Using a squeegee on a layer of viscous or viscoplastic fluid

We use lubrication theory to analyze the shape of the bow-wave ahead of a squeegee moving through a layer of viscous fluid like a bulldozer being used to clear up a large pool of spilt molasses or slurry. For a relatively long squeegee, the key is to find quasi-steady cross-sections normal to the squeegee, and then to determine their slow variation along the squeegee by considering the lateral flux required to divert the flow around the ends. Our simple flux-balance arguments can be straightforwardly adapted to squeegees of arbitrary shape and to other rheologies such as viscoplastic fluids.