String-wound cartridge filters are replaceable filter media fabricated by spirally winding yarn around a porous core. Owing to their ease of handling, they are widely used in a variety of applications. These filters capture particles within the filter layer, and, due to the presence of a density gradient, coarse particles are retained near the outer surface while finer particles are captured in the inner layers, resulting in depth filtration. This structure provides a high particle-holding capacity with relatively low pressure loss. However, as particle deposition increases and the voids between yarn layers become clogged, the filtration mechanism gradually shifts from depth filtration to cake filtration, leading to a significant rise in pressure loss.

In this study, we investigated a method for determining the onset of cake filtration based on Ruth’s constant-rate filtration theory. Prior to cake formation, the filtration process was assumed to be governed solely by depth filtration, and the simplified analytical model for depth filtration proposed by Tien et al. for membrane filtration was applied to string-wound cartridge filters with a thickness of approximately 10–15 mm. Tien et al. proposed that the permeability...