The cross-slot stagnation point flow is one of the benchmark problems in non-Newtonian fluid mechanics as it allows large strains to develop and can therefore be used for extensional rheometry measurements or, once instability arises, as a mixing device. In such a flow, beyond a critical value for which the ratio of elastic force to viscous force is high enough, elasticity can break symmetry even in the absence of significant inertial forces (i.e. creeping flow), which is an unwanted phenomenon if the device is to be used as a rheometer but beneficial from a mixing perspective. In this work, a passive control mechanism is introduced to the cross-slot by adding a cylinder at the geometric centre to replace the ‘free’ stagnation point with ‘pinned’ stagnation points at the surface of the cylinder. In the current modified geometry, effects of the blockage ratio (the ratio of the diameter of the cylinder to the width of the channel), the Weissenberg number (the ratio of elastic forces to viscous forces) and extensibility parameters ($\unicode[STIX]{x1D6FC}$ and $L^{2}$) are investigated in two-dimensional numerical simulations using both the simplified Phan-Thien and Tanner and finitely extensible nonlinear elastic models. It is shown that the blockage ratio for fixed solvent-to-total-viscosity ratio has a stabilizing effect on the associated symmetry-breaking instability. The resulting data show that the suggested modification, although significantly changing the flow distribution in the region near the stagnation point, does not change the nature of the symmetry-breaking instability or, for low blockage ratio, the critical condition for onset. Using both numerical and physical experiments coupled with a supporting theoretical analysis, we conclude that this instability cannot therefore be solely related to the extensional flow near the stagnation point but it is more likely related to streamline curvature and the high deformation rates towards the corners, i.e. a classic ‘curved streamlines’ purely elastic instability. Our work also suggests that the proposed geometric modification can be an effective approach for enabling higher flow rates to be achieved whilst retaining steady symmetric flow.

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Combining and separating fluid streams at the microscale has many scientific, industrial, and medical applications. This numerical and experimental study explores inertial instabilities in so-called mixing-separating micro-geometries. The geometry consists of two straight square parallel channels with flow from opposite directions and a central gap that allows the streams to interact, mix, or remain separate (often also referred to as the H-geometry). Under creeping-flow conditions (the Reynolds number tending to zero), the flow is steady, two-dimensional, and produces a sharp interface between fluid streams entering the geometry from opposite directions. When Re exceeds a critical value, one of two different supercritical, inertial instabilities appears which leads to significant changes in the flow pattern and an increased level of interaction between the two streams, although the flow remains steady. The exact form of the instability is dependent on the gap size and the Reynolds number, and we identify two distinct instabilities, one of which appears in devices with large gaps and another which appears in devices with small gaps. At intermediate gap sizes, both instabilities can occur in the same device (at different onset Re). The experimental results for one gap size are used to validate our numerical method, which is then applied to a wider range of gap sizes. The results suggest that the gap size is of primary importance in determining the type of instability that occurs. With a judicious choice of gap size, the instabilities can be exploited (or avoided) in scientific, medical, or other microfluidic applications.

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