Surface Tension and Energy

Question 1

Surface Tension

Answer 1

y

1. Contracting force per unit length along perimeter of a surface
2. Work required to create a new unit area of a liquid
3. Specific surface energy - excess surface free energy per
   unit area
4. Restoring force to resist increase in area

γ = force/length or surface energy/area (i.e., ΔW/ΔA)

Question 2

Slider and Floating Needle

Answer 2

Moving slider does work to create new surface

W = Fslider.∆l = 2.γ.L.∆l = γ.∆A (where ∆A = 2.l.∆l)

Question 3

Capillary Action

Answer 3

Water-glass: adh>coh, wetting, 0ᵒ < θ < 90ᵒ

• Thermo: Adhesive force vertical component = weight
  
  • F=γ*circumf=γ*2pi*r
  • m=p/V
  • V=pi*r^2*h
• Mechanics: Pressure lower in liquid than gas phase
  
  • ΔP = 2γ/R=(2γcosθ)/r
  • ΔP must equal the hydrostatic pressure drop in capillary = ρΔhg = (2γcosθ)/r

Mercury-glass:coh>adh, dry, 90ᵒ < θ < 180ᵒ

Question 4

Pressure inside drop of liquid

Answer 4

Pi - Po = 2γ / R

Surface tension contracts the balloon. To counteract this tendency, the balloon has a greater interior air pressure acting to expand the balloon.

Question 5

Spreading coefficient

Answer 5

Question 6

Young’s Equation

Answer 6

Can’t measure γSG or γSL experimentally - need multiple liquid probe to estimate (Zisman).

Assumptions

• Solid surface is rigid and non-deformable
• Solid surface is immobile and cannot reorient in
  response to liquid probe
• Solid surface is typically smooth (tested with AFM)
• Homogeneous and uniform
• Liquid phase is known and remains constant
• Liquid vapor does not adsorb on the solid surface to
  change free energy - gass bubbles?

Susceptible to

• Roughness
  
  • Wetting or de-wetting amplified
  • Increases SA, increases tension of surface in adhesion forces, increases wettability, decreases angle
• Contamination
  
  • Grease film presence will increase angle and hydrophobicity
• Hysteresis
  
  • Heterogeneities and rearrangments
• Uneven spreading of liquid
  
  • Anisotropy and higher energy directions

Question 7

Zisman Method

Answer 7

Critical surface tension (γC) for a solid

• Zisman Plot: Plot contact angles (θ or cos θ) against surface tensions of the probe liquids
• γLV = Linear plot
• Extrapolate line to θ=0ᵒ (i.e., complete spreading)
• Critical surface tension (γc) of the solid surface is equal to the liquid surface tension where θ = 0ᵒ (i.e., cos θ = 1).

Finding γSL given assumption that γSG=γLG, the liquid and solid have interfacial tension γSL=0 (polymer solid, liquid saturated hydrocarbons)

• This is principle of critical surface tension of wetting

Question 8

γc with Bio-response

Answer 8

Question 9

Wenzel Eq

Answer 9

On rough surgfaces

• angle on rough surface increases if hydrophobic
• angle on rough surfaces decreases if hydrophilic

amplification

Can be done through sandblasting, measured by AFM

Question 10

Cassi-Baxter Eq

Answer 10

Accounts for surfaces made of two different materials (chemically heterogeneous - air pockets formed by roughness)

• if a water droplet does not entirely wet the rough surface and leaves pockets of air between the droplet and the substrate, then the observed contact angle is influenced by the fraction f of the droplet that is actually in contact with the surface

f2 is fraction in air, f1 fraction in contact with surface, theta-1 is observed angle

Question 11

Plasma treatment

Answer 11

Plasma treatment

• Increas surface energy
• Gas (O2 or N2) disrupts molecules and creates a free radical layer
• Particles implanted on surface to promote reactivity

Question 12

Glass Functionalization (silanization)

Answer 12

• Surface reaction yields strong – Si-O-Si bonds and
  ethanol in this case
• Amine groups are now available on the glass surface
  to undergo additional reactions
• Can modify the surface with higher/lower energy
  groups

Question 13

SAMs

Answer 13

Hydrophilic head group, H-C tail and function group R

Can be switchable and change structure with temperature

Question 14

Young-Laplace Pressure

Answer 14

Relates the pressure difference (ΔP ) across the surface of a liquid to the surface curvature and liquid surface tension(γ) for the radius of curvature in directions 1 (R1) and 2 (R2).

ΔP = γ (1/R1 + 1/R2)

Surface tension balances the outward force due to wall pressure difference, or the surface tension tends to compress the droplet, increasing the internal P

Question 15

Cylinder

Answer 15

R2 is infinity and the 2nd term goes to 0 as cylinder is thin

Question 16

Cylinder Radius

Answer 16

Question 17

Laplace derivation

Answer 17

Question 18

Sphere

Answer 18

Air bubble in water

Question 19

Soap bubble

Answer 19

Soap bubble has 2 liquid-air interfaces so twice the surface tension.

γ = P*r / 4

Question 20

Surface tension measurement

Answer 20

Dynamic sessile drop:

• determines the largest contact angle possible (advancing angle) without increasing its solid/liquid interfacial area by adding volume dynamically.
• Volume is removed to produce the smallest possible angle, the receding angle.
• The difference is the contact angle hysteresis
• The method is used especially with super hydrophobic samples, as this is the only practical method for such a high contact angle substrate.
• Multiple droplets can be deposited in various locations on the sample to determine heterogeneity

Tilt technique:

• A drop is dispensed on a level surface, and the surface is then tilted from 0° to 90°.
• As the tilt increases the downhill contact angle will increase and represents the advancing contact angle while the uphill side will decrease; this is the receding contact angle.

Capture bubble technique:

• The contact angle is measured between an air bubble of defined volume and the solid surface immersed in the temperature controlled bath.

Question 21

Capture bubble technique for contact angle

Answer 21

Capture bubble technique:

• The contact angle is measured between an air bubble of defined volume and the solid surface immersed in the temperature controlled bath.

Question 22

Capillarity force balance

Answer 22

Question 23

Equation for any curved surface

Answer 23

Question 24

Aneurysms

Answer 24

Question 25

Needle sessile drop for contact angle

Answer 25

Dynamic sessile drop: * determines the largest contact angle possible (advancing angle) without increasing its solid/liquid interfacial area by adding volume dynamically. * Volume is removed to produce the smallest possible angle, the receding angle. * The difference is the contact angle hysteresis * The method is used especially with super hydrophobic samples, as this is the only practical method for such a high contact angle substrate. * Multiple droplets can be deposited in various locations on the sample to determine heterogeneity

Question 26

Tilting for Contact Angle

Answer 26

Tilt technique: * A drop is dispensed on a level surface, and the surface is then tilted from 0° to 90°. * As the tilt increases the downhill contact angle will increase and represents the advancing contact angle while the uphill side will decrease; this is the receding contact angle. * The advancing and receding angles are measured at the point at which the droplet starts to move on the substrate. * At the same point, the roll-off angle can be defined. * The method allows for the mapping of the substrate but is often criticized as the size of the drop can have an impact on the measured values.

Question 27

Capture bubble technique for contact angle

Answer 27

Capture bubble technique: * The contact angle is measured between an air bubble of defined volume and the solid surface immersed in the temperature controlled bath.