The viscoplastic circular hydraulic jump

We examine theoretically the spread of a jet impacting on circular disk and hydraulic jump viscoplastic fluid Herschel–Bulkley type. The depth-averaging approach is employed in supercritical region, subcritical flow assumed to be inertialess lubrication treated as shock, where balance mass momentum established radial direction, including effect surface tension across jump. show that, contrast Newtonian jet, which requires separate formulations developing-boundary layer fully viscous layers, formulation for yielded pseudo-plug layers uniformly valid between impingement zone Consequently, does not experience discontinuity film height, velocity gradient, shear stress, exhibited by at transition location. found occur closer impingement, with growing yield stress increases; region becomes invaded layer. viscosity influence sensibly location height except small stress; only yielded-layer remain sensitive power-law rheology any stress. In particular, thickening can cause drop despite surface. also find that would if was smaller than critical size, but tends enhance formation compared jet. an almost constant local downstream Froude number exists fluid. Finally, our results reduce limiting cases Bingham, power-law, fluids.