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

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!

Even a piece of steel can do this trick if it is small (steel ~ 8x water)

http://www.sita-messtechnik.de/englisch/oberfl/

4 H2O molecules

separated in space from each otherhave partial + and – charges

what would they do???

but what’s surface tension, really?

4 H2O molecules

they clump together

+ and – charges snuggle up close

potential energy of system has dropped

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

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 it

dominates and you can walk on water (Vogel pp 72, 104-109)

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 cm, how much area has been created?

Surface Tension

2 W2

Surface Tension

2 W2

(front and back side)

OK so remember this? (steel ~ 8x water)

http://www.sita-messtechnik.de/englisch/oberfl/

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?

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 –

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

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?

http://hyperphysics.phy-astr.gsu.edu/hbase/surten.html

water at surface has less binding partners

energy at surface is higher

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?

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 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

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 -

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…

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