Cleaning is an important process step in the food industry, especially to avoid contamination during increasingly frequent product changes. The equipment is cleaned almost daily causing high ecological and economic expenses. Predicting the cleaning time required to remove a thin soil layer for given operating conditions can prevent the use of unneeded resources. The purpose of the present contribution is to apply a recently published model for an adhesively detaching soil at the next level of geometrical complexity. To this end, a square duct with a stepwise expansion of each wall is considered. The Reynolds numbers of the flows investigated are between 13,000 and 39,000, based on the hydraulic diameter of the upstream duct. In a square duct, the flow is three-dimensional due to secondary flows of the second kind, and the existing model for two-dimensional flow needs to be extended in the first step. In course of that, a simple method is presented for the consideration of turbulent fluctuations in the calculation of the hydrodynamic loads. The model is validated using cleaning experiments in a fully developed channel flow without step. After that, it is applied to the channel flow with sudden expansion. Various cleaning parameters, such as the soil mass coverage and the flow velocity, are varied and the quality of the model predictions is investigated. The results are compared with experiments in a channel flow with sudden expansion. Good agreement between experiments and simulation is achieved, proofing that the model can be used to investigate the cleaning in complex, three-dimensional flow scenarios.