Colloids
Lecture 03
Soft Condensed Matter (Spring 2019) Instructor: Jihoon Choi 100
Colloidal Dispersion
• Colloidal dispersion: a heterogeneous system in which particles of solid or droplets of liquid with dimensions of order 10 um or less are dispersed in a liquid medium.
(e.g., paints, inks, mayonnaise, ice cream, blood, milk, etc.) (1) Extremely high area of interface
for 1kg of polymer spheres (r = 200 nm), the total surface area ~ 15,000 m2
→
substantial amount of interfacial energy
→
→ why do not combine to form larger aggregates to reduce this interfacial energy ? (2) Questions
→ how about gravity ?
→ how about density ? (3) Brownian motion
(4) Increase of viscosity (5) Non-Newtonian
Soft Condensed Matter (Spring 2019) Instructor: Jihoon Choi 106
A Single Colloidal Particle in a Liquid
If one takes a solid sphere and drops it in a fluid, it accelerates under gravity until the drag force balances the gravitational force and it attains terminal velocity. The mechanism causing the drag depends on the value of a dimensionless group called the Reynolds number.
• Reynolds number (Re) for a sphere of radius a moving with velocity v in a liquid of viscosity η and density ρ
Re = η ρva
predict flow patterns in different fluid flow situations
→
George Stokes Osborne Reynolds
The concept was introduced by George Gabriel Stokes in 1851,[2] but the Reynolds number was named by Arnold Sommerfeld in 1908[3] after Osborne Reynolds (1842–1912), who popularized its use in 1883.
Reynolds Number
Soft Condensed Matter (Spring 2019) Instructor: Jihoon Choi 113
F
d= 6πηav
F
g=
3 4 πa
3∆ρg
v
t=
9η 2a
2∆ρg
• For colloidal particles with lower velocities and larger viscosities, direct viscous effects increasingly dominate, leading to very low Re.
• For an isolated sphere whose density differs from the density of the liquid by ∆ρ, the gravitational force Fd is given by
A Single Colloidal Particle in a Liquid
• In this viscous-dominated regime, the drag force Fs is given by Stokes’ Law
• The terminal velocity vt, when the drag force is balanced by the gravitational force
• Brownian motion (by botanist, Robert Brown)
Many Colloidal Particles in a Liquid
This motion was discovered in 1827 while looking at plant pollen under the microscope. Each particle moves about with a continuous but random jiggling motion.
Colloidal particles are constantly bombarded by the random impacts of the molecules of the liquid. Because these collisions are random, in the long run the total force acting on the particle is zero, but at any one time there will be more collisions on one side of the particle than another and the result is that there is a constantly fluctuating net force.
How can this Brownian motion of a particle be characterized ?
→ Random walk
Clarkia pulchella
pollen
Soft Condensed Matter (Spring 2019) Instructor: Jihoon Choi 115
Many Colloidal Particles in a Liquid
D = ξ k
BT ξ = 6πηa
• In this viscous-dominated regime, the drag force Fd is given by Stokes’ Law
• Drag coefficient ξ
• Assume that there is a drag force on the particle proportional to the velocity
F
d= 6πηav
• The motion of the particle is diffusive, with a diffusion coefficient D given by the Einstein relation
• For the case of a sphere diffusing in a liquid, Stokes-Einstein equation
