Related papers: Line Stretching in Random Flows

As a streak of dye is advected by a chaotic flow, it stretches and folds and becomes indistinguishable from a one-dimensional idealized material line. The variation along a material line of the total stretching experienced by fluid elements…

We investigate the transport dynamics of elongated particles in cellular vortical flows that undergo spatial oscillations over time. Experimental flow visualizations reveal mixed flow fields with chaotic and elliptic regions coexisting.…

We study the relation between flow structure and fluid deformation in steady two-dimensional random flows. Beyond the linear (shear flow) and exponential (chaotic flow) elongation paradigms, we find a broad spectrum of stretching behaviors,…

Fluid stretching in porous media governs the mixing of reactants, contaminants, and nutrients, yet how the solid microstructure controls the stretching statistics remains poorly understood. We investigate how porous-medium heterogeneity…

The stretching of a polymer chain by a large scale chaotic flow is considered. The steady state which emerges as a balance of the turbulent stretching and anharmonic resistance of the chain is quantitatively described, i.e. the dependency…

We use nonequilibrium molecular dynamics simulations to verify recent tube-model predictions that associative polymer networks exhibit broad stretch fluctuations during elongational flow. Simulations further show that these fluctuating…

We analyse the flow curves of a two-dimensional assembly of granular particles which are interacting via frictional contact forces. For packing fractions slightly below jamming, the fluid undergoes a large scale instability, implying a…

The mixing of an impurity into a flowing fluid is an important process in many areas of science, including geophysical processes, chemical reactors, and microfluidic devices. In some cases, for example periodic flows, the concepts of…

We review several competing chaining methods to estimate the supremum, the diameter of the range or the modulus of continuity of a stochastic process in terms of tail bounds of their two-dimensional distributions. Then we show how they can…

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…

The effects of chaotic advection and diffusion on fast chemical reactions in two-dimensional fluid flows are investigated using experimentally measured stretching fields and fluorescent monitoring of the local concentration. Flow symmetry,…

At the macroscopic scale, many important models of collective motion fall into the class of kinematic flows for which both velocity and diffusion terms depend only on particle density. When total particle numbers are fixed and finite,…

Polymer solutions exhibit anomalous flow thickening -- marked by an abrupt increase in the macroscopic flow resistance -- above a threshold flow rate in a porous medium, but not in bulk solution. This phenomenon has evaded a mechanistic…

We here present two simplified models aimed at describing the long-term, irregular behaviours observed in the rheological response of certain complex fluids, such as periodic oscillations or chaotic-like variations. Both models exploit the…

We address the evaluation of mixing efficiency in experiments of chaotic mixing inside an open-flow channel. Since the open flow continuously brings new fluid into the limited mixing region, it is difficult to define relevant mixing…

Strong nonlinear effects combined with diffusive coupling may give rise to unpredictable evolution in spatially extended deterministic dynamical systems even in the presence of a fully negative spectrum of Lyapunov exponents. This regime,…

Microscopic flows are almost universally linear, laminar and stationary because Reynolds number, $Re$, is usually very small. That impedes mixing in micro-fluidic devices, which sometimes limits their performance. Here we show that truly…

Scalar mixing fronts develop at the interface of agitated fluids of different solute concentrations. In such fronts, scalar fluctuations form at both microscopic and macroscopic scales, due to stretching-enhanced molecular diffusion and…

Dense granular flows are often unstable and form inhomogeneous structures. Although significant advances have been recently made in understanding simple flows, instabilities of such flows are often not understood. We present experimental…

Being able to accurately model and predict the dynamics of dispersed inclusions transported by a turbulent flow, remains a challenge with important scientific, environmental and economical issues. One critical and difficult point is to…