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Colloid chemistry - Chapter 7: Kinetic properties of colloids - Ngo Thanh An

· D is known as the diffusion coefficient (area per unit time).

· The negative sign is because diffusion occurs in the direction of decreasing concentration.

Let us represent the gravity, buoyant and drag forces by Fg , Fb and Fd , respectively.

Let the mass of the particle be m, and its velocity relative to the fluid be v

The resultant force on the particle is Fg - Fb - Fd . The acceleration of the particle is dv/dt . Therefore, we can write the following force balance.

 

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Nội dung text: Colloid chemistry - Chapter 7: Kinetic properties of colloids - Ngo Thanh An

  1. 1. Brownian motion
  2. 2. Diffusion Diffusion coefficient/ diffusivity No. of atoms dn dc crossing area A = −DS Cross-sectional area per unit time dt dx Concentration gradient Matter transport is down the concentration gradient Fick’s I law Flow direction A • D is known as the diffusion coefficient (area per unit time). • The negative sign is because diffusion occurs in the direction of decreasing concentration.
  3. 2. Diffusion
  4. 3. Sedimentation • By Archimedes’ principle, the buoyant force is the product of the mass of fluid displaced by the particle and the acceleration under gravity. m g Fb = p where ρ is the density of the liquid and ρp is the density of the particle. The drag force on the particle is given by Stokes’ law Fd = 3 vd = 6 vr
  5. 3. Sedimentation 4 m = r 3 3 2r 2 g( − ) dx v = p = t 9 dt
  6. 3. Sedimentation
  7. 3. Sedimentation dx dC At equilibrium: CS = −DS dt dx 2 dx 2r g( p − ) Where: = dt 9 RT D = 6 rN A 4 3 R dC r g( p − )dx = − T 3 N A C dC V g( − )dx = −kT p p C
  8. 4. Osmosis
  9. 4. Osmosis
  10. 4. Osmosis
  11. 5. Viscosity Einstein developed an equation of flow applicable to dilute colloidal dispersions of spherical particles:  = o (1 + 2.5 ) o = viscosity of the dispersion medium  = viscosity of the dispersion medium when the volume fraction of colloidal particles is The volume fraction is defined as the volume of the particles divided by the total volume of the dispersion. 8 January 2023