Optimisation of T-shaped microchannels for investigating the extensional behaviour of complex fluids

Extensional dominated flows are widely encountered and their study is of high importance. Microfluidic T-shaped platforms are often considered for investigating the underlying mechanisms of these kind of flows. In this study, we optimise T-shaped microchannels with and without recirculating cavity, where the fluid flows into the device from two opposed symmetric inlets, and exits through a perpendicular channel, in which there is a stagnation point followed by a region of strong extensional ow. Our aim is to design a device that will produce known and desired characteristics, useful for measuring extensional properties of complex fluids. Hence, we require that the velocity along a region of the centreline of the outlet channel increases linearly, resulting in a region where the strain rate deformation applied to the fluid elements is constant and therefore amenable to perform extensional rheometry measurements. We consider two cases: initially we optimise a standard T- channel with no cavity, in which the position of the stagnation point remains fixed; additionally, we consider the case with a cavity and optimise the shape of the cavity since in this configuration the stagnation point will be free to move. Our studies are performed using an in-house finite volume CFD code together with a mesh deformation code, coupled under NOMAD optimiser. The optimisation is performed considering Newtonian fluid ow under creeping ow conditions (R -> 0) which is a reasonable approximation in microfluidics. Our numerical results show that the ow in both optimised shapes exhibit long regions of constant strain rate along the centreline of the outlet segment. However, the case with a cavity is able to reproduce better the target profile in the whole of the desired region. Furthermore, the optimised shapes are shown to perform well also for different types of fluids exhibiting viscoelastic behaviour.