On the role of initial velocities in pair dispersion in a microfluidic chaotic flow

Harnessing elastic instabilities for enhanced mixing and reaction kinetics in porous media

Turbulent flows have been used for millennia to mix solutes; a familiar example is stirring cream into coffee. However, many energy, environmental, and industrial processes rely on the mixing of solutes in porous media where confinement suppresses inertial turbulence. As a result, mixing is drastically hindered, requiring fluid to permeate long distances for appreciable mixing and introducing additional steps to drive mixing that can be expensive and environmentally harmful. Here, we demonstrate that this limitation can be overcome just by adding dilute amounts of flexible polymers to the fluid. Flow-driven stretching of the polymers generates an elastic instability, driving turbulent-like chaotic flow fluctuations, despite the pore-scale confinement that prohibits typical inertial turbulence. Using in situ imaging, we show that these fluctuations stretch and fold the fluid within the pores along thin layers ("lamellae") characterized by sharp solute concentration gradients, driving mixing by diffusion in the pores. This process results in a [Formula: see text] reduction in the required mixing length, a [Formula: see text] increase in solute transverse dispersivity, and can be harnessed to increase the rate at which chemical compounds react by [Formula: see text]-enhancements that we rationalize using turbulence-inspired modeling of the underlying transport processes. Our work thereby establishes a simple, robust, versatile, and predictive way to mix solutes in porous media, with potential applications ranging from large-scale chemical production to environmental remediation.

Geometry-Dependent Elastic Flow Dynamics in Micropillar Arrays

Regular device-scale DNA waves for high DNA concentrations and flow velocities have been shown to emerge in quadratic micropillar arrays with potentially strong relevance for a wide range of microfluidic applications. Hexagonal arrays constitute another geometry that is especially relevant for the microfluidic pulsed-field separation of DNA. Here, we report on the differences at the micro and macroscopic scales between the resulting wave patterns for these two regular array geometries and one disordered array geometry. In contrast to the large-scale regular waves visible in the quadratic array, in the hexagonal arrays, waves occur in a device-scale disordered zig-zag pattern with fluctuations on a much smaller scale. We connect the large-scale pattern to the microscopic flow and observe flow synchronization that switches between two directions for both the quadratic and hexagonal arrays. We show the importance of order using the disordered array, where steady-state stationary and highly fluctuating flow states persist in seemingly random locations across the array. We compare the flow dynamics of the arrays to that in a device with sparsely distributed pillars. Here, we observe similar vortex shedding, which is clearly observable in the quadratic and disordered arrays. However, the shedding of these vortices couples only in the flow direction and not laterally as in the dense, ordered arrays. We believe that our findings will contribute to the understanding of elastic flow dynamics in pillar arrays, helping us elucidate the fundamental principles of non-Newtonian fluid flow in complex environments as well as supporting applications in engineering involving e.g., transport, sorting, and mixing of complex fluids.

Active open-loop control of elastic turbulence

We demonstrate through numerical solutions of the Oldroyd-B model in a two-dimensional Taylor-Couette geometry that the onset of elastic turbulence in a viscoelastic fluid can be controlled by imposed shear-rate modulations, one form of active open-loop control. Slow modulations display rich and complex behavior where elastic turbulence is still present, while it vanishes for fast modulations and a laminar response with the Taylor-Couette base flow is recovered. We find that the transition from the laminar to the turbulent state is supercritical and occurs at a critical Deborah number. In the state diagram of both control parameters, Weissenberg versus Deborah number, we identify the region of elastic turbulence. We also quantify the transition by the flow resistance, for which we derive an analytic expression in the laminar regime within the linear Oldroyd-B model. Finally, we provide an approximation for the transition line in the state diagram introducing an effective critical Weissenberg number in comparison to constant shear. Deviations from the numerical result indicate that the physics behind the observed laminar-to-turbulent transition is more complex under time-modulated shear flow.

Calibration Routine for Quantitative Three-Dimensional Flow Field Measurements in Drying Polymer Solutions Subject to Marangoni Convection

Surface-tension induced flows may have a significant impact on the surface topography of thin films or small printed structures derived from polymer solution processing. Despite a century of research on Marangoni convection, the community lacks quantitative experimental flow field data, especially from within drying solutions. We utilize multifocal micro particle tracking velocimetry (µPTV) to obtain these data and show a calibration routine based on point spread function (PSF) simulations as well as experimental data. The results account for a varying sample refractive index, beneficial cover-glass correction collar settings as well as a multifocal lens system. Finally, the calibration procedure is utilized exemplarily to reconstruct a three-dimensional, transient flow field within a poly(vinyl acetate)-methanol solution dried with inhomogeneous boundary conditions.

Calcium signals are necessary to establish auxin transporter polarity in a plant stem cell niche

In plants mechanical signals pattern morphogenesis through the polar transport of the hormone auxin and through regulation of interphase microtubule (MT) orientation. To date, the mechanisms by which such signals induce changes in cell polarity remain unknown. Through a combination of time-lapse imaging, and chemical and mechanical perturbations, we show that mechanical stimulation of the SAM causes transient changes in cytoplasmic calcium ion concentration (Ca²⁺) and that transient Ca²⁺ response is required for downstream changes in PIN-FORMED 1 (PIN1) polarity. We also find that dynamic changes in Ca²⁺ occur during development of the SAM and this Ca²⁺ response is required for changes in PIN1 polarity, though not sufficient. In contrast, we find that Ca²⁺ is not necessary for the response of MTs to mechanical perturbations revealing that Ca²⁺ specifically acts downstream of mechanics to regulate PIN1 polarity response.

Auxin transport and microtubule orientation respond to mechanical stimulation at the shoot apical meristem. Here Li et al. show that mechanical stimulation causes cytosolic calcium concentration transients, and preventing such changes impairs reorientation of the PIN1 auxin efflux carrier, but not of microtubules.

Particle-laden two-dimensional elastic turbulence

The aggregation properties of heavy inertial particles in the elastic turbulence regime of an Oldroyd-B fluid with periodic Kolmogorov mean flow are investigated by means of extensive numerical simulations in two dimensions. Both the small- and large-scale features of the resulting inhomogeneous particle distribution are examined, focusing on their connection with the properties of the advecting viscoelastic flow. We find that particles preferentially accumulate on thin highly elastic propagating structures and that this effect is the largest for intermediate values of particle inertia. We provide a quantitative characterization of this phenomenon that allows to relate it to the accumulation of particles in filamentary highly strained flow regions producing clusters of correlation dimension close to 1. At larger scales, particles are found to undergo turbophoretic-like segregation. Indeed, our results indicate a close relationship between the profiles of particle density and fluid velocity fluctuations. The large-scale inhomogeneity of the particle distribution is interpreted in the framework of a model derived in the limit of small, but finite, particle inertia. The qualitative characteristics of different observables are, to a good extent, independent of the flow elasticity. When increased, the latter is found, however, to slightly reduce the globally averaged degree of turbophoretic unmixing.