Flows at Low Reynolds Number

Flows at low Reynolds numbers (Re) are characterized by the dominance of viscosity and are encountered in small channels, at low flow velocities and for very viscous fluids. The linear Stokes equation, which governs such flows, is valid because the non-linear convective term of the Navier–Stokes equation is negligible: several general properties of these flows (reversibility, additivity and minimum dissipation) result from this linearity. Unlike in Chapter 8, the geometry of these flows is arbitrary. Flows around small objects like in the suspensions of particles and in porous media (and the model Hele–Shaw cell) are important applications. Non-linear terms need to be taken into account at large distances and this leads to Oseen’s equation.