## Péclet Number

### Quick Start

The Péclet number for particulate systems is the ratio of flow effects to diffusion effects. It tells us whether particles are driven by flow (Pe>1) or by their own diffusion (Pe<1).

### Péclet Number

η cP
γ̇max /s
r nm

Whether particles are driven by shear flow or by diffusion is important in terms of their rheology. The Péclet number tells us which is more important. It depends on the particle radius r, the shear rate γ̇ and the diffusion coefficient D. D in turn depends on the viscosity of the liquid η and the Boltzmann energy kT, with T assumed to be 300K.

Pe = (r^2γ̇)/D = (6πr^3γ̇η)/(kT)

What this tells us is that most of the time and for most of our particles, Pe >> 1 so particle diffusion is irrelevant. This feeds into the Mode Coupling Theory app