Chapter 3 Colloids and Fine Particles

7/21/2019 Chapter 3 Colloids and Fine Particles

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Brownian motion

Illustration of the random walk of a Brownian particle.

The distance the particle has moved over a period of time is L

Robert Brown (1827)

Thermal energy fromenvironment causes the

molecules of the liquid to

vibrate.

These vibrating

molecules collide

with each other

and with the

surface of the

particles.


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x is the particle diameter

3kT

m

(Einstein, 1956)

f: friction coefficient = FD/U

k: Boltzmann constant = 1.381 x 10-23J/K

Extension to 3D case:

tL 6

2

2

1

2

3mvkT

Random thermal energyIgnoring drag, collision and other factors

Based on statistical analysis of 1-D random walk to determine root mean square

distance traveled.


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Surface forces

dVF

dD


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Van der Waals Forces

A group of

electrohydrodynamicinteractions that occur

between the atoms in

two different particles.


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Notation used to indicate the type of

material for each particle and the

intervening medium

Dielectric properties of medium 2 is between materials 1 & 3.


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Electrical double layer forces


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Number density per unit area of neutral (M-OH), positive (M-OH2+)

and negative (M-O-)surface sites as a function of pH


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-13.29 [ ] (nm )c

2

EDL 0 0

D

V x e

A measure of the counterion cloud (thus the range of the repulsion)

is the Debye length , k-1

Approximate EDL potential energy


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Zeta potential of alumina particles as a function of pH and salt concentration


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Adsorbing polymers, bridging and steric forces

Schematic representation of (a) bridging flocculation and (b) steric repulsion

i i f


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Net interaction force DLVO Theory:


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Result of surface forces on behaviour in air and water


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Influences of particle size and surface forces on

solid/liquid separation by sedimentation

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P f

kTt

g x

m

223 18

P f x gkT

L t tx

m m


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Suspension rheology


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Relative viscosity ( ) of hard sphere silica particle

suspensions (black circles) and Einsteins relationship (line)

/s l

m m

Einstein (1906), < 7% volume solids)

Batchelor (1977), 7-15%, volume solids


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The transition from Brownian dominated random structures to preferred flow structuresas shear rate is increased is the mechanism for the shear thinning behaviour of

concentrated suspensions of hard sphere colloids


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Repulsive forces

Influences of surface forces on suspension flow

eff

volume of solid + excluded volume

total volume


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Attractive forces


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Force versus separation distance curves for alumina particles


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Force versus separation distance curves for oil droplets

Chapter 3 Colloids and Fine Particles

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