Due to the nature of viscoplastic fluids, fouling is a very common phenomenon in the flow of yield stress fluids in non-smooth/complex geometries. By fouling we mean that the fluid becomes stationary in layers attached to the wall of the duct. Although yield stress is necessary to have fouling in the flow, it is not sufficient and we need to have effect of geometry as well. For example the flow of a yield stress fluid along a uniform plane channel or circular pipe exhibits maximal shear stress at the wall with unyielded fluid is found only in the center of the duct. So neither effect alone is able to cause fouling. From another perspective, fouling is often associated with physicochemical changes in the fluid in the flowing fluid, e.g. dried deposits of milk solids [1,2], precipitation of asphaltene deposits [3,4]. However we only consider the combination of rheological and geometric causes of fouling. We take the simplest non-trivial case, of a Bingham fluid in Stokes flow along a channel with a sinusoidal wavy-wall, as studied in [5,6] for long-thin wavy-walled channels. The geometry is described by a wavelength and amplitude of the wall oscillation and by the channel width and the fluid is characterized by Bingham number (B). We carry out an extensive computational study of these flows over wide range of the three dimensionless parameters of the flow. Results suggest that fouling layers develop if the dimensionless amplitude of the wall perturbation exceeds some critical value. Fouling can occur over a range of channel aspect ratios, and progressively at larger Bingham number. At moderate B, when a sufficiently significant fouling has appeared the fluid appears to self-select the flowing region, i.e. the shape of the fouling layer. This can be partly understood as the selection of a new length-scale for the flow in the widest part of the channel. Following this line of reasoning we are able to establish the relevant similarity scalings to collapse our results, but understanding is not complete. We have also developed empirical expressions that give both necessary and sufficient conditions for fouling to occur.
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