Elastohydrodynamic interactions in soft hydraulic knots

Soft intertwined channel systems are frequently found in fluid flow networks in nature. The passage geometry of these systems can deform due to fluid flow, which can cause the relationship between flow rate and pressure drop to deviate from the Hagen-Poiseuille linear law. Although fluid-structure interactions in single deformable channels have been extensively studied, such as in Starling's resistor and its variations, the flow transport capacity of an intertwined channel with multiple self-intersections (a 'hydraulic knot'), is still an open question. We present experiments and theory on soft hydraulic knots formed by interlinked microfluidic devices comprising two intersecting channels separated by a thin elastomeric membrane. Our experiments show flow-pressure relationships similar to flow limitation, where the limiting flow rate depends on the knot configuration. To explain our observations, we develop a mathematical model based on lubrication theory coupled with tension-dominated membrane deflections that compares favourably with our experimental data. Finally, we present two potential hydraulic knot applications for microfluidic flow rectification and attenuation.