Brownian Motion Formula

In a fluid, the particles move in a random direction. These particles collide with each other when they move. Brownian Motion refers to the random movement of the small particles that are suspended in fluids.

The Formula To Calculate Diffusion Constant

\(\begin{array}{l}D=\frac{RT}{N_{a}6\pi \eta a} = \frac{k_{B}T}{6\pi \eta a}\end{array} \)


R is the gas constant

Na = 6.06 x 10 23 mol-1  referred to as Avogadro’s number

T is the temperature

η is the viscosity of the liquid

a is the radius of the Brownian particle

kB = R/NA is Boltzmans constant

Considering a large Brownian particle immersed in a fluid of much smaller particles (atoms). The radius of the Brownian particle is typically 10−9m < a < 5 × 10−7m.

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