Surface Tension.ppt 987KB Jun 23 2011 10:23:54 AM
Surface Tension
Spring 2004 BIOEN 301
Extra bonus lecture!
WILL NOT BE ON FINAL!
F. Reitz, Ph.D., 6/2/04
more bugs that think they’re all that and a bag
of chips: the Water Strider
http://www-math.mit.edu/~dhu/Striderweb/striderweb.html
Water striders are light (like ants)
thus don’t “break” surface
• Ooh! Look
at me! I have
hydrophobic
feet and I
weigh less
than Fritz
does! I’m
soooo great!
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)
http://www.sita-messtechnik.de/englisch/oberfl/
4 H 2O
molecules
separated in
space from
each other
have partial
+ and –
charges
what would
they do???
but what’s surface tension, really?
4 H 2O
molecules
they clump
together
+ and –
charges
snuggle up
close
potential
energy of
system has
dropped
Surface Tension
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
increase surface
area takes work
http://hyperphysics.phy-astr.gsu.edu/hbase/surten.html
Surface Tension
E = FX, energy =
force * distance
dE = F dX
F = dE/dX
e.g. spring
energy = ½ kx2,
dE/dX = kx = F
Surface Tension
creating surface
area in 20C
water droplet
takes
73 ergs/cm^2
droplet thus
seems springy
if mg l, so
more likely to get
torn apart by its
own weight
Floating without floating
anyway so if the outlines of your feet are long enough for L to
add up to more than your weight (and your contact angle is
high) you too can walk on water
“and your contact angle is high”?
need to push off water, not have it wick up onto you
contact angle is a measure of hydrophobicity among other things
“other things”?...
Contact Angles
here’s a droplet on a surface -
Contact
Angle
here’s a slice of
it –
tangent to
droplet edge is
“contact angle”
why is theta
theta?
Contact
Angle
balance of
forces
surface tension
pulls up
gravity &
adhesion pulls
down
what are the
other two?
Remember this?
water at surface
has less binding
partners
energy at surface
is higher
http://hyperphysics.phy-astr.gsu.edu/hbase/surten.html
What if
what if the circles
are aluminum
atoms in a solid?
what if the space
above it is liquid
ethanol?
http://hyperphysics.phy-astr.gsu.edu/hbase/surten.html
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
energy/distance, not
area?! what’s the
deal?
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
back to ergs/cm2
Obtuse contact
Angles
hydrophobic
surface
“gravity &
adhesion” is
now “gravity &
repulsion”
if no gravity,
drop leaves
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
(adhesion/repulsion) is
another factor...
surface adhesion energy
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
are favorable and spontaneous
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
dE = F dX = dL dX = dA
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
h = 2 T cos / (r g)
An example from nature - xylem
channels in plants that draw up water
Current record holder
for world’s tallest tree
“Stratosphere Giant”,
sequoia, 112.6 m tall
this is a formidable
water head
can surface tension
really bring water from
the roots up to the top?
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/cm3, g
= 981 cm/s2, h = ??? …
drumroll please -
h = 87 cm
ahem
apparently osmotic
effects (root pressure,
evaporation) dominate
Back to this
water at surface
has less binding
partners
potential energy
of water at
surface is higher
what if we do
this…
http://hyperphysics.phy-astr.gsu.edu/hbase/surten.html
Hmm…
what
molecule is
that?
how does
surface
water energy
change?
what
happens to
surface
tension?
Soap!
this
particular
detergent
molecule is
SDS
(sodium dodecyl
sulfate, minus the
Na+)
water happy,
SDS happy
tension
reduced
We now have COMPLETE POWER
OVER WATER STRIDERS!!!
simply add soap and they’re SCREWED!
HA HA!
and so it is that we have the last laugh
Spring 2004 BIOEN 301
Extra bonus lecture!
WILL NOT BE ON FINAL!
F. Reitz, Ph.D., 6/2/04
more bugs that think they’re all that and a bag
of chips: the Water Strider
http://www-math.mit.edu/~dhu/Striderweb/striderweb.html
Water striders are light (like ants)
thus don’t “break” surface
• Ooh! Look
at me! I have
hydrophobic
feet and I
weigh less
than Fritz
does! I’m
soooo great!
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)
http://www.sita-messtechnik.de/englisch/oberfl/
4 H 2O
molecules
separated in
space from
each other
have partial
+ and –
charges
what would
they do???
but what’s surface tension, really?
4 H 2O
molecules
they clump
together
+ and –
charges
snuggle up
close
potential
energy of
system has
dropped
Surface Tension
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
increase surface
area takes work
http://hyperphysics.phy-astr.gsu.edu/hbase/surten.html
Surface Tension
E = FX, energy =
force * distance
dE = F dX
F = dE/dX
e.g. spring
energy = ½ kx2,
dE/dX = kx = F
Surface Tension
creating surface
area in 20C
water droplet
takes
73 ergs/cm^2
droplet thus
seems springy
if mg l, so
more likely to get
torn apart by its
own weight
Floating without floating
anyway so if the outlines of your feet are long enough for L to
add up to more than your weight (and your contact angle is
high) you too can walk on water
“and your contact angle is high”?
need to push off water, not have it wick up onto you
contact angle is a measure of hydrophobicity among other things
“other things”?...
Contact Angles
here’s a droplet on a surface -
Contact
Angle
here’s a slice of
it –
tangent to
droplet edge is
“contact angle”
why is theta
theta?
Contact
Angle
balance of
forces
surface tension
pulls up
gravity &
adhesion pulls
down
what are the
other two?
Remember this?
water at surface
has less binding
partners
energy at surface
is higher
http://hyperphysics.phy-astr.gsu.edu/hbase/surten.html
What if
what if the circles
are aluminum
atoms in a solid?
what if the space
above it is liquid
ethanol?
http://hyperphysics.phy-astr.gsu.edu/hbase/surten.html
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
energy/distance, not
area?! what’s the
deal?
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
back to ergs/cm2
Obtuse contact
Angles
hydrophobic
surface
“gravity &
adhesion” is
now “gravity &
repulsion”
if no gravity,
drop leaves
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
(adhesion/repulsion) is
another factor...
surface adhesion energy
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
are favorable and spontaneous
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
dE = F dX = dL dX = dA
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
h = 2 T cos / (r g)
An example from nature - xylem
channels in plants that draw up water
Current record holder
for world’s tallest tree
“Stratosphere Giant”,
sequoia, 112.6 m tall
this is a formidable
water head
can surface tension
really bring water from
the roots up to the top?
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/cm3, g
= 981 cm/s2, h = ??? …
drumroll please -
h = 87 cm
ahem
apparently osmotic
effects (root pressure,
evaporation) dominate
Back to this
water at surface
has less binding
partners
potential energy
of water at
surface is higher
what if we do
this…
http://hyperphysics.phy-astr.gsu.edu/hbase/surten.html
Hmm…
what
molecule is
that?
how does
surface
water energy
change?
what
happens to
surface
tension?
Soap!
this
particular
detergent
molecule is
SDS
(sodium dodecyl
sulfate, minus the
Na+)
water happy,
SDS happy
tension
reduced
We now have COMPLETE POWER
OVER WATER STRIDERS!!!
simply add soap and they’re SCREWED!
HA HA!
and so it is that we have the last laugh