Non-universal parameters, corrections and universality in Kardar-Parisi-Zhang growth

We present a comprehensive numerical investigation of non-universal parameters and corrections related to interface fluctuations of models belonging to the Kardar-Parisi-Zhang (KPZ) universality class, in d=1+1, for both flat and curved geometries. We analyzed two classes of models. In the isotropic models the non-universal parameters are uniform along the surface, whereas in the anisotropic growth they vary. In the latter case, that produces curved surfaces, the statistics must be computed independently along fixed directions. The ansatz h = v t + (\Gamma t)^{1/3} \chi + \eta, where \chi is a Tracy-Widom (geometry-dependent) distribution and \eta is a time-independent correction, is probed. Our numerical analysis shows that the non-universal parameter \Gamma determined through the first cumulant leads to a very good accordance with the extended KPZ ansatz for all investigated models in contrast with the estimates of \Gamma obtained from higher order cumulants that indicate a violation of the generalized ansatz for some of the studied models. We associate the discrepancies to corrections of unknown nature, which hampers an accurate estimation of \Gamma at finite times. The discrepancies in \Gamma via different approaches are relatively small but sufficient to modify the scaling law t^{-1/3} that characterize the finite-time corrections due to \eta. Among the investigated models, we have revisited an off-lattice Eden model that supposedly disobeyed the shift in the mean scaling as t^{-1/3} and showed that there is a crossover to the expected regime. We have found model-dependent (non-universal) corrections for cumulants of order n > 1. All investigated models are consistent with a further term of order t^{-1/3} in the KPZ ansatz.Comment: 25 pages, 21 figures and 4 table

On the origins of scaling corrections in ballistic growth models

We study the ballistic deposition and the grain deposition models on two-dimensional substrates. Using the Kardar-Parisi-Zhang (KPZ) ansatz for height fluctuations, we show that the main contribution to the intrinsic width, which causes strong corrections to the scaling, comes from the fluctuations in the height increments along deposition events. Accounting for this correction in the scaling analysis, we obtained scaling exponents in excellent agreement with the KPZ class. We also propose a method to suppress these corrections, which consists in divide the surface in bins of size $\varepsilon$ and use only the maximal height inside each bin to do the statistics. Again, scaling exponents in remarkable agreement with the KPZ class were found. The binning method allowed the accurate determination of the height distributions of the ballistic models in both growth and steady state regimes, providing the universal underlying fluctuations foreseen for KPZ class in 2+1 dimensions. Our results provide complete and conclusive evidences that the ballistic model belongs to the KPZ universality class in $2+1$ dimensions. Potential applications of the methods developed here, in both numerics and experiments, are discussed.Comment: 8 pages, 7 figure

Extensional rheology and elastic instabilities of a wormlike micellar solution in a microfluidic cross-slot device

Wormlike micellar surfactant solutions are encountered in a wide variety of important applications, including enhanced oil recovery and ink-jet printing, in which the fluids are subjected to high extensional strain rates. In this contribution we present an experimental investigation of the flow of a model wormlike micellar solution (cetyl pyridinium chloride and sodium salicylate in deionised water) in a well-defined stagnation point extensional flow field generated within a microfluidic cross-slot device. We use micro-particle image velocimetry (m-PIV) and full-field birefringence microscopy coupled with macroscopic measurements of the bulk pressure drop to make a quantitative characterization of the fluid’s rheological response over a wide range of deformation rates. The flow field in the micromachined cross-slot is first characterized for viscous flow of a Newtonian fluid, and m-PIV measurements show the flow field remains symmetric and stable up to moderately high Reynolds number, Re z 20, and nominal strain rate, _3nom z 635 s1. By contrast, in the viscoelastic micellar solution the flow field remains symmetric only for low values of the strain rate such that _3nom # lM1, where lM ¼ 2.5 s is the Maxwell relaxation time of the fluid. In this stable flow regime the fluid displays a localized and elongated birefringent strand extending along the outflow streamline from the stagnation point, and estimates of the apparent extensional viscosity can be obtained using the stressoptical rule and from the total pressure drop measured across the cross-slot channel. For moderate deformation rates (_3nom $ lM1) the flow remains steady, but becomes increasingly asymmetric with increasing flow rate, eventually achieving a steady state of complete anti-symmetry characterized by a dividing streamline and birefringent strand connecting diagonally opposite corners of the cross-slot. Eventually, as the nominal imposed deformation rate is increased further, the asymmetric divided flow becomes time dependent. These purely elastic instabilities are reminiscent of those observed in crossslot flows of polymer solutions, but seem to be strongly influenced by the effects of shear localization of the micellar fluid within the microchannels and around the re-entrant corners of the cross-slot

Shear viscosity and nonlinear behaviour of whole blood under large amplitude oscillatory shear

We investigated experimentally the rheological behavior of whole human blood subjected to large amplitude oscillatory shear under strain control to assess its nonlinear viscoelastic response. In these rheological tests, the shear stress response presented higher harmonic contributions, revealing the nonlinear behavior of human blood that is associated with changes in its internal microstructure. For the rheological conditions investigated, intra-cycle strain-stiffening and intra-cycle shear-thinning behavior of the human blood samples were observed and quantified based on the Lissajous–Bowditch plots. The results demonstrated that the dissipative nature of whole blood is more intense than its elastic component. We also assessed the effect of adding EDTA anticoagulant on the shear viscosity of whole blood subjected to steady shear flow. We found that the use of anticoagulant in appropriate concentrations did not influence the shear viscosity and that blood samples without anticoagulant preserved their rheological characteristics approximately for up to 8 minutes before coagulation became significant

Optimized cross-slot flow geometry for microfluidic extension rheometry

A precision-machined cross-slot flow geometry with a shape that has been optimized by numerical simulation of the fluid kinematics is fabricated and used to measure the extensional viscosity of a dilute polymer solution. Full-field birefringence microscopy is used to monitor the evolution and growth of macromolecular anisotropy along the stagnation point streamline, and we observe the formation of a strong and uniform birefringent strand when the dimensionless flow strength exceeds a critical Weissenberg number Wicrit 0:5. Birefringence and bulk pressure drop measurements provide self consistent estimates of the planar extensional viscosity of the fluid over a wide range of deformation rates (26 s1 "_ 435 s1) and are also in close agreement with numerical simulations performed by using a finitely extensible nonlinear elastic dumbbell model

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

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