surface tension spring 2004 bioen 301 extra bonus lecture! will not be on final! f. reitz, ph.d.,...
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Surface Tension
Spring 2004 BIOEN 301
Extra bonus lecture!
WILL NOT BE ON FINAL!
F. Reitz, Ph.D., 6/2/04
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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
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Water striders are light (like ants) thus don’t “break” surface
http://encarta.msn.com/encnet/refpages/RefMedia.aspx?refid=461560390
• Ooh! Look at me! I have hydrophobic feet and I weigh less than Fritz does! I’m soooo great!
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Even a piece of steel can do this trick if it is small (steel ~ 8x water)
http://www.sita-messtechnik.de/englisch/oberfl/
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4 H2O molecules
separated in space from each otherhave partial + and – charges
what would they do???
but what’s surface tension, really?
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4 H2O molecules
they clump together
+ and – charges snuggle up close
potential energy of system has dropped
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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 increase surface area takes work
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Surface Tension
E = FX, energy = force * distance
dE = F dX F = dE/dX
e.g. spring energy = ½ kx2, dE/dX = kx = F
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Surface Tension
creating surface area in 20C water droplet takes
73 ergs/cm^2 droplet thus
seems springy if mg << l it
dominates and you can walk on water (Vogel pp 72, 104-109)
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Surface Tension
surface area in 20C water costs
73 ergs/cm2
= “ ”
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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 cm, how much area has been created?
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Surface Tension
2 W2
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Surface Tension
2 W2
(front and back side)
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OK so remember this? (steel ~ 8x water)
http://www.sita-messtechnik.de/englisch/oberfl/
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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 wait, why sin ? why not pull them all at 90 degrees?
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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 profitable –
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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 more likely to get torn apart by its own weight
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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
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“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”?...
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Contact Angles
here’s a droplet on a surface -
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Contact Angle
here’s a slice of it –
tangent to droplet edge is “contact angle”
why is theta theta?
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Contact Angle
balance of forces
surface tension pulls up
gravity & adhesion pulls down
what are the other two?
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Remember this?
http://hyperphysics.phy-astr.gsu.edu/hbase/surten.html
water at surface has less binding partners
energy at surface is higher
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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 above it is liquid ethanol?
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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?
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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
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Obtuse contact Angles
hydrophobic surface
“gravity & adhesion” is now “gravity & repulsion”
if no gravity, drop leaves
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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...
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surface adhesion energy
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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
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Same thing as drop on surface, different geometry
so fluid scoots along the surface until equilibrium reachedlike water rising in a tube until forces add to mg (gravity) = r2 h gsurface tension trying to pull water up tube rather than round up a beadequivalently - surface energies are being minimized
dE = F dX = dL dX = dA
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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)
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An example from nature - xylem
channels in plants that draw up water
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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?
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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 -
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h = 87 cm
ahem
apparently osmotic effects (root pressure, evaporation) dominate
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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 this…
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Hmm… what molecule is that?how does surface water energy change?what happens to surface tension?
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Soap! this particular detergent molecule is SDS (sodium dodecyl sulfate, minus the Na+)
water happy, SDS happy
tension reduced
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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