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!

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 20C water droplet takes

73 ergs/cm^2

 droplet thus

seems springy

 if mg << _l it

Surface Tension

 surface area in

20C water costs 73 ergs/cm2

Surface Tension

 surface area in

20C 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!