Time-dependent Velocity Distribution Research Articles

Doppler Passive Acoustic Mapping.

In therapeutic ultrasound using microbubbles, it is essential to drive the microbubbles into the correct type of activity and the correct location to produce the desired biological response. Although passive acoustic mapping (PAM) is capable of locating where microbubble activities are generated, it is well known that microbubbles rapidly move within the ultrasound beam. We propose a technique that can image microbubble movement by estimating their velocities within the focal volume. Microbubbles embedded within a wall-less channel of a tissue-mimicking material were sonicated using 1-MHz focused ultrasound. The acoustic emissions generated by the microbubbles were captured with a linear array (L7-4). PAM with robust Capon beamforming was used to localize the microbubble acoustic emissions. We spectrally analyzed the time trace of each position and isolated the higher harmonics. Microbubble velocity maps were constructed from the position-dependent Doppler shifts at different time points during sonication. Microbubbles moved primarily away from the transducer at velocities on the order of 1 m/s due to primary acoustic radiation forces, producing a time-dependent velocity distribution. We detected microbubble motion both away and toward the receiving array, revealing the influence of acoustic radiation forces and fluid motion due to the ultrasound exposure. High-speed optical images confirmed the acoustically measured microbubble velocities. Doppler PAM enables passive estimation of microbubble motion and may be useful in therapeutic applications, such as drug delivery across the blood-brain barrier, sonoporation, sonothrombolysis, and drug release.

Plasma simulation to analyze velocity distribution characteristics of pseudospark-sourced electron beam**Project supported by the Sichuan Science and Technology Program, China (Grant No. 2019YJ0188) and the National Natural Science Foundation of China (Grant Nos. 61671116 and 11905026).

Pseudospark-sourced electron beam is a promising candidate for driving vacuum electronic devices to generate millimeter wave and terahertz wave radiation as it has a very high combined beam current density. However, the inherent velocity spread of the beam, which is difficult to measure in experiment, has a great influence on the operating frequency and efficiency of the vacuum electronic device. In this paper, the velocity distribution characteristics of the electron beam produced by a single-gap hollow cathode electron gun are numerically studied and a three-dimensional kinetic plasma simulation model of a single-gap hollow cathode electron gun is built by using particle in cell and Monte Carlo collision methods in Vorpal. Based on the simulation model, the time-dependent evolution of the plasma formation inside the hollow cathode and electron beam generation process are observed. It is demonstrated that the pseudospark-sourced electron beam has a relatively large velocity spread. The time-dependent velocity distribution of the beam is analyzed, and the dependence of the beam velocity distribution under various operating conditions such as anode–cathode potential difference, gas pressure, and cathode aperture size are also studied.

Characterisation and modeling of a pulsed molecular beam

Standard techniques used in real-time reaction dynamics experiments, namely photoionization by a pulsed laser and velocity imaging are applied to document the time dependent velocity distribution of 2-hydroxypyridine (2-HP) molecules in a pulsed beam where 2-HP is seeded in either helium or argon. The purpose is to identify features which cannot be assigned to a pure free molecular (effusive in the present case) or a pure continuum (supersonic here) flow regime. The beam is generated in a two stage expansion, where the first stage is driven by a pulsed valve. The experimental work is complemented by simulations. Two phenomena retain the attention: (i) a slow return to the effusive flow regime after the valve opening has generated an intense supersonic flow; (ii) development of a shock wave a short time after the valve opening.

Time-dependent kinetic theory of the plasma-wall transition layer in a weakly ionized plasma

An analytic solution of the time-dependent Boltzmann kinetic equation is found for the first time. The plasma-wall transition (PWT) layer is analyzed using time-dependent velocity distribution functions for electrons and ions. The process of wall charging by electrons is described and estimated. For states close to the time-independent (stationary) state, for which the time dependence of the PWT parameters is weak, (i) the potential shapes in the pre-sheath (PS) and the Debye sheath (DS) are analyzed and (ii) the intermediate region, which bridges the PS and DS sublayers, is defined and its characteristic length is determined. The ion kinetics are dominated by charge exchange with cold neutrals and electron-impact ionization collisions of neutrals. The charge-exchange mean free path λcx is assumed to be constant and much larger than the electron Debye length λDe. The detailed time dependence of the PS sublayer's approach of the stationary state is found. It is proved that the stationary state can be realized only if the floating-potential condition is fulfilled.

Quantum dynamics of Rb atoms desorbing off the surface of He nanodroplets

The desorption of excited rubidium (Rb) atoms off the surface of helium (He) nanodroplets is studied in detail using femtosecond time-resolved photoion and photoelectron imaging spectroscopy in combination with quantum wave packet simulations. The good agreement of the measured time-dependent velocity distributions with the simulation when exciting the Rb dopant atoms into the 6p-state supports the pseudo-diatomic model (PDM) for the Rb-He droplet interaction, even on the level of quantum wave packet dynamics. Time-resolved photoelectron spectra reveal the partitioning of excitation energy into the dopant and the droplet degrees of freedom.

Kappa and other nonequilibrium distributions from the Fokker-Planck equation and the relationship to Tsallis entropy.

This paper considers two nonequilibrium model systems described by linear Fokker-Planck equations for the time-dependent velocity distribution functions that yield steady state Kappa distributions for specific system parameters. The first system describes the time evolution of a charged test particle in a constant temperature heat bath of a second charged particle. The time dependence of the distribution function of the test particle is given by a Fokker-Planck equation with drift and diffusion coefficients for Coulomb collisions as well as a diffusion coefficient for wave-particle interactions. A second system involves the Fokker-Planck equation for electrons dilutely dispersed in a constant temperature heat bath of atoms or ions and subject to an external time-independent uniform electric field. The momentum transfer cross section for collisions between the two components is assumed to be a power law in reduced speed. The time-dependent Fokker-Planck equations for both model systems are solved with a numerical finite difference method and the approach to equilibrium is rationalized with the Kullback-Leibler relative entropy. For particular choices of the system parameters for both models, the steady distribution is found to be a Kappa distribution. Kappa distributions were introduced as an empirical fitting function that well describe the nonequilibrium features of the distribution functions of electrons and ions in space science as measured by satellite instruments. The calculation of the Kappa distribution from the Fokker-Planck equations provides a direct physically based dynamical approach in contrast to the nonextensive entropy formalism by Tsallis [J. Stat. Phys. 53, 479 (1988)JSTPBS0022-471510.1007/BF01016429].

Dynamic characteristics and mechanisms of compressible metallic vapor plume behaviors in transient keyhole during deep penetration fiber laser welding

The compressible metallic vapor plume or plasma plume behaviors in the keyhole during deep penetration laser welding have significant effects on the joint quality. However, these behaviors and their responses to process parameter variations have not been well understood. In this paper, we first systematically study the dynamic characteristics and mechanisms of compressible metallic vapor plume behaviors in transient keyhole during fiber laser welding of 304 stainless steels based on a multiple timescale multiphase model. The time-dependent temperature, pressure, velocity and Mach number distributions of vapor plume under different process parameters are theoretically predicted. It is found that the distributions of the main physical characteristics of vapor plume such as pressure, velocity as well as Mach number in keyhole are usually highly uneven and highly time dependent. The peak difference of the velocity, pressure, temperature and Mach number of the vapor plume in a keyhole could be greater than 200 m/s, 20 kPa, 1000 K and 0.6 Mach, respectively. The vapor plume characteristics in a transient keyhole can experience significant changes within several hundreds of nanoseconds. The formation mechanisms of these dynamic characteristics are mainly due to the mesoscale keyhole hump (sized in several tens of microns) dynamics. It is also demonstrated that it is possible to suppress the oscillations of compressible vapor plume in the keyhole by improving the keyhole stability through decreasing the heat input. However, stabilizing the keyhole could only weaken, but not eliminate, the observed highly uneven and transient characteristics. This finding may pose new challenges for accurate experimental measurements of vapor plume induced by laser welding.

Experimental Investigation and CFD Simulation of Top Spray Fluidized Bed Coating System

Experimentally investigated in this work is the hydrodynamics of particulates motion in a cylindrical fluidized bed equipped with a pneumatic nozzle jet flow. Subsequently, the computational fluid dynamics (CFD) is combined with the Eulerian formulation of multiphase flow to describe the hydrodynamics of particulates motion. Similar to free spray jet velocity profile, the velocity profile of output gas from nozzle is obtained based on the Schlichting equation. Particle trajectories, time dependent fluidization height, gas and solid particles velocity distributions and the fluidization height distribution of particles in different radial positions within the bed have been also considered in the course of experimental and modeling studies. The comparison between the predicted and experimental height of fluidized bed indicates a good agreement between simulation results and experimental data.

Time-Dependent Pressure and Flow Behavior of a Self-oscillating Laryngeal Model With Ventricular Folds

The purpose of the study was to better understand the pressure-flow behavior of a self-oscillating vocal fold model at various stages of the glottal cycle. An established self-oscillating vocal fold model was extended to include the false vocal folds (FVFs) and was used to study time-dependent pressure and velocity distributions through the larynx (including the true vocal folds [TVFs] and FVFs). Vocal fold vibration was modeled with a finite element method, laryngeal flow was simulated with the solution of unsteady Navier-Stokes equations, and the acoustics of the vocal tract was modeled with a wave reflection method. The results demonstrate realistic phonatory behaviors and therefore may be considered as a pedagogical tool for showing detailed aerodynamic, kinematic, and acoustic characteristics. The TVFs self-oscillated regularly with reasonable amplitude and mucosal waves. There were large pressure gradients in the glottal region. The centerline velocity was highest during glottal closing and sharply dropped near the center of the flow vortex. The average centerline velocity was about 25m/second in the glottal region. The transglottal pressure was higher during glottal closing when the glottal shape was divergent and pressure recovery was present within the glottis. The centerline velocity increased as expected throughout the convergent glottis, tended to decrease throughout the divergent glottis, and decreased past the TVFs within the ventricle-FVF region. This model produces realistic results and demonstrates interactions among phonation variables of a highly instructive nature, including the influence of the FVFs.

Methanol along the path from envelope to protoplanetary disc

Interstellar methanol is considered to be a parent species of larger, more complex organic molecules. A physicochemical simulation of infalling parcels of matter is performed for a low-mass star-forming system to trace the chemical evolution from cloud to disc. An axisymmetric 2D semi-analytic model generates the time-dependent density and velocity distributions, and full continuum radiative transfer is performed to calculate the dust temperature and the UV radiation field at each position as a function of time. A comprehensive gas-grain chemical network is employed to compute the chemical abundances along infall trajectories. Two physical scenarios are studied, one in which the dominant disc growth mechanism is viscous spreading, and another in which continuous infall of matter prevails. The results show that the infall path influences the abundance of methanol entering each type of disc, ranging from complete loss of methanol to an enhancement by a factor of > 1 relative to the prestellar phase. Critical chemical processes and parameters for the methanol chemistry under different physical conditions are identified. The exact abundance and distribution of methanol is important for the budget of complex organic molecules in discs, which will be incorporated into forming planetary system objects such as protoplanets and comets. These simulations show that the comet-forming zone contains less methanol than in the precollapse phase, which is dominantly of prestellar origin, but also with additional layers built up in the envelope during infall. Such intriguing links will soon be tested by upcoming data from the Rosetta mission.

Estimation of aortic pulse pressure using fourier velocity encoded M‐mode MR

To use a simplified hemodynamic model and Fourier-encoded velocity data to measure pulse pressure (PP) in the descending aorta. A one-dimensional, cylindrically localized pulse sequence with Fourier velocity encoding (FVE) was used to obtain time-dependent velocity distributions along the descending aorta. Numerical evaluation of a simplified hemodynamic model, based on a cross-sectionally averaged form of the mass conservation equation, allowed estimation of the average pressure waveform and PP along 6-cm-long segments located within the descending aorta. Magnetic resonance (MR)-derived pressures were compared against applanation tonometry (AT) performed in healthy subjects (n = 18) and intravascular pressure measurements (IVPM) obtained in patients (n = 4) undergoing diagnostic cardiac angiography and then found to be either normal or with clinically insignificant coronary artery disease. The root mean square (RMS) error between MR- and AP-derived pressure waveforms was 11.7 ± 5.8%. With respect to IVPM, the RMS error ranged from 4.2% to 14.7%. In terms of pulse pressures, there was good agreement with both AT (bias = 0.99 mmHg; 95% limits of agreement (LOA) = [-5.0 to 7.0 mmHg]; range = 12.0 mmHg) and IVPM (bias = -1.82 mmHg; 95% LOA = [-7.2 to 3.5 mmHg]; range = 10.7 mmHg). FVE M-mode and numerical evaluation of a simplified flow model can be used to estimate central pulse pressures noninvasively and accurately with respect to well-established gold standards.

PREDICTION OF UNSTEADY STATES IN LID-DRIVEN CAVITIES FILLED WITH AN INCOMPRESSIBLE VISCOUS FLUID

In this work, a numerical study devoted to the two-dimensional and three-dimensional flow of a viscous, incompressible fluid inside a lid-driven cavity is undertaking. All transport equations are solved using the finite volume formulation on a staggered grid system and multi-grid acceleration. Quantitative aspects of two and three-dimensional flows in a lid-driven cavity for Reynolds number Re = 1000 show good agreement with benchmark results. An analysis of the flow evolution demonstrates that, with increments in Re beyond a certain critical value Rec, the steady flow becomes unstable and bifurcates into unsteady flow. It is observed that the transition from steadiness to unsteadiness follows the classical Hopf bifurcation. The time-dependent velocity distribution is studied in detail and the critical Reynolds number is localized for both 2D and 3D cases. Benchmark solutions for 2D and 3D lid-driven cavity flows are performed for Re = 1500 and 6000.

Use of a novel dual-sensor probe array and electrical resistance tomography for characterization of the mean and time-dependent properties of inclined, bubbly oil-in-water pipe flows

An array of dual-sensor conductance probes, which contains a number of dual-sensor probes equispaced across the diameter of an 80 mm pipe, is introduced in this paper for characterizing bubbly oil-in-water pipe flows inclined at angles from 15° to 60° to the vertical. Each dual-sensor probe measures the local axial oil velocity and the local oil volume fraction at the position of the probe. Choosing an averaging interval of 0.05 s, values of the local oil volume fraction and the local oil velocity were measured simultaneously at the different probe positions, enabling the time-dependent structure of the two-phase flow to be investigated. After data processing, time-dependent variations of volume fraction along the pipe were found which are consistent with the presence of intermittent Kelvin–Helmholtz wave structures in the flow. A high-speed dual-plane ERT system was used to measure the axial propagation speed of these Kelvin–Helmholtz waves, using cross correlation. This paper presents results for the measured characteristics of inclined oil-in-water flows including (i) time-averaged and time-dependent oil volume fraction and velocity distributions and (ii) the Kelvin–Helmholtz wave properties including the wave speed, wave amplitude, wavelength and wave frequency.

Phase-Resolved Measurements of Ion Velocity in a Radio-Frequency Sheath

The time-dependent argon-ion velocity distribution function above and within the plasma sheath of an rf-biased substrate has been measured using laser-induced fluorescence in a commercial plasma processing tool. Discharge parameters were such that the 2.2 MHz rf-bias period was on the order of the ion transit time through the sheath (τ{ion}/τ{rf}=0.3). This work embodies the first time-resolved measurement of ion velocity distribution functions within an rf-biased sheath over a large area (30 cm diameter) silicon wafer substrate.

Application of laser-based instrumentation for measurement of time-resolved temperature and velocity fields in the thermoacoustic system

This work aims to develop reliable laser-based measurement techniques to enable fundamental heat transfer and fluid flow studies in thermoacoustic systems. The challenge is to better understand the modes of energy transfer between the key components, such as stacks (or regenerators) and the hot and cold heat exchangers (located on two sides of the stack/regenerator structure), under the oscillatory flow conditions imposed by the acoustic field. The measurement methodologies adopted in this work include combined two-dimensional temperature and velocity field measurements using Planar Laser-Induced Fluorescence (PLIF) and Particle Image Velocimetry (PIV), respectively. These are investigated around the fins of a pair of mock-up heat exchangers placed side by side in a quarter-wavelength standing-wave acoustic resonator, to mimic the working conditions of a thermoacoustic system. The fins are kept at constant temperatures by means of resistive heating and water cooling, respectively. The velocity and temperature field distributions for 20 phases in the acoustic cycle have been obtained. The impact of the inertial, viscous and thermal effects on the time-dependent local temperature and velocity distributions is discussed. Mutual interaction between both fields is also shown. Future work towards obtaining useful heat transfer correlations in oscillatory conditions is outlined.

Propulsive Force of a Flexible Flapping Thin Airfoil

The propulsive force generated by the leading-edge suction of a flapping thin airfoil can be obtained using unsteady aerodynamic notions based on the potential flow theory. Because the potential theory fails to predict the viscous forces, for flapping airfoils, in general there exists a net propulsive force generation. For low Reynolds numbers and for oscillations at low reduced frequencies, however, the viscous forces overcome the propulsive forces to give a net force against the flight direction. In the case of higher Reynolds numbers, flappings with large amplitudes, and high frequencies, the leading-edge suction force generated by the airfoil overcomes the viscous forces. In this study, the critical Reynolds number, the amplitude, and the reduced frequency values that yield the net propulsive force for an oscillating airfoil are predicted with unsteady viscous-inviscid interaction. The airfoil motions are modeled as 1) a thin rigid plate in vertical oscillation, that is, a heaving-plunging motion; 2) a flexibly cambered airfoil whose camber is changing periodically; and 3) the heaving-plunging motion of a flexibly cambered airfoil. The leading-edge suction force for all cases is predicted by means of the well-known Blasius theorem, and the time dependent surface velocity distribution of the airfoil is determined by unsteady aerodynamic considerations. This surface velocity distribution is used as the edge velocity of the unsteady boundary layer to predict the viscous effects. The coefficient of the propulsive force predicted with the present method agrees well with the values given in the literature up to the effective angle of attack at which the dynamic stall takes place.

Dynamics of DNA molecules in a cross-slot microchannel

The conformation and dynamics of double-stranded DNA molecules in cross-slots with equal arm length are examined with the use of fluorescent labeled λ-DNA at 1.2 ⩽ De ⩽ 4.1. The stretching and diffusing of individual DNA molecules in the flow was visualized/recorded with confocal laser scanning microscopy (CLSM). The onset of coil–stretch transition of DNA molecules in the elongational flow was determined at the microscale. Time-dependent velocity distribution with a mean velocity of 50 µm s−1 for DNA molecules was observed by using FluoSpheres, carboylate-modified microspheres over a time period of 1.12 s. The effect of channel geometry (corner and outlet regions) and the solution viscosity (1.9 cP and 9.5 cP) on the conformation and diffusion are also studied and discussed. We report the maximum and the distribution of the fractional extension of DNA molecules, and show that the maximum fractional extension may be up to 0.64 at De = 4.1, and at a strain of 1.8 there is a corresponding stretching force of about 200 pN.

Surface evolution models in abrasive jet micromachining

The paper presents model predictions and experimental data related to the abrasive jet micromachining of masked and unmasked channels in glass. The spatial and velocity distributions of particles in the jet of an abrasive jet micromachining (AJM) setup were measured using a novel technique. It was found that the velocity decreased linearly from the centerline of the jet to the periphery, and that the probability of a particle arriving at the surface a given radial distance from the center of the impacting jet followed a Weibull distribution. These distributions were then used with an extension of an existing erosion model to predict the cross-sectional profiles of unmasked micromachined channels in borosilicate glass. The effect of a scanning nozzle was modelled using time-dependent particle mass flux and velocity distributions. It was demonstrated that the distribution of the net erosive power across a given cross-section passing under the round nozzle had the same form as the distribution along the diameter of a stationary nozzle. The profiles of unmasked channels machined with the nozzle scanned normal to the target surface were predicted accurately to a depth of 0.4 mm. A second, semi-empirical model for unmasked channels was developed using the erosive power distribution of the jet obtained from the measured channel profile after the first pass of the scanned nozzle. A similar approach was taken to provide the effective erosive power distribution across a masked channel resulting from mask edge scattering. The model predicted the depth of masked channels with a maximum error of 8% up to an aspect ratio of 1, while the best model available in the literature had an error of 32%. The improvements also resulted in a much more accurate prediction of the channel cross-sectional shape to an aspect ratio of 0.5; however, a discrepancy in shape occurred as the aspect ratio increased further, probably because of particle second-strike erosion.

Experimental and Computational Studies of Jet Fuel Flow near the Freeze Point

To study the flow behavior of jet fuel at low temperatures, a wing-tank thermal simulator, which represents the fuel tank of a commercial aircraft, was fabricated. The simulator was subjected to cooling in an environmental chamber. Experimental results show that fuel flowability and pumpability decrease substantially as temperature is reduced. Time-dependent temperature and velocity distributions were numerically simulated for static cooling. Viscosities were obtained from viscometer measurements using different jet fuel samples. It was observed that near the freeze-point temperature, low freeze-point fuels tend to have higher viscosities than high freeze-point fuels. Measured viscosities were used in computational-fluid-dynamics simulations of jet fuel that was cooled. The calculations show that stringers, ribs, and other structures strongly promote fuel cooling. Also, the cooler, denser fuel resides near the bottom surface of the fuel tank simulator. The presence of an ullage space within the tank was found to strongly influence the fuel temperature profile by sometimes reducing cooling from the upper surface. In other instances, the ullage space enhanced cooling.

Time-dependent behaviour of electron transport in methane–argon mixtures

The Boltzmann transport equation is solved to determine the time-dependent electron velocity distribution function in various mixtures of methane and argon subjected to an external electric field, E. In the solution of the equation no expansion of the distribution function is made. The concentration of methane in the mixture is varied systematically. The distribution function is used to calculate several time-dependent electron swarm parameters in these gas mixtures. For each gas mixture a wide range of E/N values, from 0.1 to 1000 Td, is investigated. Steady-state values of various calculated swarm parameters (drift velocity, Townsend ionization coefficient and characteristic energy) agree quite well with the corresponding experimental values.