Steady viscoelastic flow around high-aspect-ratio, low-blockage-ratio microfluidic cylinders

Abstract

We employ a state-of-the-art microfabrication technique (selective laser-induced etching, SLE) to produce microfluidic cylinder geometries that explore new geometrical regimes. Using SLE, two microchannels are fabricated in monolithic fused silica substrate with height H=2 mm and width W=0.4 mm (aspect ratio α=H/W=5) containing cylinders of radius r=0.02 mm (blockage ratio β=2r/W=0.1), centered at the channel mid-width, W/2. An ‘sc’ channel contains a single cylinder, while a ‘dc’ channel contains two axially-aligned cylinders separated by a distance L=1 mm (L=50r). Compared with cylinder geometries fabricated by soft lithography (which typically have α ≪ 1 and β ≳ 0.5), these rigid glass devices provide a quasi-two-dimensional flow along the direction of the cylinder axis and also more clearly reveal the effects of the strong extensional wake regions located at the leading and trailing stagnation points. Using flow velocimetry and quantitative birefringence measurement techniques, we study the behaviour of a well-characterized viscoelastic polymer solution in flow around the cylinders. The small cylinder radii result in low inertia and very high elasticity numbers El ≈ 2400. For the sc device, we report strong flow modification effects around the cylinder as the flow rate is incremented. This is associated with the deformation of polymer molecules primarily in the upstream wake region, leading to the onset of a purely elastic flow asymmetry upstream of the cylinder. Stretched polymer molecules are advected around the cylinder and relax downstream of the cylinder, resulting in an extremely long elastic wake extending for > 300r downstream. In the dc channel, at lower flow rates, similar flow modification effects are observed to develop around, and downstream of, both cylinders. However, at higher flow rates the wake of the first cylinder extends > 50r downstream, and begins to interact with the second cylinder. The second cylinder becomes encapsulated by the wake of the first and is effectively obviated from the flow field. The results will be of relevance to understanding practical applications of viscoelastic fluids, for example in particle suspension and porous media flows, and also for benchmarking against numerical simulations using viscoelastic constitutive models.