# Stokes-Einstein Equation

on . Posted in Fluid Dynamics

Stokes-Einstein equation, abbreviated as SE, is a fundamental relationship in physics and physical chemistry that relates the diffusion coefficient of a particle to its temperature, viscosity of the surrounding medium, and the particle's radius.  The Stokes-Einstein equation is particularly useful for understanding the Brownian motion of small particles suspended in a fluid.  Brownian motion is the random motion of particles as they collide with surrounding molecules.  The equation helps to quantify how fast these particles diffuse through the medium, with smaller particles diffusing more rapidly than larger ones.

The equation has applications in various fields, including chemistry, biology, and nanotechnology, where it is used to predict and understand the movement of particles and molecules in different environments.  It provides valuable insights into the behavior of colloids, nanoparticles, and other small entities in solution.

## Stokes-Einstein Equation

$$\large{ D = \frac{ k_b \; T }{ 6 \; \pi \; \mu \; r } }$$
Symbol English Metric
$$\large{ D }$$ = diffusion coefficient $$\large{lbf}$$ $$\large{N}$$
$$\large{ k_b }$$ = Boltzmann constant $$\large{\frac{lbm-ft^2}{sec^2}}$$ $$\large{\frac{kJ}{molecule-K}}$$
$$\large{ T }$$ = temperature $$\large{F}$$ $$\large{K}$$
$$\large{ \pi }$$ = Pi $$\large{3.141 592 653 ...}$$
$$\large{ \mu }$$ (Greek symbol mu) = dynamic viscosity $$\large{\frac{lbf-sec}{ft^2}}$$ $$\large{Pa-s}$$
$$\large{ r }$$ = radius of spherical parcticle $$\large{in}$$ $$\large{mm}$$ Tags: Soil Diffusion