Diffusion coefficient of spherical Brownian particles from temperature and dynamic viscosity

Brownian motion is the random motion of microscopic visible suspended particles of a solid substance in a liquid or gas caused by the thermal motion of particles of a liquid or gas. The diffusion coefficient is a quantitative characteristic of the diffusion rate, equal to the amount of matter passing per unit time through a section of a unit area as a result of the thermal motion of molecules with a concentration gradient equal to one (corresponding to a change from \(1 \frac{\text{mol}}{\text{L}}\) to \(0 \frac{\text{mol}}{\text{L}}\) per unit length). The diffusion coefficient is determined by the properties of the medium and the type of diffusing particles. This law is also known as the Stokes—Einstein—Sutherland relation.

Notation:

1. \(R\) (R) is molar_gas_constant.

2. \(N_\text{A}\) (N_A) is avogadro_constant.

Conditions:

1. Particle displacements are equally likely in any direction.

2. The inertia of a Brownian particle can be neglected compared to the influence of friction forces.

3. Particles are spherical.

4. Low Reynolds number, i.e. non-turbulent flow.

Links:

1. Wikipedia.

diffusion_coefficient

diffusion_coefficient of the particles.

Symbol:

D

Latex:

\(D\)

Dimension:

area/time

temperature

temperature of the system.

Symbol:

T

Latex:

\(T\)

Dimension:

temperature

particle_radius

radius of the particles.

Symbol:

r

Latex:

\(r\)

Dimension:

length

dynamic_viscosity

dynamic_viscosity of the particles.

Symbol:

mu

Latex:

\(\mu\)

Dimension:

pressure*time

law

D = R * T / (6 * N_A * pi * r * mu)

Latex:

\[D = \frac{R T}{6 N_\text{A} \pi r \mu}\]