Predicting the distribution of yield-stress fluids in branched pipe manifolds

We develop a one-dimensional network model to predict the steady-state distribution of yield-stress fluids in branched pipe manifolds under wall-slip conditions. The model accounts for major friction losses between junctions and incorporates wall slip through a power-law relation calibrated independently via capillary rheometry. Predictions from the model are validated against both bench-scale experiments and fully resolved computational fluid dynamics simulations, showing excellent agreement across a range of flow conditions. Our results demonstrate that wall slip strongly influences the uniformity of fluid distribution by modifying the relative resistance between outlet branches. Furthermore, we show that the problem can be inverted: measured distribution profiles can be used to estimate slip parameters, offering a practical method for slip characterisation without pressure measurement. This modelling framework is computationally inexpensive, robust, and adaptable to various network configurations, making it a valuable tool for the design and analysis of industrial manifold systems involving viscoplastic fluids.