 Normal-stress smallness in lubrication

For gap $h\ll \ell$ and speed $U$, shear stress scales as $\mu U/h$ and viscoelastic normal stresses as ${\psi }_i{U}^2/h^2$. Their force contributions scale respectively as $\mu U/h^2$ and ${\psi }_i{U}^2/(h^2\ell )$. Thus the displayed criterion permits neglecting the normal-stress corrections in the leading lubrication approximation. It is weaker than requiring the normal stresses themselves to be smaller than the shear stress. Rapid time dependence can impose an additional material-time criterion.