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All sourcesNASA NTRSDOE OSTI
NASA NTRS2016

System Level Aerothermal Testing for the Adaptive Deployable Entry and Placement Technology (ADEPT)

The Adaptive Deployable Entry and Placement Technology (ADEPT), a mechanically deployable entry vehicle technology, has been under development at NASA since 2011. As part of the technical maturation of ADEPT, designs capable of delivering small payloads (10 kg) are being considered to rapidly mature sub 1 m deployed diameter designs. The unique capability of ADEPT for small payloads comes from its ability to stow within a slender volume and deploy to achieve a mass efficient drag surface with a high heat rate capability. The low ballistic coefficient results in entry heating and mechanical loads that can be met by a revolutionary three-dimensionally woven carbon fabric supported by a deployable skeleton structure. This carbon fabric has test proven capability as both primary structure and payload thermal protection system. In order to rapidly advance ADEPTs technical maturation, the project is developing test methods that enable thermostructural design requirement verification of ADEPT designs at the system level using ground test facilities. Results from these tests are also relevant to larger class missions and help us define areas of focused component level testing in order to mature material and thermal response design codes. The ability to ground test sub 1 m diameter ADEPT configurations at or near full-scale provides significant value to the rapid maturation of this class of deployable entry vehicles. This paper will summarize arc jet test results, highlight design challenges, provide a summary of lessons learned and discuss future test approaches based upon this methodology.

Hypersonic↗
DOE OSTI2022

Constructing A New CHF Look-Up Table Based on the Domain Knowledge Informed Machine Learning Methodology

Accurate prediction of CHF under various fluid flow conditions continues to be required for design, operation and safety analysis of light water reactor rod bundles. Due to the lack of in-depth physical understanding as well as limited high-resolution data in the micro-scale flow and heat transfer, the existing models feature a sub-optimal uncertainty band. In this study, driven by the prior domain knowledge information obtained, an improved CHF look-up table is developed through unified machine learning algorithms for the vertical flow conditions within tube and annulus geometry. The Groeneveld 2006 look-up table is used as the domain knowledge to train machine learning process against tube and annulus CHF data for both DNB and DO type. The new look-up table shows improved accuracy for conditions relevant to PWRs and BWRs. In addition, its domain knowledge informed nature ensures that a rationale prediction can be made, thus accounting for previous valuable information in the machine learning model training process.

Jin, Yue↗
DOE OSTI2021

Thermal fluctuations and carrier localization induced by dynamic disorder in MAPbI 3 described by first-principles based tight-binding model

Halide perovskites are strongly influenced by large amplitude anharmonic lattice fluctuations at room temperature. We develop a tight binding model for dynamically disordered MAPbI$_3$ based on density functional theory (DFT) calculations to calculate electronic structure for finite temperature crystal structures at the length scale of thermal disorder and carrier localization. The model predicts individual Hamiltonian matrix elements and band structures with high accuracy, owing to the inclusion of additional matrix elements and descriptors for non-Coulombic interactions. We apply this model to electronic structure at length and time scales inaccessible to first principles methods, finding an increase in band gap, carrier mass, and the sub-picosecond fluctuations in these quantities with increasing temperature as well as the onset of carrier localization in large supercells induced by thermal disorder at 300 K. Finally, we identify the length scale $L^*= 5$ nm as the onset of localization in the electronic structure, associated with associated with decreasing band edge fluctuations, increasing carrier mass, and Rashba splitting approaching zero.

36 MATERIALS SCIENCE↗
NASA NTRS1995

Light response of phytoplankton in the South Atlantic Ocean: Interpretation of observations and application to remote sensing

A simplified, nonspectral derivation of a classical theory in plant physiology is presented and used to derive an absorption-based primary productivity algorithm. Field observations from a meridional transect (4 deg N to 42 deg S) in the Atlantic Ocean are then described and interpreted in this theoretical context. The observations include photosynthesis-irradiance curve parameters (alpha and P(sub max)), chlorophyll a and phaeopigment concentration, and estimated phytoplankton absorption coefficients at wavelength = 440 nm (a(sub ph)(440)). Observations near the top (50% I(sub 0)) and bottom (6% I(sub 0)) of the euphotic zone are contrasted. At both light levels, alpha, P(sub max), a(sub ph)(440), and pigment concentration varied similarly along the transect: values were highest at the equator and at the southern end of the transect and lowest in the central South Atlantic. It is concluded that this pattern was related to increased nutrient availability due to equatorial upwelling in the north, and increased wind mixing in the south. At the 50% light level, alpha increased relative to a(sub ph) at the southern end of the transect. This result appears to reflect a large-scale meridional (southward) increase in the average quantum efficiency of the photosynthetic units of the phytoplankton. A correlation analysis of the data reveals that at the 50% light level, variations in P(sub max) were more closely related to a(sub ph)(440) than chlorophyll concentration and that phytoplankton absorption explains 90% of the variability in P(sub max). In theory, this shows that the ratio of the average quantum efficiency of the photosynthetic units of the phytoplankton to the product of their average absorption cross section and turnover time is relatively constant. This result is used to simplify the absorption-based primary productivity algorithm derived previously. The feasibility of using this model to estimate production rate from satellite ocean color observations is discussed. It is concluded that an absorption-based algorithm should provide more accurate production rate estimates than one based upon chlorophyll (pigment) concentration.

Hood, Raleigh R.↗
NASA NTRS1994

On the absence of plasma wave emissions and the magnetic field orientation in the distant magnetosheath

In early September, 1983 ISEE-3 made a long traversal of the distant dawnside magnetosheath starting near x = -150 R(sub E) downstream. The distant magnetosheath often contains moderately intense plasma wave emissions at frequencies from several hundred Hz to 5 kHz. However, over time scales of many days, a clear correlation exists between the occurrence of the plasma waves and the cone angle (theta(sub xB)) between the magnetic field and the plasma flow velocity (x-direction). For theta(sub xB) large (small), the plasma wave amplitudes are near background (high). Sudden (less than 1 minute) changes in the local magnetic field orientation produce correspondingly sudden changes in the wave amplitudes. Statistically, the wave amplitudes decrease continuously with increasing theta(sub xB).

Coroniti, F. V.↗
DOE OSTI2021

Building Intelligent Cyberinfrastructure to Learn Iteratively from both Observations and Models for Understanding Watershed Dynamics

Focal Area(s): Predictive modeling through the use of AI techniques and AI-derived model components; the use of AI and other tools to design a prediction system comprising of a hierarchy of models (e.g., AI-driven model/component/parameterization selection). Science Challenge: Watershed processes, such as the fate and transport of sediment, carbon and nutrients across landscapes and their fluxes to water bodies (e.g., streams, rivers and lakes), have important implications for global and regional carbon and nutrient dynamics, biogeochemical functioning of terrestrial ecosystems, and soil functions. The magnitude of lateral surface/subsurface transport and fluxes of sediment, carbon and nutrients are key factors controlling the vulnerability of watersheds to climate extremes such as droughts, wildfires, and floods. Recent field observations and other scientific evidence suggest that the magnitudes of lateral transport and fluxes of sediment, carbon and nutrients are governed primarily by the spatial and vertical heterogeneity of landscape and soil properties and by pedogenic processes. However, the current generation of land surface and watershed models do not mechanistically couple the terrestrial and hydrologic systems, nor do they represent sufficiently the spatial and vertical heterogeneity of land surface and subsurface properties. On the other hand, increasing complexity of coupled watershed and land surface models requires more data to parameterize, calibrate and validate. Remote sensing (RS) provides a means to acquire spatial data and characterize their heterogeneity at the watershed scale, overcoming a major limitation associated with conventional point measurements. To improve the representation of land-surface and surface/subsurface process coupling and sub-grid heterogeneity in watershed models, it is essential to build our predictive understanding by learning from both the multi-scale multi-process modeling and diverse multi-scale data while leveraging powerful artificial intelligence (AI) techniques.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Demonstration of a MOT in a sub-millimeter membrane hole

Abstract We demonstrate the generation of a cold-atom ensemble within a sub-millimeter diameter hole in a transparent membrane, a so-called “membrane MOT”. With a sub-Doppler cooling process, the atoms trapped by the membrane MOT are cooled down to 10 $$\upmu$$ μ K. The atom number inside the unbridged/bridged membrane hole is about $$10^4$$ 10 4 to $$10^5$$ 10 5 , and the $$1/e^2$$ 1 / e 2 -diameter of the MOT cloud is about 180 $$\upmu$$ μ m for a 400 $$\upmu$$ μ m-diameter membrane hole. Such a membrane device can, in principle, efficiently load cold atoms into the evanescent-field optical trap generated by the suspended membrane waveguide for strong atom-light interaction and provide the capability of sufficient heat dissipation at the waveguide. This represents a key step toward the photonic atom trap integrated platform (ATIP).

74 ATOMIC AND MOLECULAR PHYSICS↗
NASA NTRS2003

Mass Redistribution in the Core and Time-varying Gravity at the Earth's Surface

The Earth's liquid outer core is in convection, as suggested by the existence of the geomagnetic field in much of the Earth's history. One consequence of the convection is the redistribution of mass resulting from relative motion among fluid parcels with slightly different densities. This time dependent mass redistribution inside the core produces a small perturbation on the gravity field of the Earth. With our numerical dynamo solutions, we find that the mass redistribution (and the resultant gravity field) symmetric about the equator is much stronger than that anti-symmetric about the equator. In particular, J(sub 2) component is the strongest. In addition, the gravity field variation increases with the Rayleigh number that measures the driving force for the geodynamo in the core. With reasonable scaling from the current dynamo solutions, we could expect that at the surface of the Earth, the J(sub 2) variation from the core is on the order of l0(exp -16)/year relative to the mean (i.e. spherically symmetric) gravity field of the Earth. The possible shielding effect due to core-mantle boundary pressure variation loading is likely much smaller and is therefore negligible. Our results suggest that time-varying gravity field perturbation due to core mass redistribution may be measured with modem space geodetic observations, which will result a new means of detecting dynamical processes in the Earth's deep interior.

Kuang, Wei-Jia↗
NASA NTRS1983

Scale lengths in quasi-parallel shocks

Examples of an interplanetary and the bow shock illustrate the small relative size of the electrostatic layer relative to the scale of the magnetic fluctuations in quasi-parallel shocks. While both examples are supercritical, the interplanetary example is marginally so, showing a thickness in absolute and convected ion larmor radii units that is thicker (approximately 13 U/omega sub ci) than at the bow shock (approximately omega sub ci). The fluid speed changes abruptly in the quasi-parallel shock on this shorter scale. The increase in electron and ion random energies also is clearly seen on this shorter scale. In the interplanetary example the scale of the electric layer is certainly less than 1/60th that of the up or downstreams magnetic fluctuations. The thickness of the earth's bow shock deceleration layer is dramatically narrower than any domain of upstream waves as controlled by reflected, intermediate, or diffuse ions.

Scudder, J. D.↗
NASA NTRS2015

Towards the 1 mm/y Stability of the Radial Orbit Error at Regional Scales

An estimated orbit error budget for the Jason-1 and Jason-2 GDR-D solutions is constructed, using several measures of orbit error. The focus is on the long-term stability of the orbit time series for mean sea level applications on a regional scale. We discuss various issues related to the assessment of radial orbit error trends; in particular this study reviews orbit errors dependent on the tracking technique, with an aim to monitoring the long-term stability of all available tracking systems operating on Jason-1 and Jason-2 (GPS, DORIS, SLR). The reference frame accuracy and its effect on Jason orbit is assessed. We also examine the impact of analysis method on the inference of Geographically Correlated Errors as well as the significance of estimated radial orbit error trends versus the time span of the analysis. Thus a long-term error budget of the 10-year Jason-1 and Envisat GDR-D orbit time series is provided for two time scales: interannual and decadal. As the temporal variations of the geopotential remain one of the primary limitations in the Precision Orbit Determination modeling, the overall accuracy of the Jason-1 and Jason-2 GDR-D solutions is evaluated through comparison with external orbits based on different time-variable gravity models. This contribution is limited to an East-West "order-1" pattern at the 2 mm/y level (secular) and 4 mm level (seasonal), over the Jason-2 lifetime. The possibility of achieving sub-mm/y radial orbit stability over interannual and decadal periods at regional scales and the challenge of evaluating such an improvement using in situ independent data is discussed.

Precision Orbit Determination (POD)↗
NASA NTRS1989

Gas density effect on dropsize of simulated fuel sprays

Two-phase flow in pneumatic two-fluid fuel nozzles was investigated experimentally to determine the effect of atomizing-gas density and gas mass-flux on liquid-jet breakup in sonic-velocity gas-flow. Dropsize data were obtained for the following atomizing-gases: nitrogen; argon; carbon dioxide; and helium. They were selected to cover a gas molecular-weight range of 4 to 44. Atomizing-gas mass-flux ranged from 6 to 50 g/sq cm-sec and four differently sized two-fluid fuel nozzles were used having orifice diameters that varied from 0.32 to 0.56 cm. The ratio of liquid-jet diameter to SMD, D sub o/D sub 32, was correlated with aerodynamic and liquid-surface forces based on the product of the Weber and Reynolds number, We*Re, and gas-to-liquid density ratio, rho sub g/rho sub l. To correlate spray dropsize with breakup forces produced by using different atomizing-gases, a new molecular-scale dimensionless group was derived. The derived dimensionless group was used to obtain an expression for the ratio of liquid-jet diameter to SMD, D sub o/D sub 32. The mathematical expression of this phenomenon incorporates the product of the Weber and Reynolds number, liquid viscosity, surface tension, acoustic gas velocity, the RMS velocity of gas molecules, the acceleration of gas molecules due to gravity, and gas viscosity. The mathematical expression encompassing these parameters agrees well with the atomization theory for liquid-jet breakup in high velocity gas flow. Also, it was found that at the same gas mass-flux, helium was considerably more effective than nitrogen in producing small droplet sprays with SMD's in the order of 5 micrometers.

Ingebo, Robert D.↗
NASA NTRS1989

Gas density effect on dropsize of simulated fuel sprays

Two-phase flow in pneumatic two-fluid fuel nozzles was investigated experimentally to determine the effect of atomizing-gas density and gas mass-flux on liquid-jet breakup in sonic-velocity gas-flow. Dropsize data were obtained for the following atomizing-gases: nitrogen; argon; carbon dioxide; and helium. They were selected to cover a gas molecular-weight range of 4 to 44. Atomizing-gas mass-flux ranged from 6 to 50 g/sq cm-sec and four differently sized two-fluid fuel nozzles were used having orifice diameters that varied from 0.32 to 0.56 cm. The ratio of liquid-jet diameter to SMD, D sub o/D sub 32, was correlated with aerodynamic and liquid-surface forces based on the product of the Weber and Reynolds number, and gas-to-liquid density ratio, rho sub g/rho sub 1. To correlate spray dropsize with breakup forces produced by using different atomizing-gases, a new molecular-scale dimensionless group was derived. The derived dimensionless group was used to obtain an expression for the ratio of liquid-jet diameter to SMD, D sub o/D sub 32. The mathematical expression of this phenomenon incorporates the product of the Weber and Reynolds number, liquid viscosity, surface tension, acoustic gas velocity, the RMS velocity of gas molecules, the acceleration of gas molecules due to gravity, and gas viscosity. The mathematical expression encompassing these parameters agrees well with the atomization theory for liquid-jet breakup in high velocity gas flow. Also, it was found that at the same gas mass-flux, helium was considerably more effective than nitrogen in producing small droplet sprays with SMD's in the order of 5 micrometers.

Ingebo, Robert D.↗
NASA NTRS1981

Corrosion of 310 stainless steel in H2-H2O-H2S gas mixtures: Studies at constant temperature and fixed oxygen potential

Corrosion of SAE 310 stainless steel in H2-H2O-H2S gas mixtures was studied at a constant temperature of 1150 K. Reactive gas mixtures were chosen to yield a constant oxygen potential of approximately 6 x 10 to the minus 13th power/cu Nm and sulfur potentials ranging from 0.19 x 10 to the minus 2nd power/cu Nm to 33 x 10 to the minus 2nd power/cu Nm. The kinetics of corrosion were determined using a thermobalance, and the scales were analyzed using metallography, scanning electron microscopy, and energy dispersive X-ray analysis. Two corrosion regimes, which were dependent on sulfur potential, were identified. At high sulfur potentials (p sub S sub 2 less than or equal to 2.7 x 10 to the minus 2nd power/cu Nm) the corrosion rates were high, the kinetics obeyed a linear rate equation, and the scales consisted mainly of sulfide phases similar to those observed from pure sulfication. At low sulfur potentials (P sub S sub 2 less than or equal to 0.19 x 10 to the minus 2nd power/cu Nm) the corrosion rates were low, the kinetics obeyed a parabolic rate equation, and scales consisted mainly of oxide phases.

Rao, D. B.↗
NASA NTRS1959

Space-Time Correlations and Spectra of Wall Pressure in a Turbulent Boundary Layer

Measurements of the statistical properties of the fluctuating wall pressure produced by a subsonic turbulent boundary layer are described. The measurements provide additional information about the structure of the turbulent boundary layer; they are applicable to the problems of boundary-layer induced noise inside an airplane fuselage and to the generation of waves-on water. The spectrum of the wall pressure is presented in dimensionless form. The ratio of the root-mean-square wall pressure to the free-stream dynamic pressure is found to be a constant square root of bar P(sup 2)/q(sub infinity) = 0.006 independent of Mach number and Reynolds number. In addition, space- time correlation measurements in the stream direction show that pressure fluctuations whose scale is greater than or equal to 0.3 times the boundary-layer thickness are convected with the convection speed U(sub c) = 0.82U(sub infinity) where U(infinity) is the free-stream velocity and have lost their identity in a distance approximately equal to 10 boundary-layer thicknesses.

Willmarth, W. W.↗
DOE OSTI2025

Operation of helium sub-atmospheric multistage cryogenic centrifugal compressor trains: Part 1 – Steady state modeling and speed ratio selection

Helium cryogenic systems which can provide cooling below the normal boiling point of helium (approximately 4.2 K) are often required by superconducting radio-frequency niobium resonators utilized in modern high-energy particle accelerators. Achieving temperatures below 4.2 K generally involves operating a cryogenic vessel with liquid helium under sub-atmospheric conditions, thereby lowering the saturation pressure and corresponding saturation temperature. Over the last several decades, multi-stage cryogenic centrifugal compressor trains (CC’s) have been operated efficiently and reliably within large-scale cryogenic systems to continuously evacuate helium vapor generated by a device within the vessel, maintaining sub-atmospheric conditions in the vessel while pressurizing the return vapor to above atmospheric conditions. Traditionally, these CC systems have been operated using empirically derived control philosophies and insight gathered from previous operational experience. Recent efforts at the Facility for Rare Isotope Beams (FRIB) have been aimed at the development of a theoretical basis to characterize the operation of multi-stage cryogenic centrifugal compressor train and utilizing predictive model results to generate control parameters. The objective of this research was identifying operational points which adequately balance cryogenic system efficiency, stability, and overall ease of operation. Furthermore, this manuscript provides an overview of the predictive model development, characterization of the FRIB cryogenic centrifugal compressors and implementation of the predicted performance results during steady-state system operation.

Compressor train control↗
DOE OSTI2023

On the Role of Macrophysics and Microphysics in Km-Scale Simulations of Mixed-Phase Clouds During Cold Air Outbreaks

Regional atmospheric models struggle to maintain supercooled liquid in mixed-phase clouds during polar cold-air outbreaks (CAOs). Previous studies focused on the parameterization of aerosol, microphysics and turbulence to understand the origin of this widespread model bias. This study investigates the role of sub-grid cloud fraction parameterizations (CFP) in the simulation of mixed-phase cloud. Km-scale simulations are performed for a large number of CAO cases over Norway, for which continuous ground observations were collected at one site over 6 months. We use a novel analysis that attributes the cloud-radiative errors to deficiencies in specific cloud regimes. We show that the CFP matters for cloud-radiative effects in CAOs, but that it is probably not the primary cause of the lack of liquid water in simulated mixed-phase clouds. Of all the CFP sensitivities explored in this study, the prognostic representation of both liquid and ice shows most promise in increasing the liquid water path. A newly proposed hybrid CFP with prognostic frozen and diagnostic liquid cloud fraction reproduces some of the benefits of the prognostic scheme at reduced cost and complexity. All simulations appear to produce too large precipitation particles. As a result, reducing the snow deposition rate increases the liquid water path and improves the precipitation size distributions, while simulations are less sensitive to reduced riming rates.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2020

Bathymetric Influences on Antarctic Ice-Shelf Melt Rates

Ocean bathymetry exerts a strong control on ice sheet-ocean interactions within Antarctic ice-shelf cavities, where it can limit the access of warm, dense water at depth to the underside of floating ice shelves. However, ocean bathymetry is challenging to measure within or close to ice-shelf cavities. It remains unclear how uncertainty in existing bathymetry datasets affect simulated sub-ice-shelf melt rates. In this work, we infer linear sensitivities of ice-shelf melt rates to bathymetric shape with grid-scale detail by means of the adjoint of an ocean general circulation model. Both idealized and realistic-geometry experiments of sub-ice-shelf cavities in West Antarctica reveal that bathymetry has a strong impact on melt in localized regions such as topographic obstacles to flow. Moreover, response of melt to bathymetric perturbation is found to be non-monotonic, with deepening leading to either increased or decreased melt depending on location. Our computational approach provides a comprehensive way of identifying regions, where refined knowledge of bathymetry is most impactful, and also where bathymetric errors have relatively little effect on modeled ice sheet-ocean interactions.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS1999

Dynamics of Single Chains of Suspended Ferrofluid Particles

We present an experimental study of the dynamics of isolated chains made of super-paramagnetic particles under the influence of a magnetic field. The motivation of this work is to understand if the chain fluctuations exist and, if it does, how does the fluctuation affect chain aggregation. We find that single chains strongly fluctuate and that the characteristic frequency of their fluctuations is inversely proportional to the magnetic field strength. The higher the field the lower the characteristic frequency of the chain fluctuations. In the high magnetic field limit, chains behave like rigid rods without any internal motions. In this work, we used ferrofluid particles suspended in water. These particles do not have any intrinsic magnetization. Once a magnetic field is applied, a dipole moment is induced in each particle, proportional to the magnetic field. A dipolar magnetic interaction then occurs between particles. If dipole-dipole magnetic energy is higher than the thermal energy, the result is a structure change inside the dipolar fluid. The ratio of these two energies is expressed by a coupling constant lambda as: lambda = (pi(a(exp 3))(chi(exp 2))(mu(sub 0))(H(sub 0))(exp 2))/18kT Where a is the particle radius, mu(sub 0) is the vacuum magnetic permeability, H(sub 0) the applied magnetic field, k the Boltzmann constant and T the absolute temperature. If lambda > 1, magnetic particles form chains along the field direction. The lateral coalescence of several chains may form bigger aggregates especially if the particle volume fraction is high. While many studies and applications deal with the rheological properties and the structural changes of these dipolar fluids, this work focuses on the understanding of the chain dynamics. In order to probe the chain dynamics, we used dynamic light scattering (DLS) in self-beating mode as our experimental technique. The experimental geometry is such that the scattering plane is perpendicular to the magnetic field. Therefore, only motions in this plane are probed. A very dilute sample of a ferrofluid emulsion with a particle volume fraction of 10(exp -5) is used in this experiment. We chose such a low volume fraction to avoid multiple light scattering as well as lateral chain-chain aggregation. DLS measures the dynamic structure factor S(q,t) of the sample (q is the scattering wave vector, t is the time). In the absence of the magnetic field, identical particles of ferrofluid droplets are randomly distributed and S(q,t) reduces to exp(-q(exp 2)2D(sub 0)t). D(sub 0)=(kT/(6(pi)(eta)(a)) is the diffusion coefficient of Brownian particles (where Xi = (6(pi)(eta)(a)) is the Stokes frictional coefficient of a spherical particle in a fluid of viscosity eta). If interactions or polydispersity can not be ignored, an effective diffusion coefficient is introduced. Formally, D(sub eff) is defined as: D(sub eff) = - q(exp -2) partial derivative of (ln(S(q,t)) with respect to time, as t goes to 0. D(sub eff) reduces to D(sub 0) if no interactions and only a few particles size are present. Therefore, we can use DLS to measure particle size. The particle radius was found to be a=0.23 mu m with 7% of polydispersity. In this case, if we vary the scattering angle theta (and so q) we do not have any change in the measured diffusion coefficient: it is q-independent. When a magnetic field is applied, particles aggregate into chains if lambda > 1. We first studied the kinetics of the chain formation when lambda = 406. At a fixed scattering angle, we measured diffusion coefficient D(sub eff) as a function of time. Experimentally, we find that D(sub eff) decreases monotonously with time. Physically, this means that chains are becoming longer and longer. Since we are only sensitive to motions in the scattering plane and since chains have their main axis perpendicular to this plane, the measured diffusion coefficient is the trans-verse diffusion coefficient. We can relate D(sub eff) to the mean number of particles per chain N(t) at a given time and to the diffusion coefficient of an isolated particle D(sub 0) as D(sub eff)=f(N(t))D(sub 0). Since f(N) is known from other recent work, N can be expressed as a function of the time. We found a square root dependency: N(t) proportional to the square root of t. As expected for very low volume fraction, this behavior is characteristic of a diffusion-limited aggregation as suggested by several authors and by our previous work. In this study, we focus on the dependence of the effective diffusion coefficient on the scattering angle and the magnetic field strength. After the magnetic field is applied (lambda = 406) for a long time, typically 6 hours, kinetics of chain formation becomes very slow. Chain size does not vary much over the next hour period. Thus, we can perform different interesting experiments. First, at a fixed magnetic field, we measure the effective diffusion coefficient as a function of the scattering angle (from 5 to 130 deg). Our results show that the measured diffusion coefficient increases linearly with the scattering angle: D(sub eff) proportional to q. If we do the same experiment for different lambda values, D(sub eff) depends on lambda as D(sub eff) proportional to lambda(exp -1/2). We also find for different lambda values that the same asymptotic D(sub eff) value is obtained when q approaches zero. The angle dependency of D(sub eff) suggests that an additional motion exists besides chain drifting. Chain size is constant during experiment, which was verified by measuring the same diffusion coefficient at the beginning and at the end of the angle switching. If chains are rigid, D(sub eff) is independent of q. Therefore, we found that D(sub eff) not only measures the motion of the entire chain but also its internal fluctuations. These internal motions are the fluctuations of the particles in the chain. To understand the q dependency of D(sub eff), let us look at the probing length used. In our study, the characteristic length scale probed is l=2pi/q which is in the range of 0.9<l/a<20. When l is much larger than the particle radius (l/a going to infinity) we are mainly sensitive to the center of mass diffusion of the chain. D(sub eff) is then the diffusion of the entire chain and depends only on N but not on q and lambda. The value D(sub eff) allows us to obtain the number of particles per chain N. In the opposite limit (i.e. l/a < 1), we are sensitive to motions on the size of individual particles. The main contributions to the measured diffusion coefficient come from internal motions of the chains (i.e. particles' fluctuations inside the chain). We investigated also the effect of the chain size on D(sub eff). For the same value of the magnetic interaction lambda and different chain sizes, we found that the slope of D(sub eff) versus q decreases when N increases as a power law D(sub eff) proportional to N(exp -0.7). This is an important behavior because this means that the longer the chain the slower its internal fluctuations besides the whole chain motion.

Cutillas, S.↗