lecture 2 wetting and adhesion - colloidal dispersions · acs© 2007 lecure 2 - wetting and...

ACS© 2007

Wetting and adhesion

Lecture 2

Lecure 2 - Wetting and adhesion 1ACS© 2007

Surface tension is a pull


The Molecular Origin of Surface Tension

The molecules at the liquid surface are pulled towards the bulk liquid. To expand the surface requires work. The work is the surface tension times the change in area.


Thermodynamics for surfaces

F AσΔ = Δ

The free energy (work at constant temperature) to compress a gas is:

Where σ is the surface tension.

Δ = ΔF p V

The free energy to stretch a surface is:

When ΔF is negative, the process is spontaneous.

When ΔF is positive, the process reverses.


Coalescence of Droplets

The change in energy is:+

( ) 0

final initial

final initial

F F FA AA

σσ

Δ = −

= −

= Δ<

Therefore the drops coalesce spontaneously.


Coalescence of Droplets with Emulsifier

+

When droplets covered with emulsifier coalesce, some emulsifier must be desorbed. This requires work.

work of desorptionF AσΔ = Δ +

If the emulsifier is strongly adsorbed, the work to remove it is large, and the drops do not coalesce.


Spreading

The energy change per unit area for liquid 2 (top) to spread across the surface 1 (bottom) is:

2 12 1( )F σ σ σΔ = + −

Surfactants reduce the two terms positive terms allowing the drop to spread.


Detergency

Holmberg et al. pp 474-5.

Requires only that the energy of surfactant adsorption is greater than the energy of the new liquid surface created.

Also requires that the surfactant lower the new solid/liquid interface to be less than the previous solid/oil interface.

Requires spontaneous absorption of oil into micelles.


Liquids have different contact angles on different solids


Contact angles: Liquids on solids

The contact angle of 140o is the same for each drop, independent of drop size.

The observation is that the contact angle depends on the materials but not the particular geometry.

Mercury drops on glass.*

Drops vary in size from 4 to 24 grains (1 grain = 64.8 mg)

* Bashforth and Adams, 1883.


The equation for contact angles

σ σ θ σ

σ σ σ θ

= +

− =

cos or

cos

sv lv sl

sv sl lv

The Young-Dupré introduces the idea of a solid surface/vapor surface tension, σsv and a solid/liquid interfacial tension, σsl. The contact angle, q, is independent of the geometry.

σsv

σlv

σslθ

The idea is that the three tensions are balanced:

A sessile liquid drop on a solid:


Works of Cohesion and Adhesion

σsl

σlvσsv

σσ

σ σ σ= + −adhsv lv slW

σ= 2cohW

The work of adhesion is the separation to create two new surfaces from one interface:

The work of cohesion is the separation to create two new surfaces.

Using the Young-Dupré equation: σ θ σ= +cosadhlv lvW


Large surface heterogeneities - contact angle hysteresis

Advancing liquids are held up by low energy spots and show high contact angles.

Receding liquids are held by high energy spots and show low contact angles.

High energy spots –low contact angles.

Low energy spots –high contact angles.


Motion of liquids due to surface energies

Capillary flow –

Motion as a consequence of shape.

Key idea: pressure drop across a curvedsurface

Marangoni flow –

Motion as a consequence of variation insurface tension.


Pressure drops across a curved surface

R1

R2

x x+dx

dz

y

y+dy

1 2

1 1Lp

R Rσ

⎛ ⎞Δ = +⎜ ⎟

⎝ ⎠

The pressure is larger on the concave (inside) of the curved surface.

The Laplace equation:

R1 and R2 are the radii of curvature.


Capillary rise

The final position is determined by 2 principles:(1) The pressure drops across curved interfaces.(2) The pressure in the liquid must be the same at the same depth.

In the final state the pressure drop across the AC interface equals the hydrostatic pressure from C to B.

2 c o sL g hR

σ θ ρ=


Capillary rise is another example of Laplace pressure


Bubbles are difficult to nucleate


“Controlled” nucleation of bubbles


Ostwald Ripening

The pressure inside > pressure outside2prσ

Δ =

This equation implies that in an emulsion with a range of drop sizes or a foam with a range of bubble sizes, material diffuses from small drops to large drops.

Also, this equation implies that bubbles are difficult to nucleate.


The Kelvin Equation

2ln m

o

P VP rRT

σ⎛ ⎞=⎜ ⎟

⎝ ⎠

0

2ln mc Vc rRT

σ⎛ ⎞=⎜ ⎟

⎝ ⎠

Similarly, the “curvature” of small particles changes the solubility:

Both these effects cause Ostwald ripening.

The curvature of small drops changes the vapor pressure:


Marangoni Flow

Marangoni flow –

flow resulting from local differences in surface tension.

Causes of Variation in Surface Tension –

Local temperature differences.

Local differences in composition due todifferential evaporation.

Electric charges at surfaces.

Local compression or dilatation ofadsorbed films.


Liquid will flow away from a low surface tension region


Liquid flows to the higher surface tension


“Tears of Wine”

σ+

σ

EthOH/H O2


Flow due to surface tension differences


Liquid flows away from a hot spot


Liquid flows to a cold spot

lecture 2 wetting and adhesion - colloidal dispersions · acs© 2007 lecure 2 - wetting and...

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