Self-generated Flows Research Articles

Self-generated vortex flows in a tokamak magnetic island with a background flow

We present a gyrokinetic theory of self-generated E × B vortex flows in a magnetic island in a collisionless tokamak plasma with a background vortex flow. We find that the long-term evolution of the self-generated vortex flows can be classified into two regimes by the background vortex flow potential Φ, with an asymptotic criterion given by , where T is temperature, ε is the inverse aspect ratio and r is the radial coordinate. We find that the background vortex flow above the criterion significantly weakens the toroidal precession-induced long-term damping and structure change of the self-generated vortex flows. That is, the finite background vortex flow is beneficial to maintain the self-generated vortex flows, favorable to an internal transport barrier formation. Our result indicates that the island boundary region is a prominent location for triggering the transition to an enhanced confinement state of the magnetic island.

Modeling Active Colloids: From Active Brownian Particles to Hydrodynamic and Chemical Fields

Active colloids are self-propelled particles moving in viscous fluids by consuming fuel from their surroundings. Here, we review the numerical and theoretical modeling of active colloids propelled by self-generated near-surface flows. We start with the generic model of an active Brownian particle taking into account potential forces and effective pairwise interaction, which include hydrodynamic and phoretic interactions. Also, the squirmer as a model microswimmer is introduced. We then discuss the explicit modeling of self-generated fluid flow and the full hydrodynamic-chemical coupling. Finally, we discuss recent advances in selected topics in which modeling of active colloids is used to study motion in crowded and complex environments, microrheology in active baths, active colloidal engines, adaptive responses of active colloids with the help of machine learning techniques, as well as effects of colloid and fluid inertia.

Self-Generated Convective Flows Enhance the Rates of Chemical Reactions.

In chemical solutions, the products of catalytic reactions can occupy different volumes compared to the reactants and thus give rise to local density variations in the fluid. These density variations generate solutal buoyancy forces, which are exerted on the fluid and thus "pump" the fluid to flow. Herein, we examine if the reaction-induced pumping accelerates the chemical reaction by transporting the reactants to the catalyst at a rate faster than passive diffusion. Using both simulations and experiments, we show a significant increase in reaction rate when reaction-generated convective flow is present. In effect, through a feedback loop, catalysts speed up reactions not only by lowering the energy barrier but also by increasing the collision frequency between the reactants and the catalyst.

Generation of shear flows and vortices in rotating anelastic convection

We consider the effect of stratification on systematic, large-scale flows generated in anelastic convection. We present results from three-dimensional numerical simulations of convection in a rotating plane layer in which the angle between the axis of rotation and gravity is allowed to vary. This model is representative of different latitudes of a spherical body. We consider two distinct parameter regimes: (i) weakly rotating and (ii) rapidly rotating. In each case, we examine the effect of stratification on the flow structure and heat transport properties focussing on the difference between Boussinesq and anelastic convection. Furthermore, we show that regimes (i) and (ii) generate very different large-scale flows and we investigate the role stratification has in modifying these flows. The stratified flows possess a net helicity not present in the Boussinesq cases which we suggest, when combined with the self-generated shear flows, could be important for dynamo action.

Enhancement of chemical oscillations by self-generated convective flows

Chemical feedback loops in fluids can produce not only chemical oscillations, but also density variations that generate solutal buoyancy forces, which in turn initiate fluid flow. Using analytical and computational models, we herein examine how the reaction-induced flows alter the chemical oscillations in a fluid-filled chamber whose top and bottom walls are coated with different enzymes. Due to this chemo-fluidic coupling, the systems form oscillating flow patterns, which combine the characteristic size of the buoyancy-driven convection rolls with the frequency of the chemical oscillations. With changes in the distance between the enzyme-coated walls, the convective flows not only enhance or suppress the chemical oscillations, but also substantially increase the amplitude and frequency of the oscillations and extend the regime of the oscillatory behavior. These design principles can facilitate the development of artificial biochemical networks that act as chemical clocks.

Slip Length Dependent Propulsion Speed of Catalytic Colloidal Swimmers near Walls.

Catalytic colloidal swimmers that propel due to self-generated fluid flows exhibit strong affinity for surfaces. Here, we report experimental measurements of a significant dependence of such microswimmers' speed on the nearby substrate material. We find that speeds scale with the solution contact angle θ on the substrate, which relates to the associated hydrodynamic substrate slip length, as V∝(cosθ+1)^{-3/2}. We show that such dependence can be attributed to osmotic coupling between swimmers and substrate. Our work points out that hydrodynamic slip at nearby walls, though often unconsidered, can significantly impact microswimmer self-propulsion.

Active turbulence in a gas of self-assembled spinners

Colloidal particles subject to an external periodic forcing exhibit complex collective behavior and self-assembled patterns. A dispersion of magnetic microparticles confined at the air-liquid interface and energized by a uniform uniaxial alternating magnetic field exhibits dynamic arrays of self-assembled spinners rotating in either direction. Here, we report on experimental and simulation studies of active turbulence and transport in a gas of self-assembled spinners. We show that the spinners, emerging as a result of spontaneous symmetry breaking of clock/counterclockwise rotation of self-assembled particle chains, generate vigorous vortical flows at the interface. An ensemble of spinners exhibits chaotic dynamics due to self-generated advection flows. The same-chirality spinners (clockwise or counterclockwise) show a tendency to aggregate and form dynamic clusters. Emergent self-induced interface currents promote active diffusion that could be tuned by the parameters of the external excitation field. Furthermore, the erratic motion of spinners at the interface generates chaotic fluid flow reminiscent of 2D turbulence. Our work provides insight into fundamental aspects of collective transport in active spinner materials and yields rules for particle manipulation at the microscale.

Investigation of the interaction between competing types of nondiffusive transport in drift wave turbulence

Radial transport in turbulence dominated tokamak plasmas has been observed to deviate from classical diffusion in certain regimes relevant for magnetic confinement fusion. These situations at least include near-marginal turbulence, where radial transport becomes superdiffusive and mediated by elongated radial structures (or avalanches) and transport across radially sheared poloidal flows, where radial subdiffusion often ensues. In this paper, the interaction between very different physical ingredients responsible for these two types of nondiffusive dynamics (namely, turbulent profile relaxation close to a local threshold and the interaction with radially sheared zonal flows) is studied in detail in the context of a simple two-dimensional electrostatic plasma fluid turbulence model based on the dissipative trapped electron mode. It is shown that, depending on the relative relevance of each of these ingredients, which can be tuned in various ways, a variety of non-diffusive radial transport behaviors can be found in the system. The results also illustrate the fact that the classical diffusion paradigm is often insufficient to describe turbulent transport in systems with self-generated flows and turbulent profile relaxations.

Self-diffusiophoresis of chemically active colloids

Chemically active colloids locally change the chemical composition of their solvent via catalytic reactions which occur on parts of their surface. They achieve motility by converting the released chemical free energy into mechanical work through various mechanisms, such as phoresis. Here we discuss the theoretical aspects of self-diffusiophoresis, which – despite being one of the simplest motility mechanisms – captures many of the general features characterizing self-phoresis, such as self-generated and maintained hydrodynamic flows “driven” by surface activity induced inhomogeneities in solution. By studying simple examples, which provide physical insight, we highlight the complex phenomenology which can emerge from self-diffusiophoresis.

Light-controlled flows in active fluids

Many photosynthetic microorganisms are able to detect light and move towards optimal intensities. This ability, known as phototaxis, plays a major role in ecology by affecting natural phytoplankton mass transfers, and has important applications in bioreactor and artificial micro-swimmers technologies. Here we show that this property can be exploited to generate macroscopic fluid flows using a localized light source directed towards shallow suspensions of phototactic microorganisms. Within the intensity range of positive phototaxis, algae accumulate beneath the excitation light, where collective effects lead to the emergence of radially symmetric convective flows. These flows can thus be used as hydrodynamic tweezers to manipulate small floating objects. At high cell density and layer depth, we uncover a new kind of instability, wherein the viscous torque exerted by self-generated fluid flows on the swimmers induces the formation of travelling waves. A model coupling fluid flow, cell concentration and orientation finely reproduces the experimental data. The ability of phototactic microorganisms to move towards optimal light intensities is exploited to generate fluid flows on scales several orders larger than the swimmers themselves. These flows are shown to function as hydrodynamic tweezers.

Flow-induced nonequilibrium self-assembly in suspensions of stiff, apolar, active filaments.

Active bodies in viscous fluids interact hydrodynamically through self-generated flows. A stiff, apolar, active filament generates symmetric fluid flow around it and thus cannot self-propel. Here we study the mobility and aggregation induced by hydrodynamic flow in a suspension of stiff, apolar, active filaments. We consider two types of active filaments, with those producing extensile or contractile flows along their long axis. Lateral hydrodynamic attractions in extensile filaments lead, independent of the volume fraction, to anisotropic aggregates which translate and rotate ballistically. Lateral hydrodynamic repulsions in contractile filaments lead to microstructured states, where the degree of clustering increases with the volume fraction and the filament motion is always diffusive. Our results demonstrate that the interplay between active hydrodynamic flows and anisotropic excluded volume interactions provides a generic nonequilibrium mechanism for hierarchical self-assembly of active soft matter.

Coarsening dynamics of binary liquids with active rotation.

Active matter comprised of many self-driven units can exhibit emergent collective behaviors such as pattern formation and phase separation in both biological (e.g., mussel beds) and synthetic (e.g., colloidal swimmers) systems. While these behaviors are increasingly well understood for ensembles of linearly self-propelled "particles", less is known about the collective behaviors of active rotating particles where energy input at the particle level gives rise to rotational particle motion. A recent simulation study revealed that active rotation can induce phase separation in mixtures of counter-rotating particles in 2D. In contrast to that of linearly self-propelled particles, the phase separation of counter-rotating fluids is accompanied by steady convective flows that originate at the fluid-fluid interface. Here, we investigate the influence of these flows on the coarsening dynamics of actively rotating binary liquids using a phenomenological, hydrodynamic model that combines a Cahn-Hilliard equation for the fluid composition with a Navier-Stokes equation for the fluid velocity. The effect of active rotation is introduced though an additional force within the Navier-Stokes equations that arises due to gradients in the concentrations of clockwise and counter-clockwise rotating particles. Depending on the strength of active rotation and that of frictional interactions with the stationary surroundings, we observe and explain new dynamical behaviors such as "active coarsening" via self-generated flows as well as the emergence of self-propelled "vortex doublets". We confirm that many of the qualitative behaviors identified by the continuum model can also be found in discrete, particle-based simulations of actively rotating liquids. Our results highlight further opportunities for achieving complex dissipative structures in active materials subject to distributed actuation.

Pulsatory Patterns in Active Fluids

We show that pulsatory patterns arise in thin active films in which two chemical species regulate active stress. The regulating species diffuse within the film and are advected by self-generated flows resulting from active stress gradients. Spontaneous pulsatory patterns emerge when the following conditions are met: (i) the fast-diffusing species up-regulates and the slow-diffusing species down-regulates active stress, or (ii) the active stress up-regulator turns over faster compared to the active stress down-regulator. Our study, motivated by pulsatory patterns in the actomyosin cortex in cells and tissues, provides a simple generic mechanism for oscillatory patterns in active fluids.

Spontaneous division and motility in active nematic droplets.

We investigate the mechanics of an active droplet endowed with internal nematic order and surrounded by an isotropic Newtonian fluid. Using numerical simulations we demonstrate that, due to the interplay between the active stresses and the defective geometry of the nematic director, this system exhibits two of the fundamental functions of living cells: spontaneous division and motility, by means of self-generated hydrodynamic flows. These behaviors can be selectively activated by controlling a single physical parameter, namely, an active variant of the capillary number.

Collective chemotactic dynamics in the presence of self-generated fluid flows

In microswimmer suspensions locomotion necessarily generates fluid motion, and it is known that such flows can lead to collective behavior from unbiased swimming. We examine the complementary problem of how chemotaxis is affected by self-generated flows. A kinetic theory coupling run-and-tumble chemotaxis to the flows of collective swimming shows separate branches of chemotactic and hydrodynamic instabilities for isotropic suspensions, the first driving aggregation, the second producing increased orientational order in suspensions of "pushers" and maximal disorder in suspensions of "pullers." Nonlinear simulations show that hydrodynamic interactions can limit and modify chemotactically driven aggregation dynamics. In puller suspensions the dynamics form aggregates that are mutually repelling due to the nontrivial flows. In pusher suspensions chemotactic aggregation can lead to destabilizing flows that fragment the regions of aggregation.

Production of internal transport barriers via self-generated mean flows in Alcator C-Mod

New results suggest that changes observed in the intrinsic toroidal rotation influence the internal transport barrier (ITB) formation in the Alcator C-Mod tokamak [E. S. Marmar and Alcator C-Mod group, Fusion Sci. Technol. 51, 261 (2007)]. These arise when the resonance for ion cyclotron range of frequencies (ICRF) minority heating is positioned off-axis at or outside of the plasma half-radius. These ITBs form in a reactor relevant regime, without particle or momentum injection, with Ti ≈ Te, and with monotonic q profiles (qmin < 1). C-Mod H-mode plasmas exhibit strong intrinsic co-current rotation that increases with increasing stored energy without external drive. When the resonance position is moved off-axis, the rotation decreases in the center of the plasma resulting in a radial toroidal rotation profile with a central well which deepens and moves farther off-axis when the ICRF resonance location reaches the plasma half-radius. This profile results in strong E × B shear (>1.5 × 105 rad/s) in the region where the ITB foot is observed. Gyrokinetic analyses indicate that this spontaneous shearing rate is comparable to the linear ion temperature gradient (ITG) growth rate at the ITB location and is sufficient to reduce the turbulent particle and energy transport. New and detailed measurement of the ion temperature demonstrates that the radial profile flattens as the ICRF resonance position moves off axis, decreasing the drive for the ITG the instability as well. These results are the first evidence that intrinsic rotation can affect confinement in ITB plasmas.

Observation of Self-Generated Flows in Tokamak Plasmas with Lower-Hybrid-Driven Current

In Alcator C-Mod discharges lower hybrid waves have been shown to induce a countercurrent change in toroidal rotation of up to 60 km/s in the central region of the plasma (r/a approximately <0.4). This modification of the toroidal rotation profile develops on a time scale comparable to the current redistribution time (approximately 100 ms) but longer than the energy and momentum confinement times (approximately 20 ms). A comparison of the co- and countercurrent injected waves indicates that current drive (as opposed to heating) is responsible for the rotation profile modifications. Furthermore, the changes in central rotation velocity induced by lower hybrid current drive (LHCD) are well correlated with changes in normalized internal inductance. The application of LHCD has been shown to generate sheared rotation profiles and a negative increment in the radial electric field profile consistent with a fast electron pinch.

Shear flow generation in stellarators—configurational variations

Plasma momentum transport within magnetic surfaces plays a fundamental role in a number of toroidal plasma physics issues, such as turbulence suppression, impurity transport, bootstrap current generation and the shielding of resonant magnetic error field perturbations. Stellarators provide opportunities for improved understanding of plasma flow effects because (a) new forms of quasi-symmetry (e.g. helical, poloidal) can be produced that differ significantly from the tokamak and (b) symmetry-breaking effects (always present to some degree) reduce the close coupling between parallel and cross-field transport characteristics of symmetric systems. External control coils can also be used to further enhance or suppress such effects. A method has been developed to evaluate the variation of neoclassical self-generated plasma flows in stellarators both within and across magnetic surfaces. This introduces a new dimension into both the optimization of stellarators and to the improved understanding of the existing confinement database. Application of this model to a range of configurations indicates that flow directionality and shearing rates are significantly influenced by the magnetic structure. In addition, it is demonstrated that flows in stellarators are sensitive to profile effects and the presence of external momentum sources, such as neutral beams.

Overview of the Alcator C-Mod program

Research on the Alcator C-Mod tokamak has emphasized RF heating, self-generated flows, momentum transport, scrape-off layer (SOL) turbulence and transport and the physics of transport barrier transitions, stability and control. The machine operates with PRF up to 6 MW corresponding to power densities on the antenna of 10 MW m−2. Analysis of rotation profile evolution, produced in the absence of external drive, allows transport of angular momentum in the plasma core to be computed and compared between various operating regimes. Momentum is clearly seen diffusing and convecting from the plasma edge on time scales similar to the energy confinement time and much faster than neo-classical transport. SOL turbulence and transport have been studied with fast scanning electrostatic probes situated at several poloidal locations and with gas puff imaging. Strong poloidal asymmetries are found in profiles and fluctuations, confirming the essential ballooning character of the turbulence and transport. Plasma topology has a dominant effect on the magnitude and direction of both core rotation and SOL flows. The correlation of self-generated plasma flows and topology has led to a novel explanation for the dependence of the H-mode power threshold on the ∇B drift direction. Research into internal transport barriers has focused on control of the barrier strength and location. The foot of the barrier could be moved to larger minor radius by lowering q or BT. The barriers, which are produced in C-Mod by off-axis RF heating, can be weakened by the application of on-axis power. Gyro-kinetic simulations suggest that the control mechanism is due to the temperature dependence of trapped electron modes which are destabilized by the large density gradients. A set of non-axisymmetric coils was installed allowing intrinsic error fields to be measured and compensated. These also enabled the determination of the mode locking threshold and, by comparison with data from other machines, provided the first direct measurement of size scaling for the threshold. The installation of a new inboard limiter resulted in the reduction of halo currents following disruptions. This effect can be understood in terms of the change in plasma contact with the altered geometry during vertical displacement of the plasma column. Unstable Alfven eigenmodes (AE) were observed in low-density, high-power ICRF heated plasmas. The damping rate of stable AEs was investigated with a pair of active MHD antennae.

Electromagnetic transport components and sheared flows in drift-Alfvén turbulence

Results from three-dimensional numerical simulations of drift-Alfvén turbulence in a toroidal geometry with sheared magnetic field are presented. The simulations show a relation between self-generated poloidal shear flows and magnetic field perturbations. For large values of the plasma β we observe an increase of the transport if the viscous damping of the self-generated shear flows is absent. This behavior is in contrast to the standard argument that sheared flows suppress turbulence and transport via a decorrelation mechanism. An explanation of this behavior in terms of the transport related to magnetic flutter is proposed. The characteristics of the E×B flux are investigated using probability density distribution functions (PDFs). Although they are not Gaussian, no signs of algebraic tails in the PDFs are observed. The PDFs of the pointwise transport are found to agree well with a folded Gaussian, while the PDFs of the spatially averaged transport are in good agreement with an extreme value distribution.