Turbulence in Microchannels

Synonyms

Friction factor in microchannels; Pressure drop in microchannels; Transition in microchannels

Definition

Fluid flows can be generally described as being either laminar or turbulent. As opposed to laminar flows, in which the fluid moves in smooth layers (or laminae), turbulent flows are characterized by chaotic motion of fluid elements and seemingly random fluctuations in instantaneous velocities. One result of the chaotic fluid motion in turbulent flows is a tremendous increase in heat and mass transfer compared to laminar flows.

Overview

The governing equations for viscous fluid flow are conservation of mass (or continuity) and the Navier-Stokes equations (conservation of momentum or Newton’s Second Law applied to a fluid). For steady-state, incompressible flow, these equations can be written as

$$ \nabla \cdot \mathbf{u}=0 $$

(1)

$$ \rho \left(\mathbf{u}\cdot \nabla \right)\mathbf{u}=-\nabla p+\mu {\nabla}^2\mathbf{u} $$

(2)

where u is the velocity, ρ is the fluid density, p...