text: Mathematically, lubrication theory can be seen as exploiting the disparity between two length scales.  The first is the characteristic film thickness, , and the second is a characteristic substrate length scale .  The key requirement for lubrication theory is that the ratio  is small, that is, .
  The Navier–Stokes equations (or Stokes equations, when fluid inertia may be neglected) are expanded in this small parameter, and the leading-order equations are then
  where  and  are coordinates in the direction of the substrate and perpendicular to it respectively. Here  is the fluid pressure, and  is the fluid velocity component parallel to the substrate;  is the fluid viscosity.  The equations show, for example, that pressure variations across the gap are small, and that those along the gap are proportional to the fluid viscosity.  A more general formulation of the lubrication approximation would include a third dimension, and the resulting differential equation is known as the Reynolds equation.       
  Further details can be found in the literature or in the textbooks given in the bibliography.