Thermocapillary convection in a target irradiated by an intense charged particle beam

A mathematical model is proposed for the heat-and-mass transfer in a target irradiated by an intense charged particle beam. It includes mechanics of continua equations and a kinetic equation for fast particles that are closed by a wide-range equation of state. A method for solving the model equations, which is based on the division of motion into vortex and potential flows, is proposed, and a numerical experiment is performed. Thermocapillary convection is shown to be the main mechanism of liquid-phase mixing in the target. Convective mixing is found to be effected when the pulse duration is much shorter than the characteristic thermal diffusivity time. Thermocapillary convection is shown to provide mixing on scales of 1–20 μm depending on the irradiation conditions.     

Matrix formulation of hydrodynamics and extension of ptolemaic flows to three-dimensional motions

A new matrix formulation of Lagrange hydrodynamic equations is proposed. Exact solutions of those equations are obtained in matrix form. It is found that precession of vortex lines around some fixed axis in space is a general property of the flows described by those solutions. Two types of fluid motion are studied. Flows of the first type have straight vortex lines, and their particle trajectories are windings on toroidal surfaces. The other flows have plane particle trajectories, and their vortex lines are arbitrarily shaped plane curves. All these motions are shown to be three-dimensional generalizations of plane Ptolemaic flows [1,2].Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 39, No. 6, pp. 783–796, June, 1996.The authors express their gratitude to the Russian Foundation for Fundamental Research for support of these investigations under Grant No. 96-01-00585 and to INTAS Foundation for support under Grant No. 93-1373.     

Anomalous diffusion and lévy flights in a two-dimensional time periodic flow

One of the main consequences of chaos is that transport is enhanced with respect to the fluid at rest, where only molecular diffusion is present. Considering long times and spatial scales much larger than the length scale of the velocity field, particles typically diffuse with a diffusion constant, usually much bigger than the molecular one. Nevertheless there are some important physical systems in which the particle motion is not a normal diffusive process: in such a case one speaks of anomalous diffusion. In this paper, anomalous diffusion is experimentally studied in an oscillating two-dimensional vortex system. In particular, scalar enhanced diffusion due to the synchronization between different characteristic frequencies of the investigated flow (i.e., resonance) is investigated. The flow has been generated by applying an electromagnetic forcing on a thin layer of an electrolyte solution and measurements are made through image analysis. In particular, by using the Feature Tracking (FT) technique, we are able to obtain a large amount of Lagrangian data (i.e., the seeding density can be very high and trajectories can be followed for large time intervals) and transport can be characterized by analyzing the growth of the variance of particle displacements versus time and the dependence of the diffusion coefficient on the flow characteristic frequencies.     

Anomalous dispersion in correlated porous media: a coupled continuous time random walk approach

We study the causes of anomalous dispersion in Darcy-scale porous media characterized by spatially heterogeneous hydraulic properties. Spatial variability in hydraulic conductivity leads to spatial variability in the flow properties through Darcy’s law and thus impacts on solute and particle transport. We consider purely advective transport in heterogeneity scenarios characterized by broad distributions of heterogeneity length scales and point values. Particle transport is characterized in terms of the stochastic properties of equidistantly sampled Lagrangian velocities, which are determined by the flow and conductivity statistics. The persistence length scales of flow and transport velocities are imprinted in the spatial disorder and reflect the distribution of heterogeneity length scales. Particle transitions over the velocity length scales are kinematically coupled with the transition time through velocity. We show that the average particle motion follows a coupled continuous time random walk (CTRW), which is fully parameterized by the distribution of flow velocities and the medium geometry in terms of the heterogeneity length scales. The coupled CTRW provides a systematic framework for the investigation of the origins of anomalous dispersion in terms of heterogeneity correlation and the distribution of conductivity point values. We derive analytical expressions for the asymptotic scaling of the moments of the spatial particle distribution and first arrival time distribution (FATD), and perform numerical particle tracking simulations of the coupled CTRW to capture the full average transport behavior. Broad distributions of heterogeneity point values and lengths scales may lead to very similar dispersion behaviors in terms of the spatial variance. Their mechanisms, however are very different, which manifests in the distributions of particle positions and arrival times, which plays a central role for the prediction of the fate of dissolved substances in heterogeneous natural and engineered porous materials.     

Experimental Simulation of the Generation of a Vortex Flow on a Water Surface by a Wave Cascade

The generation of a vortex flow by waves on a water surface, which simulate an energy cascade in a system of gravity waves at frequencies of 3, 4, 5, and 6 Hz, has been studied experimentally. It has been found that pumping is accompanied by the propagation of waves on the surface at different angles to the fundamental mode and by a nonlinear interaction between waves resulting in the generation of new harmonics. It has been shown that large-scale flows are formed by modes of the lowest frequency of 3 Hz intersecting at acute angles. The energy distribution of the vortex motion can be described by a power-law function of the wavenumber and is independent of the energy distribution in a system of surface waves. The energy coming to large-scale vortex flows directly from the wave system is transferred to small scales. A direct rather than inverse energy flux is established in the system of vortices.     

Where do inertial particles go in fluid flows?

We derive a general reduced-order equation for the asymptotic motion of finite-size particles in unsteady fluid flows. Our inertial equation is a small perturbation of passive fluid advection on a globally attracting slow manifold. Among other things, the inertial equation implies that particle clustering locations in two-dimensional steady flows can be described rigorously by the Q parameter, i.e., by one-half of the squared difference of the vorticity and the rate of strain. Use of the inertial equation also enables us to solve the numerically ill-posed problem of source inversion, i.e., locating initial positions from a current particle distribution. We illustrate these results on inertial particle motion in the Jung-Tél-Ziemniak model of vortex shedding behind a cylinder in crossflow.     

A Triangulated Vortex Method for the Axisymmetric Euler Equations

A new method is presented for the prediction of unsteady axisymmetric inviscid flows. By combining a triangulated vortex approach with a novel evaluation technique for the Biot–Savart integrals, a Lagrangian vortex method is developed which eliminates the singularities usually present in axisymmetric methods, without recourse to normalizations or other approximations. Furthermore, the computational effort scales as the number of control points N and, in the large N limit, depends only on the order of quadrature employed. The accuracy and computational effort are assessed by comparison with the velocity field of a Gaussian core vortex ring and the use of the technique is illustrated by computation of the motion of Norbury rings and of vortex ring pairing.     

Brownian motion at short time scales

Brownian motion has played important roles in many different fields of science since its origin was first explained by Albert Einstein in 1905. Einstein's theory of Brownian motion, however, is only applicable at long time scales. At short time scales, Brownian motion of a suspended particle is not completely random, due to the inertia of the particle and the surrounding fluid. Moreover, the thermal force exerted on a particle suspended in a liquid is not a white noise, but is colored. Recent experimental developments in optical trapping and detection have made this new regime of Brownian motion accessible. This review summarizes related theories and recent experiments on Brownian motion at short time scales, with a focus on the measurement of the instantaneous velocity of a Brownian particle in a gas and the observation of the transition from ballistic to diffusive Brownian motion in a liquid.     

Statistics of particle pair relative velocity in the homogeneous shear flow

Small scale clustering of inertial particles and relative velocity of particle pairs have been fully characterized for statistically steady homogeneous isotropic flows. Depending on the particle Stokes relaxation time, the spatial distribution of the disperse phase results in a multi-scale manifold characterized by local particle concentration and voids and, because of finite inertia, the two nearby particles have high probability to exhibit large relative velocities. Both effects might explain the speed-up of particle collision rate in turbulent flows. Recently it has been shown that the large scale geometry of the flow plays a crucial role in organizing small scale particle clusters. For instance, a mean shear preferentially orients particle patterns. In this case, depending on the Stokes time, anisotropic clustering may occur even in the inertial range of scales where the turbulent fluctuations which drive the particles have already recovered isotropy. Here we consider the statistics of particle pair relative velocity in the homogeneous shear flow, the prototypical flow which manifests anisotropic clustering at small scales. We show that the mean shear, by imprinting anisotropy on the large scale velocity fluctuations, dramatically affects the particle relative velocity distribution even in the range of small scales where the anisotropic mechanisms of turbulent kinetic energy production are sub-dominant with respect to the inertial energy transfer which drives the carrier fluid velocity towards isotropy. We find that the particles’ populations which manifest strong anisotropy in their relative velocities are the same which exhibit small scale clustering. In contrast to any Kolmogorov-like picture of turbulent transport these phenomena may persist even below the smallest dissipative scales where the residual level of anisotropy may eventually blow-up. The observed anisotropy of particle relative velocity and spatial configuration is suggested to influence the directionality of the collision probability, as inferred on the basis of the so-called “ghost collision” model.     

Electric field and Lorentz force contribution to atmospheric vortex phenomena

The physics that initiate and sustain tornados and dust devils is still under investigation. Forces that operate throughout a wide range of scales and could contribute to atmospheric vortex phenomena are the Lorentz force and the force of electric fields. The Lorentz force results in a circular motion of charged particles in a magnetic field. An electric field will pull or repel a charged particle in the direction of the field. This paper will demonstrate that the Lorentz force and the force of electric fields, acting on charged particles that exist in atmospheric vortex phenomena, plausibly contribute to the set of physics that will explain tornados and other atmospheric vortex phenomena.     

Lagrangian Particle Approach to Large Eddy Simulations of Hydrodynamic Turbulence

The flux of energy from large to small scales in hydrodynamic turbulence controls the dissipation of energy at a given scale in the fluid. An accurate parametrization of this flux is a prerequisite in order to devise reliable methods to simulate turbulent flows without resolving all the scales of motion. This problem is discussed in the context of a particle method based on the Smooth Particles Hydrodynamics algorithm. Motivated by the von Karman–Howarth–Kolmogorov exact relation for the energy flux, and by Lagrangian dynamics considerations we postulate an energy transfer term which is quadratic in the velocity and formally time reversal invariant. The numerical simulation of the model however is observed to spontaneously break the time reversal symmetry, demonstrating that the proposed term acts on average as the desired eddy damping.     

Vortex core deformation and stepper-motor ratchet behavior in a superconducting aluminum film containing an array of holes

We investigated experimentally the frequency dependence of a superconducting vortex ratchet effect by means of electrical transport measurements and modeled it theoretically using the time-dependent Ginzburg-Landau formalism. We demonstrate that the high frequency vortex behavior can be described as a discrete motion of a particle in a periodic potential, i.e., the so-called stepper-motor behavior. Strikingly, in the more conventional low frequency response a transition takes place from an Abrikosov vortex rectifier to a phase slip line rectifier. This transition is characterized by a strong increase in the rectified voltage and the appearance of a pronounced hysteretic behavior.     

Regular and chaotic transport of impurities in steady flows

This paper considers the properties of the transport of impurity particles in steady fluid flows and describes the principal modes of particle motion. An impurity consisting of particles with a lower density than that of the medium is localized at stationary points of the flow, whereas a heavy impurity can perform a spatially unbounded motion. The conditions for the transition from the bounded motion of a heavy impurity to the long-range transport mode, which occurs as a result of a loss of the stability of the heteroclinic trajectory, are obtained for a model two-dimensional flow having an eddy-cell structure. A mode is found in which a particle, after being transported over a long distance, is trapped forever within the confines of one cell. The transition from regular to chaotic particle transport is analyzed. The question of the effect of a small noise (for example, molecular diffusion) on the character of the motion of a heavy impurity is investigated. It is shown that this effect is important at high viscosity and leads to a transition from bounded motion of the impurity particle to diffusion-type chaotic motion. (c) 1994 American Institute of Physics.     

Phase space structure and anomalous diffusion in a rotational fluid experiment

The transport of passive scalars is considered in a model of rotating annulus experiments. The system has a chain of vortices and a jet, separated by a stochastic layer. For special values of the control parameters, the boundary of the stochastic layer can contain self-similar structures of islands with regular trajectories. Two such values are identified, with the structure being on the jet boundary and on the vortex boundary, respectively. The transport properties for both cases were studied by high-precision direct numerical integration of the equations of motion. The presence of such structures is found to significantly affect the statistical properties of the trajectories and the transport exponent. The results of the computations are compared with various theoretical models of anomalous diffusion. The particle behavior was found to depend significantly on the time scale, with different theories being applicable on different time intervals. Some regimes do not match any of the existing theories. (c) 2000 American Institute of Physics.     

Dynamics and spatial organization of endosomes in mammalian cells

We combine particle tracking and stochastic simulations to analyze the dynamics and organization of early endocytic vesicles in mammalian cells. At short time scales (<10(1) sec) vesicles exhibit 1D symmetric bidirectional motor-driven transport on microtubules such that the mean squared displacement (MSD) scales as t3/2, but the MSD shows a crossover to facilitated diffusion at longer times (>10(1) sec). Facilitated diffusion results in rapid equilibration of vesicles on microtubules. The asterlike organization of microtubules causes perinuclear accumulation of vesicles despite symmetric transport.     

Temporally heterogeneous dynamics in granular flows

Granular simulations are used to probe the particle scale dynamics at short, intermediate, and long time scales for gravity-driven, dense granular flows down an inclined plane. On approach to the angle of repose, where motion ceases, the dynamics become intermittent over intermediate times, with strong temporal correlations between particle motions-temporally heterogeneous dynamics. This intermittency is characterized through large-scale structural events whereby the contact network periodically spans the system. A characteristic time scale associated with these processes increases as the stopped state is approached. These features are discussed in the context of the dynamics of supercooled liquids near the glass transition.     

Unsteady effects on flame extinction limits during gaseous and two-phase flame/vortex interactions

In highly fluctuating flows, it happens that high values of the strain-rate do not induce extinction of the flame front. Unsteady effects minimize the flame response to rapidly varying strain fields. In the present study, the effects of time-dependent flows on non-premixed flames are investigated during flame/vortex interactions. Gaseous flames and spray flames in the external sheath combustion regime are considered. To analyse the flame/vortex interaction process, the velocity field and the flame geometry are simultaneously determined using particle imaging velocimetry and laser-induced fluorescence of the CH radical. The influence of vortex flows on the extinction limits for different vortex parameters and for different gaseous and two-phase flames is examined. If the external perturbation is applied over an extended period of time, the extinction strain-rate is that corresponding to the steady-state flame, and this critical value mainly depends on the fuel and oxidizer compositions and the injection temperature. If the external perturbation is applied during a short period of time, extinction occurs at strain-rates above the steady-state extinction strain-rate. This deviation appears for flow fluctuation timescales below steady flame diffusion timescales. This behaviour is induced by diffusive processes, limiting the ability of the flame to respond to highly fluctuating flows. With respect to unsteady effects, the spray flames investigated in this article behave essentially like gaseous flames, because evaporation takes place in a thin layer before the flame front. Extinction limits are only slightly modified by the spray, controlling process being the competition between aerodynamic and diffusive timescales.     

Clustering of the low-inertia particle number density field in random divergence-free hydrodynamic flows

We consider the diffusion of the low-inertia particle number density field in random divergence-free hydrodynamic flows. The principal feature of this diffusion is the divergence of the particle velocity field, which results in clustering of the particle number density field. This phenomenon is coherent, occurs with a unit probability, and must show up in almost all realizations of the process dynamics. We calculate the statistical parameters that characterize clustering in three-dimensional and two-dimensional random fluid flows and in a rapidly rotating two-dimensional random flow. In the former case, the vortex component of the random divergence-free flow generates a vortex component of the low-inertia particle velocity field, which generates a potential component of the velocity field through advection. By contrast, in the case of rapid rotation, a potential component of the velocity field is generated directly by the vortex component of the random divergence-free flow (linear problem).