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Brownian motion and diffusion in colloids

Dr. Dmitri Kopeliovich

Brownian motion is the seemingly random movement of particles suspended in a dispersion media caused by collision with its molecules.

Due to Brownian motion the colloidal particles are capable to move (diffuse) from the regions with higher concentration to the regions with lower concentration of the dispersed phase.

The diffusion flux according to the First Fick’s law:

J = - D ( ∂C/∂x )

where:
J – diffusion flux (quantity of material that crosses a plane of unit area perpendicular to the diffusion direction for time unit), mol/ (length2 *time);
D – diffusion coefficient or diffusivity of the dispersed phase, length2/time;
∂C/∂x – concentration gradient in the diffusion direction, mol/(length3 *length).

The diffusion coefficient for colloidal system:

D = kBT/(6πμr)

where:
kB - Bolzman constant (1.38*10-3 J/K)
T - temperature, K
μ - dynamic viscosity of the dispersion media, Pa*s
r - radius of the particles, m

Outside force applied to the colloidal particles causes their sedimentation towards the force direction.
Gravity force causes the dispersed particles to sedimentate to the bottom. Diffusion counteracting to any directed force prevents complete concentration of the dispersed phase at the bottom.
An equilibrium distribution of the dispersed phase with a slight gradient in the downwards direction is formed as a result of the opposing factors: gravity and diffusion.

Since the diffusion coefficient is lower for the grater particles the concentration gradient is smaller for the colloids with finer dispersed phase.

Most colloid systems are polydispersed - contain particles of various sizes. Since the larger particles sedimentate faster (selective sedimentation) the equilibrium distribution of the dispersed phase results in not only a gradient of the particles concentration but also in various particle size distribution: more larger particles at the bottom and more smaller particles in the upper levels of the system.

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brownian_motion_and_diffusion_in_colloids.txt · Last modified: 2013/06/01 by dmitri_kopeliovich
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