The occurrence of fouling layers in the flow of a yield stress fluid along a wavy-walled channel

Slow flows of Bingham fluids through wavy-walled channels have stationary fouling layers if the amplitude of the wall perturbation h exceeds some critical value hf. We have characterised the occurrence of fouling and the main characteristics of fouling layers, using Stokes flow computations performed extensively over the parameter space (h, δ, B). Fouling can occur over a range of channel aspect ratios δ and progressively at larger Bingham number, B. Fouling begins at a value of hδ that varies mainly with B: both necessary and sufficient conditions are given. The limit of large B appears to plateau to constant values of hδ. At moderate B, for h > hf the fluid appears to self-select the flowing region, i.e. the shape of the fouling layer, which can be partly understood via selection of a new length-scale for the flow in the widest part of the channel. Fouling at small B coincides with the onset of recirculation in Newtonian fluid flows.