
http://hyperphysics.phy-astr.gsu.edu/hbase/surten.html
water at surface
has less binding partners
energy at surface
What if
-http://hyperphysics.phy-astr.gsu.edu/hbase/surten.html
what if the circles
are aluminum atoms in a solid?
what if the space
Contact
Angle
F = dE/dX
surface/air &
surface/water
interfaces also have “surface tension”, in ergs/cm2
moving water edge
back and forth incurs energy costs/profits
but units of F are
Contact
Angle
problem is 3-D
surface tension is
force per length
each dL of
perimeter
contributes dL
force
F = dE/dX => dL
dE = dL dX = dA
Obtuse contact
Angles
hydrophobic
surface
“gravity &
adhesion” is
now “gravity &
repulsion”
if no gravity,
Contact
Angle
why doesn’t drop pull or
push itself along the surface?
it did when initially set
down, it distorted itself until equilibrium
reached
edge equilibrium is one
thing
equilibrium between
(roundness) & gravity (flatness) & surface coverage
surface adhesion energy
The water at
this
surface is at a
lower
potential energy than the bulk water, so
deformations that increase this surface area
Same thing as drop on surface,
different geometry
so fluid scoots along the surface until equilibrium reached
like water rising in a tube until forces add to mg
(gravity) = r2 h g
surface tension trying to pull water up tube rather than
round up a bead
equivalently - surface energies are being
minimized
Capillary action
the fluid meets the glass at an
angle
which depends on the
glass properties
the surface tension in the tube
acts around the perimeter 2
r
if surface tension is T, total
vertical force is 2
r T cos
equating forces gives
An example from nature - xylem
Current record holder
for world’s tallest tree
“Stratosphere Giant”,
sequoia, 112.6 m tall
this is a formidable
water head
can surface tension
And the
answer is…
xylem contact angle ~
50°
vessel diameters go
down to ~ 30 microns
h = 2 T cos
/ (r
g)
if T = 73 dyne/cm, r = 15
microns,
= 1 g/cm
3, g
= 981 cm/s
2, h = ??? …
h = 87 cm
ahem
Back to this -
http://hyperphysics.phy-astr.gsu.edu/hbase/surten.html
water at surface
has less binding partners
potential energy
of water at
surface is higher
what if we do
Hmm…
what
molecule is
that?
how does
surface
water energy
change?
what
happens to
surface
Soap!
this
particular
detergent
molecule is
SDS
(sodium dodecyl sulfate, minus the Na+)water happy,
SDS happy
tension
We now have COMPLETE POWER
OVER WATER STRIDERS!!!
simply add soap and they’re SCREWED!
HA HA!
