Applications of Interfacial Phenomena

1

• Applications of Interfacial Phenomena
• Adhesion between surfaces-

• Models of adhesion
• Capillary adhesion
• Applications Powder flow

2
Adhesion of Surfaces

• Work of COHESION, W11
• Energy needed to separate two identical surfaces
  from contact to infinite separation
• Work of ADHESION, W12
• Energy needed to separate two dissimilar
  surfaces from contact to infinite separation
• Units of energy per unit area (mJ/m2 erg/cm2)

3
Van der Waals Approach to Adhesion
Considering only van der Waals attraction, what
is the energy of adhesion between two1 mm
particles with A 10-19 J. H H0 ? 3Å
What if the particles were separated by 10 nm
4
Adhesion and Surface Energy
For rigid incompressible spheres the force of
adhesion is related to the work of adhesion by
Derjaguins approximation where R1 and R2 are
the radii of the spheres. Upon further
application for identical materials F
2pRgSL two spheres in liquid F 2pRgSG two
spheres in vapor F 4pRgSL sphere and plate in
liquid F 4pRgSG sphere and plate in
vapor Unfortunately deformation needs to be
considered for many materials.
5
Hertzian Mechanics

• Derived in 1888
• Assumes no Surface Forces (limit g ? 0)
• Describes the elastic resistance of the surface
  to a sphere being pushed (or pulled) into it.
• REPULSIVE
• NO ADHESION PREDICTED

pressure
equilibrium
6
DMT Mechanics

• Derjaguin, Muller, Toporov 1975
• Applies to high modulus, low adhesion, small
  radii of curvature systems
• Sphere/plate geometry remains Hertzian (same
  functional form as Hertz but with initial
  loading, from surface forces)
• At equilibrium attractive surface forces balanced
  by repulsive Hertzian force
• DMT result coincides with a non-deformable sphere

equilibrium
pull-off
7
JKR or JKRS Mechanics

• Johnson, Kendall, Roberts, Sperling 1964, 1971
• Applies to low modulus, high adhesion, large
  radius of curvature systems
• Sphere/plate geometry not constricted to be
  Hertzian
• Upon pull-off a neck forms between adhering
  surfaces resulting in adhesion hysteresis
• Note Predicted force of adhesion is 75 of that
  predicted by DMT model

equilibrium
pull-off
8
Remarks

• Approach only predicts adhesion after contact of
  surfacesNo long range attraction.
• When evaluating adhesion between other
  geometries, the Derjaguin approximation is
  commonly applied.
• Is this valid for JKR?
• Several models exist that predict adhesion
  between that of JKR and DMT (25 difference) but
  uncertainty in g usually much larger.
• Result is that g often used as a fitting
  parameter.

9
Effect of Roughness
Force of adhesion between silica sphere/silicon
surfaces
van der Waals Prediction Fad/R A/(6H02) 185
mN/m Hamaker constant (A) 1x10-19 J Minimum
separation distance (H0) 3 Å Johnson-Kendall-Rob
erts (JKR) Prediction Fad/R 3?W12 282-688
mN/m Surface energy (W12) 30-73
mJ/m2 Experimentally Measured Adhesion Fad/R
101 mN/m
Both theoretical approaches for smooth surfaces
overestimate the measured adhesion force.
10
RUMPF Model of Adhesion
Sphere/ Asperity
Sphere/ Surface
For nanoscale roughness, radius of asperity is
small and sphere/surface term dominates.
11
PERC Model of Adhesion
RMS1,2 and ?1,2 determined experimentally.
12
Capillary Adhesion
Masuda and Gotoh in Powder Technology Handbook,
Eds.Gotoh, Masuda, Higashitani, p. 140
13
Capillary Adhesion -- Kelvin Equation --
r1 radius of capillary (meniscus), T
temperature, k Boltzmanns constant ?
relative humidity, q contact angle d 2r1cosq
for small r2 VM molar volume of water ?
surface tension of water NA Avogadros number
Radius of capillary and onset of capillary force
defined by Kelvin equation. r1 1 nm
14
Capillary Adhesion -- Laplace Equation --
R
r1
d
r2
Sphere/Plate
Sphere/Sphere
? surface tension of water ? contact angle
Limitations There is no dependence on the radius
of the capillary or relative humidity
15
Critical Humidity -- Effect of Roughness --
R
r
The relative humidity needed to produce
capillary forces expected to increase with
roughness.
16
Critical Humidity -- Effect of Roughness --
Critical humidity for capillary forces increases
with increasing roughness
17
Application Powder Flow
18
Industrial Issues

• Approximately 60 of plants worldwide handle
  powders.
• Plants handling solids perform poorly than
  gas/liquid plants.
• Plants handling powders operate at 50 of design
  
• capacity. (1/5)th of these plants fail to
  attain more than 20 of the design capacity.
• Poor performance mostly attributed to powder
  flow problems.

19
Flowability

• Acceptable flowability varies depending on the
  final product (e.g. pharmaceutical capsules,
  salt, sugar, pigments)
• Acceptable fluidity if material can be handled
  in standard equipment without extra effort.

• Flowability generally improves with increasing
  particle size and narrower size distribution.

20
Caking Formation of Weak, Irregular
Aggregates

• Reasons for Caking
• High solubility at ambient temperature results
  in solid neck formation between particles.

• High moisture adsorption.
• Irregular crystal shape.
• Smaller particles or presence of fines.

21
Prevention of Caking in Detergent Manufacture

• Detergents in form of flakes, powders (produced
  by spray drying) have sulfo-fatty acids (8-24
  carbon atoms per molecule) to prevent moisture
  adsorption in order to promote free flow.
• Non-ionic surfactants in liquid form are dried
  with carrier particle (micron sized silica
  particles) to achieve dry free flowing detergents.

22
Cohesive Strength
Defined as ability of a bulk solid to resist
shear forces.

• Factors Affecting Cohesive Strength
• van der Waals bonds.
• Moisture (capillary forces)
• Mechanical interlocking of particles
• Chemical reactions

• Measurement
• Jenike biaxial shear tester
• Biaxial rotational cells
• Uniaxial testers

23
Cohesive Strength and Effect on Powder Flow in
Hoppers
Arch of powder with strong cohesive forces may
prevent flow of powders in hoppers
24
Segregation - Variation in Bulk Density -
Variation in Chemical Composition -

• Less problem of segregation in small powders lt
  30 mm
• (no relative motion of particles due to high
  cohesive strength)

Control of Segregation using Ordered/Interactive
Mixtures

• Small particles (lt5 mm) adhered to large carrier
  particles.

• Control particle size and interparticle forces
  (van der Waals, capillary) in order to form good
  mixtures.
• Used in pharmaceutical applications.

25
Role of Capillary Forces in Powder Flow Liquid
Binders (oil) for Reducing Segregation Tendency
26
Introduction

• Addition of liquid binder (oil) leads to
  increased
• adhesion, thereby overcoming segregation
  tendencies.

• Initiation of flow of powders is
• characterized by the measurement
• of the unconfined yield strength.
• A correlation between the measured capillary
  force
• and the unconfined yield strength of the bulk
  powder
• would facilitate enhanced understanding of
  powder
• flow behavior.

27
Effect of Oil Content on FC of Quartz
An optimal dosage of oil dictates the maximum
yield strength attainable.