Revisiting detrended fluctuation analysis.

Half a century ago Hurst introduced Rescaled Range (R/S) Analysis to study fluctuations in time series. Thousands of works have investigated or applied the original methodology and similar techniques, with Detrended Fluctuation Analysis becoming preferred due to its purported ability to mitigate nonstationaries. We show Detrended Fluctuation Analysis introduces artifacts for nonlinear trends, in contrast to common expectation, and demonstrate that the empirically observed curvature induced is a serious finite-size effect which will always be present. Explicit detrending followed by measurement of the diffusional spread of a signals' associated random walk is preferable, a surprising conclusion given that Detrended Fluctuation Analysis was crafted specifically to replace this approach. The implications are simple yet sweeping: there is no compelling reason to apply Detrended Fluctuation Analysis as it 1) introduces uncontrolled bias; 2) is computationally more expensive than the unbiased estimator; and 3) cannot provide generic or useful protection against nonstationaries.

Abatement of mixing in shear-free elongationally unstable viscoelastic microflows.

The addition of minute amounts of chemically inert polyacrylamide polymer to liquids results in large instabilities under steady electro-osmotic pumping through 2 : 1 constrictions, demonstrating that laminar flow conditions can be broken in electro-osmotic flow of viscoelastic material. By excluding shear and imposing symmetry we create a platform where only elongational viscoelastic instabilities, and diffusion, affect mixing. In contrast to earlier studies with significant shear that found up to orders of magnitude increase in mixing we find that inclusion of polymers excites large viscoelastic instabilities yet mixing is reduced relative to polymer-free liquids. The absolute decrease in mixing we find is consistent with the understanding that adding polymer increases viscosity while viscoelastic flows progress towards elastic turbulence, a type of mild (Batchelor) turbulence, and indicates that electro-osmotic pumped devices are an ideal platform for studying viscoelastic instabilities without supplementary factors.

Extensional instability in electro-osmotic microflows of polymer solutions.

Fluid transport in microfluidic systems typically is laminar due to the low Reynolds number characteristic of the flow. The inclusion of suspended polymers imparts elasticity to fluids, allowing instabilities to be excited when substantial polymer stretching occurs. For high molecular weight polymer chains we find that flow velocities achievable by standard electro-osmotic pumping are sufficient to excite extensional instabilities in dilute polymer solutions. We observe a dependence in measured fluctuations on polymer concentration which plateaus at a threshold corresponding to the onset of significant molecular crowding in macromolecular solutions; plateauing occurs well below the overlap concentration. Our results show that electro-osmotic flows of complex fluids are disturbed from the steady regime, suggesting potential for enhanced mixing and requiring care in modeling the flow of complex liquids such as biopolymer suspensions.