A Viscoelastic Catastrophe
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We use a differential constitutive equation to model the flow of a viscoelastic flow in a cross-slot geometry, which is known to exhibit bistability above a critical flow rate. The novelty lies in two asymmetric modifications to the geometry, which causes a change in the bifurcation diagram such that one of the stable solutions becomes disconnected from the solution at low flow speeds. First we show that it is possible to mirror one of the modifications such that the system can be forced to the disconnected solution. Then we show that a slow decrease of the flow rate, can cause the system to go through a drastic change on a short time scale, also known as a catastrophe. The short time scale could lead to a precise and simple experimental measurement of the flow conditions at which the viscoelastic catastrophe occurs. Since the phenomena is intrinsically related to the extensional rheology of the fluid, we propose to exploit the phenomena for in-line extensional rheometry.
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