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## Applications of Interfacial Phenomena

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### For nanoscale roughness, radius of asperity is small and sphere/surface term dominates. ... Asperity. Sphere/ Surface. PERC Model of Adhesion. RMS1,2 and 1,2 ... – PowerPoint PPT presentation

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Title: Applications of Interfacial Phenomena

1
• Applications of Interfacial Phenomena
• Applications Powder flow

2
• Work of COHESION, W11
• Energy needed to separate two identical surfaces
from contact to infinite separation
• 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
For rigid incompressible spheres the force of
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

pressure
equilibrium
6
DMT Mechanics
• Derjaguin, Muller, Toporov 1975
• Applies to high modulus, low adhesion, small
• Sphere/plate geometry remains Hertzian (same
functional form as Hertz but with initial
• 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
• Sphere/plate geometry not constricted to be
Hertzian
• Upon pull-off a neck forms between adhering
• 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
101 mN/m
Both theoretical approaches for smooth surfaces
10
Sphere/ Asperity
Sphere/ Surface
For nanoscale roughness, radius of asperity is
small and sphere/surface term dominates.
11
RMS1,2 and ?1,2 determined experimentally.
12
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.
• 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
increased
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.