Squeegee lubrication model
= Squeegee lubrication model
{title2=$h_t-h_x=\nabla\cdot(h^3\nabla h)/3$}
A blade moving over a thin gravity-driven viscous film produces a moving-frame flux $\mathbf q=-h\mathbf e_x-h^3\nabla h/3$. Scaling film thickness by $h_0$ and horizontal distance by $\rho gh_0^3/(\mu U)$ yields this dimensionless volume-conservation equation. Fluid can escape beneath the blade or around its ends.