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In this work, we optimise microfluidic converging/diverging geometries in order to produce constant strain-rates along the centreline of the flow, for performing studies under homogeneous extension. The design is examined for both two-dimensional and three-dimensional flows where the effects of aspect ratio and dimensionless contraction length are investigated. Initially, pressure driven flows of Newtonian fluids under creeping flow conditions are considered, which is a reasonable approximation in microfluidics, and the limits of the applicability of the design in terms of Reynolds numbers are investigated. The optimised geometry is then used for studying the flow of viscoelastic fluids and the practical limitations in terms of Weissenberg number are reported. Furthermore, the optimisation strategy is also applied for electro-osmotic driven flows, where the development of a plug-like velocity profile allows for a wider region of homogeneous extensional deformation in the flow field.

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. Numerical simulation of the planar extrudate swell of pseudoplastic and viscoelastic fluids with the streamfunction and the VOF methods. Journal of Non-Newtonian Fluid Mechanics, 252, 1-18. DOI: 10.1016/j.jnnfm.2017 A B S T R A C TWe present an Eulerian free-surface flow solver for incompressible pseudoplastic and viscoelastic non-Newtonian fluids. The free-surface flow solver is based on the streamfunction flow formulation and the volume-of-fluid method. The streamfunction solver computes the vector potential of a solenoidal velocity field, which ensures by construction the mass conservation of the solution, and removes the pressure unknown. Pseudoplastic liquids are modelled with a Carreau model. The viscoelastic fluids are governed by differential constitutive models reformulated with the log-conformation approach, in order to preserve the positive-definiteness of the conformation tensor, and to circumvent the high Weissenberg number problem. The volume fraction of the fluid is advected with a geometric conservative unsplit scheme that preserves a sharp interface representation. For the sake of comparison, we also implemented an algebraic advection scheme for the liquid volume fraction. The proposed numerical method is tested by simulating the planar extrudate swell with the Carreau, Oldroyd-B and Giesekus constitutive models. The swell ratio of the extrudates are compared with the data available in the literature, as well as with numerical simulations performed with the open-source rheoTool toolbox in OpenFOAM ® . While the simulations of the generalized Newtonian fluids achieved mesh independence for all the methods tested, the flow simulations of the viscoelastic fluids are more sensitive to mesh refinement and the choice of numerical scheme. Moreover, the simulations of Oldroyd-B fluid flows above a critical Weissenberg number are prone to artificial surface instabilities. These numerical artifacts are due to discretization errors within the Eulerian surface-capturing method. However, the numerical issues arise from the stress singularity at the die exit corner, and the unphysical predictions of the Oldroyd-B model in the skin layer of the extrudate after the die exit, where large extensional deformations occur.

In this work, we explore two methods to simultaneously measure the electroosmotic mobility in microchannels and the electrophoretic mobility of micron‐sized tracer particles. The first method is based on imposing a pulsed electric field, which allows to isolate electrophoresis and electroosmosis at the startup and shutdown of the pulse, respectively. In the second method, a sinusoidal electric field is generated and the mobilities are found by minimizing the difference between the measured velocity of tracer particles and the velocity computed from an analytical expression. Both methods produced consistent results using polydimethylsiloxane microchannels and polystyrene micro‐particles, provided that the temporal resolution of the particle tracking velocimetry technique used to compute the velocity of the tracer particles is fast enough to resolve the diffusion time‐scale based on the characteristic channel length scale. Additionally, we present results with the pulse method for viscoelastic fluids, which show a more complex transient response with significant velocity overshoots and undershoots after the start and the end of the applied electric pulse, respectively.

We present a methodology for the shape optimization of flow-focusing devices with the purpose of creating a wide region of homogeneous extensional flow, characterized by a uniform strain-rate along the centerline of the devices. The numerical routines employed include an optimizer, a finite-volume solver, and a mesh generator operating on geometries with the walls parameterized by Bézier curves. The optimizations are carried out for devices with different geometric characteristics (channel aspect ratio and length). The performance of the optimized devices is assessed for varying Reynolds numbers, velocity ratio between streams, and fluid rheology. Brownian dynamics simulations are also performed to evaluate the stretching and relaxation of λ-DNA molecules in the devices. Overall, the optimized flow-focusing devices generate a homogeneous extensional flow over a range of conditions typically found in microfluidics. At high Weissenberg numbers, the extension of λ-DNA molecules in the optimized flow-focusing devices is close to that obtained in an ideal planar extensional flow with an equivalent Hencky strain. The devices presented in this study can be useful in microfluidic applications taking advantage of homogeneous extensional flows and easy control of the Hencky strain and strainrate.

In this work, we reveal the flow dynamics of Vitreous Humour (VH) gel and liquid phases during saccadic movements of the eye, considering the biofluids viscoelastic character as well as realistic eye chamber geometry and taking into account the saccade profile. We quantify the differences in the flow dynamics

The accuracy and stability of implicit CFD codes are frequently impaired by the decoupling between variables, which can ultimately lead to numerical divergence.Coupled solvers, which solve all the governing equations simultaneously, have the potential to fix this problem. In this work, we report the implementation of coupled solvers for transient and steady-state electrically-driven flow simulations in the finitevolumes framework. The numerical method, developed in OpenFOAM ® , is generic for Newtonian and viscoelastic fluids and is formulated for the Poisson-Nernst-Planck and Poisson-Boltzmann models. The resulting coupled systems of equations are solved efficiently with PETSc library. The performance of the coupled solvers is assessed in two test cases: induced-charge electroosmosis of a Newtonian fluid around a cylinder; electroosmotic flow of a PTT viscoelastic fluid in a contraction/expansion microchannel. The coupled solvers are more accurate in transient simulations and allow the use of larger time-steps without numerical divergence. For steady-state simulations, the coupled solvers converge in fewer iterations than segregated solvers. Although coupled solvers are much slower in a per time-step basis, the overall speedup factor obtained in this study reached a maximum value of ~100, where the highest factors have been obtained with semi-coupled solvers, which drop some coupling terms between equations. While further research is needed to improve the efficiency of the matrix solving stage, coupled solvers are already superior to segregated solvers in a number of cases.