Coupling flow directions in emulsions with wall roughness*

Dense emulsions behave as a yield stress fluid, that has a critical stress above which the material starts to flow. Typically, the yield stress behaviour is captured in the Herschel-Bulkley model, which assumes a constant yield stress as material parameter. The microscopic origin of the yield stress is still under debate. It can be argued that flow in orthogonal directions simultaneously affect the yield stress and will make the yield stress flow rate or field dependent. Therefore, it is important to understand how two orthogonal flows affect each other and how the Herschel-Bulkley equation can be generalised to explain such orthogonal flow situations. In this work, we show that wall patterning can be used to generate flow in two orthogonal directions that affect each other significantly. We induce secondary flows via shearing a common yield stress fluid in a rheometer using a concentric cylinder geometry with angled ridges. We quantify our results by calibrating the effect of wall roughness through an effective ridge depth. We also image the flow fields by employing rheoMRI methods to show that flow directions in yield stress fluids are indeed significantly coupled.