Flow of low viscosity Boger fluids through a microfluidic hyperbolic contraction

In this work we focus on the development of low viscosity Boger fluids and assess their elasticity analyzing the flow through a microfluidic hyperbolic contraction. Rheological tests in shear and extensional flows were carried out in order to evaluate the effect of the addition of a salt (NaCl) to dilute aqueous solutions of polyacrylamide at 400, 250, 125 and 50 ppm (w/w). The rheological data showed that when 1% (w/w) of NaCl was added, a significant decrease of the shear viscosity curve was observed, and a nearly constant shear viscosity was found for a wide range of shear rates, indicating Boger fluid behavior. The relaxation times, measured using a capillary break-up extensional rheometer (CaBER), decreased for lower polymer concentrations, and with the addition of NaCl. Visualizations of these Boger fluids flowing through a planar microfluidic geometry containing a hyperbolic contraction, which promotes a nearly uniform extension rate at the centerline of the geometry, was important to corroborate their degree of elasticity. Additionally, the quantification of the vortex growth upstream of the hyperbolic contraction was used with good accuracy and reproducibility to assess the relaxation time for the less concentrated Boger fluids, for which CaBER measurements are difficult to perform

Optimised cross-slot microdevices for homogeneous extension

Microfluidic cross-slot devices can generate wide regions of vorticity-free strong extensional flow near the stagnation point, resulting in large extensional deformation and orientation of the microstructure of complex fluids, with possible applications in extensional rheometry and hydrodynamic stretching of single cells or molecules. Standard cross-slot devices, with sharp or rounded corners, generate a flow field with a non-homogeneous extension rate that peaks at the stagnation point, but decays significantly with distance from the stagnation point. To circumvent this limitation, an optimized shape cross-slot extensional rheometer (OSCER) was designed numerically and shown to generate constant extension rate over a wide region of the in- and out-flowing symmetry planes [Haward et al., Phys. Rev. Lett., 2012, 109, 128301]. Since the OSCER device was based on a 2D flow approximation, the practical implementation requires a large aspect ratio, which cannot be reproduced by standard soft-lithography techniques. Here, we propose a set of new designs for optimized cross-slot geometries, considering aspect ratios of order 1 and different lengths of the homogeneous inlet/outlet-flow regions. Micro-particle image velocimetry experiments were carried out in order to validate the flow kinematics, and the velocity profiles were found to be linear along the in- and outflow centrelines in good quantitative agreement with the numerical predictions

Model Reduction of Linear Port-Hamiltonian Systems: A Structure Preserving Approach

In this note we address the problem of model reduction of a particular class of linear systems, namely, the linear port-Hamiltonian (PH) systems. Furthermore, we explore the preservation of the PH structure in the reduced model. Towards this end, we adopt the balanced truncation approach to reduced the order of the model, in particular, we study the use of extended Gramians to balance the linear PH systems. The latter provides degrees of freedom to impose a desired structure, in this case a PH one, to the reduced model. Moreover, for balanced truncation using extended Gramians, the error bound is well-known and is given in terms of the Hankel singular values of the truncated state