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NASA NTRS1997

Effect of Pressure Gradients on Plate Response and Radiation in a Supersonic Turbulent Boundary Layer

Using the model developed by the author for zero-pressure gradient turbulent boundary layers, results are obtained for adverse and favorable pressure gradients. It is shown that when a flexible plate is located in an adverse pressure gradient area, it vibrates more than if it were in a favorable pressure gradient one. Therefore the noise generated by the plate in an adverse pressure gradient is much greater than that due to the plate in a favorable pressure gradient. The effects of Reynolds number and boundary layer thickness are also analyzed and found to have the same effect in both adverse and favorable pressure gradient cases. Increasing the Reynolds number is found to increase the loading on the plate and therefore acoustic radiation. An increase in boundary layer thickness is found to decrease the level of the high frequencies and therefore the response and radiation at these frequencies. The results are in good qualitative agreement with experimental measurements.

Frendi, Abdelkader↗

NASA NTRS2000

A Study of Wake Development and Structure in Constant Pressure Gradients

Motivated by the application to high-lift aerodynamics for commercial transport aircraft, a systematic investigation into the response of symmetric/asymmetric planar turbulent wake development to constant adverse, zero, and favorable pressure gradients has been conducted. The experiments are performed at a Reynolds number of 2.4 million based on the chord of the wake generator. A unique feature of this wake study is that the pressure gradients imposed on the wake flow field are held constant. The experimental measurements involve both conventional LDV and hot wire flow field surveys of mean and turbulent quantities including the turbulent kinetic energy budget. In addition, similarity analysis and numerical simulation have also been conducted for this wake study. A focus of the research has been to isolate the effects of both pressure gradient and initial wake asymmetry on the wake development. Experimental results reveal that the pressure gradient has a tremendous influence on the wake development, despite the relatively modest pressure gradients imposed. For a given pressure gradient, the development of an initially asymmetric wake is different from the initially symmetric wake. An explicit similarity solution for the shape parameters of the symmetric wake is obtained and agrees with the experimental results. The turbulent kinetic energy budget measurements of the symmetric wake demonstrate that except for the convection term, the imposed pressure gradient does not change the fundamental flow physics of turbulent kinetic energy transport. Based on the turbulent kinetic energy budget measurements, an approach to correct the bias error associated with the notoriously difficult dissipation estimate is proposed and validated through the comparison of the experimental estimate with a direct numerical simulation result.

Thomas, Flint O.↗

NASA NTRS1997

Arterial Pressure Gradients during Upright Posture and 30 deg Head Down Tilt

Gravity alters local blood pressure within the body so that arterial pressures in the head and foot are lower and higher, respectively, than that at heart level. Furthermore, vascular responses to local alterations of arterial pressure are probably important to maintain orthostatic tolerance upon return to the Earth after space flight. However, it has been difficult to evaluate the body's arterial pressure gradient due to the lack of noninvasive technology. This study was therefore designed to investigate whether finger arterial pressure (FAP), measured noninvasively, follows a normal hydrostatic pressure gradient above and below heart level during upright posture and 30 deg head down tilt (HDT). Seven healthy subjects gave informed consent and were 19 to 52 years old with a height range of 158 to 181 cm. A Finapres device measured arterial pressure at different levels of the body by moving the hand from 36 cm below heart level (BH) to 72 cm above heart level (AH) in upright posture and from 36 cm BH to 48 cm AH during HDT in increments of 12 cm. Mean FAP creased by 85 mmHg transitioning from BH to AH in upright posture, and the pressure gradient calculated from hydrostatic pressure difference (rho(gh)) was 84 mmHg. In HDT, mean FAP decreased by 65 mmHg from BH to AH, and the calculated pressure gradient was also 65 mmHg. There was no significant difference between the measured FAP gradient and the calculated pressure gradient, although a significant (p = 0.023) offset was seen for absolute arterial pressure in upright posture. These results indicate that arterial pressure at various levels can be obtained from the blood pressure at heart level by calculating rho(gh) + an offset. The offset equals the difference between heart level and the site of measurement. In summary, we conclude that local blood pressure gradients can be measured by noninvasive studies of FAP.

Sanchez, E. R↗

NASA NTRS2002

Motion of Drops on Surfaces with Wettability Gradients

A liquid drop present on a solid surface can move because of a gradient in wettability along the surface, as manifested by a gradient in the contact angle. The contact angle at a given point on the contact line between a solid and a liquid in a gaseous medium is the angle between the tangent planes to the liquid and the solid surfaces at that point and is measured within the liquid side, by convention. The motion of the drop occurs in the direction of increasing wettability. The cause of the motion is the net force exerted on the drop by the solid surface because of the variation of the contact angle around the periphery. This force causes acceleration of an initially stationary drop, and leads to its motion in the direction of decreasing contact angle. The nature of the motion is determined by the balance between the motivating force and the resisting hydrodynamic force from the solid surface and the surrounding gaseous medium. A wettability gradient can be chemically induced as shown by Chaudhury and Whitesides who provided unambiguous experimental evidence that drops can move in such gradients. The phenomenon can be important in heat transfer applications in low gravity, such as when condensation occurs on a surface. Daniel et al have demonstrated that the velocity of a drop on a surface due to a wettability gradient in the presence of condensation can be more than two orders of magnitude larger than that observed in the absence of condensation. In the present research program, we have begun to study the motion of a drop in a wettability gradient systematically using a model system. Our initial efforts will be restricted to a system in which no condensation occurs. The experiments are performed as follows. First, a rectangular strip of approximate dimensions 10 x 20 mm is cut out of a silicon wafer. The strip is cleaned thoroughly and its surface is exposed to the vapor from an alkylchlorosilane for a period lasting between one and two minutes inside a desiccator. This is done using an approximate line source of the vapor in the form of a string soaked in the alkylchlorosilane. Ordinarily, many fluids, including water, wet the surface of silicon quite well. This means that the contact angle is small. But the silanized surface resists wetting, with contact angles that are as large as 100 degs. Therefore, a gradient of wettability is formed on the silicon surface. The region near the string is highly hydrophobic, and the contact angle decreases gradually toward a small value at the hydrophilic end away from this region. The change in wettability occurs over a distance of several mm. The strip is placed on a platform within a Plexiglas cell. Drops of a suitable liquid are introduced on top of the strip near the hydrophobic end. An optical system attached to a video camera is trained on the drop so that images of the moving drop can be captured on videotape for subsequent analysis. We have performed preliminary experiments with water as well as ethylene glycol drops. Results from these experiments will be presented in the poster. Future plans include the refinement of the experimental system so as to permit images to be recorded from the side as well as the top, and the conduct of a systematic study in which the drop size is varied over a good range. Experiments will be conducted with different fluids so as to obtain the largest possible range of suitably defined Reynolds and Capillary numbers. Also, an effort will be initiated on theoretical modeling of this motion. The challenges in the development of the theoretical description lie in the proper analysis of the region in the vicinity of the contact line, as well as in the free boundary nature of the problem. It is known that continuum models assuming the no slip condition all the way to the contact line fail by predicting that the stress on the solid surface becomes singular as the contact line is approached. One approach for dealing with this issue has been to relax the no-slip boundary condition using the Navier model. Molecular dynamics simulations of the contact line region show that for a non-polar liquid on a solid surface, the no-slip boundary condition is in fact incorrect near the contact line. Furthermore, the same simulations also show that the usual relationship between stress and the rate of deformation breaks down in the vicinity of the contact line. In developing continuum theoretical models of the system, we shall accommodate this knowledge to the extent possible.

Subramanian, R. Shankar↗

NASA NTRS1991

The role of extracellular free-calcium gradients in gravitropic signalling in maize roots

Gravitropism in roots has been proposed to depend on a downward redistribution of calcium across the root cap. However, because of the many calcium-binding sites in the apoplast, redistribution might not result in a physiologically effective change in the apoplasmic calcium activity. To test whether there is such a change, we measured the effect of gravistimulation on the calcium activity of statocyte cell walls with calcium-specific microelectrodes. Such a measurement must be made on a tissue with gravity sensing cells at the surface. To obtain such a tissue, decapped maize roots (Zea mays L. cv. Golden Cross Bantam) were grown for 31 h to regenerate gravitropic sensitivity, but not root caps. The calcium activity in the apoplasm surrounding the gravity-sensing cells could then be measured. The initial pCa was 2.60 +/- 0.28 (approx 2.5 mM). The calcium activity on the upper side of the root tip remained constant for 10 min after gravistimulation, then decreased 1.7-fold. On the lower side, after a similar lag the calcium activity increased 1.6-fold. Control roots, which were decapped but measured before recovering gravisensitivity (19 h), showed no change in calcium activity. To test whether this gradient is necessary for gravitropic curvature, we eliminated the calcium activity gradient during gravitropism by applying a mobile calcium-binding site (dinitro-BAPTA; 1,2-bis(2-amino-5-nitro-phenoxy)ethane-N,N,N',N'-tetraacetic acid) to the root cap; this treatment eliminated gravicurvature. A calcium gradient may be formed by proton-induced calcium desorption if there is a proton gradient. Preventing the formation of apoplastic pH gradients, using 10 and 50 mM 2-(N-morpholino)ethanesulfonic acid (Mes) buffer or 10 mM fusicoccin to stimulate proton excretion maximally, did not inhibit curvature; therefore the calcium gradient is not a secondary effect of a proton gradient. We have found a distinct and rapid differential in the apoplasmic calcium activity between the upper and lower sides of gravistimulated maize root tips which is necessary for gravitropism.

NASA Discipline Number 40-50↗

NASA NTRS2005

Gradient Driven Fluctuations

We have worked with our collaborators at the University of Milan (Professor Marzio Giglio and his group-supported by ASI) to define the science required to measure gradient driven fluctuations in the microgravity environment. Such a study would provide an accurate test of the extent to which the theory of fluctuating hydrodynamics can be used to predict the properties of fluids maintained in a stressed, non-equilibrium state. As mentioned above, the results should also provide direct visual insight into the behavior of a variety of fluid systems containing gradients or interfaces, when placed in the microgravity environment. With support from the current grant, we have identified three key systems for detailed investigation. These three systems are: 1) A single-component fluid to be studied in the presence of a temperature gradient; 2) A mixture of two organic liquids to be studied both in the presence of a temperature gradient, which induces a steady-state concentration gradient, and with the temperature gradient removed, but while the concentration gradient is dying by means of diffusion; 3) Various pairs of liquids undergoing free diffusion, including a proteidbuffer solution and pairs of mixtures having different concentrations, to allow us to vary the differences in fluid properties in a controlled manner.

Cannell, David↗

NASA NTRS2011

Investigation of the Crust of the Pannonian Basin, Hungary Using Low-Altitude CHAMP Horizontal Gradient Magnetic Anomalies

The Pannonian Basin is a deep intra-continental basin that formed as part of the Alpine orogeny. It is some 600 by 500 km in area and centered on Hungary. This area was chosen since it has one of the thinnest continental crusts in Europe and is the region of complex tectonic structures. In order to study the nature of the crustal basement we used the long-wavelength magnetic anomalies acquired by the CHAMP satellite. The SWARM constellation, scheduled to be launched next year, will have two lower altitude satellites flying abreast, with a separation of between ca. 150 to 200 km. to record the horizontal magnetic gradient. Since the CHAMP satellite has been in orbit for eight years and has obtained an extensive range of data, both vertically and horizontally there is a large enough data base to compute the horizontal magnetic gradients over the Pannonian Basin region using these many CHAMP orbits. We recomputed a satellite magnetic anomaly map, using the spherical-cap method of Haines (1985), the technique of Alsdorf et al. (1994) and from spherical harmonic coefficients of MF6 (Maus et aI., 2008) employing the latest and lowest altitude CHAMP data. We then computed the horizontal magnetic anomaly gradients (Kis and Puszta, 2006) in order to determine how these component data will improve our interpretation and to preview what the SW ARM mission will reveal with reference to the horizontal gradient anomalies. The gradient amplitude of an 1000 km northeast-southwest profile through our horizontal component anomaly map varied from 0 to 0.025 nT/km with twin positive anomalies (0.025 and 0.023 nT/km) separated by a sharp anomaly negative at o nT/km. Horizontal gradient indicate major magnetization boundaries in the crust (Dole and Jordan, 1978 and Cordell and Grauch, 1985). Our gradient anomaly was modeled with a twodimensional body and the anomaly, of some 200 km, correlates with a 200 km area of crustal thinning in the southwestern Pannonian Basin.

Taylor, Patrick T.↗

DOE OSTI2017

Improving the FLORIS wind plant model for compatibility with gradient-based optimization

The FLORIS (FLOw Redirection and Induction in Steady-state) model, a parametric wind turbine wake model that predicts steady-state wake characteristics based on wind turbine position and yaw angle, was developed for optimization of control settings and turbine locations. This article provides details on changes made to the FLORIS model to make the model more suitable for gradient-based optimization. Changes to the FLORIS model were made to remove discontinuities and add curvature to regions of non-physical zero gradient. Exact gradients for the FLORIS model were obtained using algorithmic differentiation. A set of three case studies demonstrate that using exact gradients with gradient-based optimization reduces the number of function calls by several orders of magnitude. The case studies also show that adding curvature improves convergence behavior, allowing gradient-based optimization algorithms used with the FLORIS model to more reliably find better solutions to wind farm optimization problems.

17 WIND ENERGY↗

DOE OSTI2014

On the processes generating latitudinal richness gradients: identifying diagnostic patterns and predictions

Many processes have been put forward to explain the latitudinal gradient in species richness. Here, we use a simulation model to examine four of the most common hypotheses and identify patterns that might be diagnostic of those four hypotheses. The hypotheses examined include (1) tropical niche conservatism, or the idea that the tropics are more diverse because a tropical clade origin has allowed more time for diversification in the tropics and has resulted in few species adapted to extra-tropical climates. (2) The productivity, or energetic constraints, hypothesis suggests that species richness is limited by the amount of biologically available energy in a region. (3) The tropical stability hypothesis argues that major climatic fluctuations and glacial cycles in extratropical regions have led to greater extinction rates and less opportunity for specialization relative to the tropics. (4) Finally, the speciation rates hypothesis suggests that the latitudinal richness gradient arises from a parallel gradient in rates of speciation. We found that tropical niche conservatism can be distinguished from the other three scenarios by phylogenies which are more balanced than expected, no relationship between mean root distance and richness across regions, and a homogeneous rate of speciation across clades and through time. The energy gradient, speciation gradient, and disturbance gradient scenarios all exhibited phylogenies which were more imbalanced than expected, showed a negative relationship between mean root distance and richness, and diversity-dependence of speciation rate estimates through time. Using Bayesian Analysis of Macroevolutionary Mixtures on the simulated phylogenies, we found that the relationship between speciation rates and latitude could distinguish among these three scenarios. We emphasize the importance of considering multiple hypotheses and focusing on diagnostic predictions instead of predictions that are consistent with more than one hypothesis.

biodiversity↗

DOE OSTI2026

Optimality of Gradient-MUSIC for Spectral Estimation

We introduce the Gradient-MUSIC algorithm for estimating the unknown frequencies and amplitudes of a nonharmonic signal from noisy time samples. While the classical MUSIC algorithm performs a computationally expensive search over a fine grid, Gradient-MUSIC is significantly more efficient and eliminates the need for discretization over a fine grid by using optimization techniques. It coarsely scans the 1D landscape to find initialization simultaneously for all frequencies followed by parallelizable local refinement via gradient descent. We also analyze its performance when the noise level is sufficiently small and the signal frequencies are separated by at least 8π/m, where π/m is the standard resolution of this problem. Even though the 1D landscape is nonconvex, we prove a global convergence result for Gradient-MUSIC: coarse scanning provably finds suitable initialization and gradient descent converges at a linear rate. In addition to convergence results, we also upper bound the error between the true signal frequencies and amplitudes with those found by Gradient-MUSIC. For example, if the noise has $\ell^\infty$ norm at most ϵ, then the frequencies and amplitudes are recovered up to error at most Cϵ/m and Cϵ respectively, which are minimax optimal in m and ϵ. Our theory can also handle stochastic noise with performance guarantees under nonstationary independent Gaussian noise. Our main approach is a comprehensive geometric analysis of the landscape, a perspective that has not been explored before.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

Converting 2D Nanofiber Membranes to 3D Hierarchical Assemblies with Structural and Compositional Gradients Regulates Cell Behavior

Abstract New methods are described for converting 2D electrospun nanofiber membranes to 3D hierarchical assemblies with structural and compositional gradients. Pore‐size gradients are generated by tuning the expansion of 2D membranes in different layers with incorporation of various amounts of a surfactant during the gas‐foaming process. The gradient in fiber organizations is formed by expanding 2D nanofiber membranes composed of multiple regions collected by varying rotating speeds of mandrel. A compositional gradient on 3D assemblies consisting of radially aligned nanofibers is prepared by dripping, diffusion, and crosslinking. Bone mesenchymal stem cells (BMSCs) on the 3D nanofiber assemblies with smaller pore size show significantly higher expression of hypoxia‐related markers and enhanced chondrogenic differentiation compared to BMSCs cultured on the assemblies with larger pore size. The basic fibroblast growth factor gradient can accelerate fibroblast migration from the surrounding area to the center in an in vitro wound healing model. Taken together, 3D nanofiber assemblies with gradients in pore sizes, fiber organizations, and contents of signaling molecules can be used to engineer tissue constructs for tissue repair and build biomimetic disease models for studying disease biology and screening drugs, in particular, for interface tissue engineering and modeling.

Chen, Shixuan↗

DOE OSTI2017

Large Continuous Mechanical Gradient Formation via Metal–Ligand Interactions

Abstract Mechanical gradients are often employed in nature to prevent biological materials from damage by creating a smooth transition from strong to weak that dissipates large forces. Synthetic mimics of these natural structures are highly desired to improve distribution of stresses at interfaces and reduce contact deformation in manmade materials. Current synthetic gradient materials commonly suffer from non‐continuous transitions, relatively small gradients in mechanical properties, and difficult syntheses. Inspired by the polychaete worm jaw, we report a novel approach to generate stiffness gradients in polymeric materials via incorporation of dynamic monodentate metal–ligand crosslinks. Through spatial control of metal ion content, we created a continuous mechanical gradient that spans over a 200‐fold difference in stiffness, approaching the mechanical contrast observed in biological gradient materials.

Neal, James A.↗

DOE OSTI2022

Static and Dynamic Gradient Based Directional Transportation of Neutral Molecules in Swollen Polymer Films

Abstract Materials which selectively transport molecules offer powerful opportunities for concentrating and separating chemical agents. Here, utilizing static and dynamic chemical gradients, transport of molecules within swollen crosslinked polymers is demonstrated. Using an ≈200 μm static hydroxyl to hexyl gradient, the neutral ambipolar nerve agent surrogate diethyl (cyanomethyl)phosphonate (DECP) is directionally transported and concentrated 60‐fold within 4 hours. To accelerate transport kinetics, a dynamic gradient (a “travelling wave”) is utilized. Here, the non‐polar dye pyrene was transported. The dynamic gradient is generated by an ion exchange process triggered by the localized introduction of an aqueous NaCl solution, which converts the gel from hydrophobic to hydrophilic. As the hydrophilic region expands, associated water enters the gel, and pyrene is pushed ahead of the expansion front. The dynamic gradient provides about 10‐fold faster transport kinetics than the static gradient.

Ali, Mohammad A.↗

DOE OSTI2022

Static and Dynamic Gradient Based Directional Transportation of Neutral Molecules in Swollen Polymer Films

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2020

Uncertainty amplification due to density/refractive index gradients in background-oriented schlieren experiments

Here, we theoretically analyze the effect of density/refractive index gradients on the measurement precision of background-oriented schlieren (BOS) experiments by deriving the Cramer–Rao lower bound (CRLB) for the 2D centroid estimation process. A model is derived for the diffraction limited image of a dot viewed through a medium containing density gradients that includes the effect of the experimental parameters such as the magnification and f-number. It is shown using the model that nonlinearities in the density gradient field lead to blurring of the dot image. This blurring amplifies the effect of image noise on the centroid estimation process, leading to an increase in the CRLB and a decrease in the measurement precision. The ratio of position uncertainties of a dot in the reference and gradient images is shown to be a function of the ratio of the dot diameters and dot intensities. We termed this parameter the amplification ratio (A F ), and a methodology for reporting position uncertainties in tracking-based BOS measurements is proposed. The theoretical predictions of the dot position estimation variance from the CRLB are compared to ray tracing simulations, and agreement is obtained. The uncertainty amplification is also demonstrated on experimental BOS images of flow induced by a spark discharge, where it is seen that regions of high amplification ratio correspond to regions of density gradients. This analysis elucidates the dependence of the position uncertainty on density and refractive index gradient-induced distortion parameters, provides a methodology for accounting its effect on uncertainty quantification and provides a framework for optimizing experiment design.

42 ENGINEERING↗

DOE OSTI2018

Effect of High-Gradient Magnetic Field on Electrical Property of Carbon Nanotube-Polypyrrole Composite; Nanotube Separation Mechanism

High- and low-gradient magnetic fields are produced by resistor-inductor-capacitor (RLC) discharge apparatuses. The maximum magnetic field is 12.5 Tesla with 1-ms pulse duration. Multiwall carbon nanotube–polypyrrole composite is prepared. The samples are exposed to high- and low-gradient magnetic fields. To understand the behavior of carbon nanotubes (CNTs) in high-gradient magnetic fields (HGMFs), we theoretically calculated the equivalent magnetic susceptibility of a CNT in the gradient magnetic field. We found that the gradient force which is exerted on a CNT could be repellent or absorbent depending on the parallel and perpendicular susceptibilities of the CNT, as well as on the initial orientation of the CNT with respect to magnetic field direction. Four-probe studies show that the electrical conductivity of CNT composites decreases after exposure to a high-gradient magnetic field. Microscopic observation of the electrical current profile of composites reveals rearrangement of CNTs under HGMF.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2025

Analytical gradient-based optimization of CALPHAD model parameters

The calibration of CALPHAD (CALculation of PHAse Diagrams) models involves the solution of a very challenging high-dimensional multiobjective optimization problem. Traditional approaches to parameter fitting predominantly rely on gradient-free methods, which while robust, are computationally inefficient and often scale poorly with model complexity. In this work, we introduce and demonstrate a generalizable framework for analytic gradient-based optimization of the parameters of the CALPHAD model enabled by the recently formalized Jansson derivative technique. This method allows for efficient evaluation of gradients of thermodynamic properties at equilibrium with respect to model parameters, even in the presence of arbitrarily complex internal degrees of freedom. Leveraging these semi-analytic gradients, we employ the conjugate gradient (CG) method to optimize thermodynamic model parameters for four binary alloy systems: Cu-Mg, Fe-Ni, Cr-Ni, and Cr-Fe. Across all systems, CG achieves comparable or superior optimality relative to Bayesian ensemble Markov Chain Monte Carlo (MCMC) with improvements in computational efficiency ranging from one to three orders of magnitude. Furthermore, our results establish a new paradigm for CALPHAD assessments in which high fidelity data-rich model calibration becomes tractable using deterministic gradient-informed algorithms.

CALPHAD↗

DOE OSTI2015

Separation of colloidal two dimensional materials by density gradient ultracentrifugation

Two-dimensional (2D) materials have been made through various approaches but obtaining monodispersed simply by synthesis optimization gained little success, which highlighted the need for introducing nanoseparation methods. Density gradient ultracentrifugation method has emerged as a versatile and scalable method for sorting colloidal 2D nanomaterials. Isopycnic separation was applied on thickness-dependent separation of graphene nanosheets. And rate-zonal separation, as a more versatile separation method, demonstrated its capability in sorting nanosheets of chemically modified single layered graphene, layered double hydroxide, and even metallic Ag. Establishing such density gradient ultracentrifugation method not only achieves monodispersed nanosheets and provides new opportunities for investigation on size dependent properties of 2D materials, but also makes the surface modification possible by introducing “reaction zones” during sedimentation of the colloids. - Graphical abstract: Two-dimensional (2D) materials have been made through various approaches but obtaining monodispersed simply by synthesis optimization gained little success, which highlighted the need for introducing nanoseparation methods. Density gradient ultracentrifugation method has emerged as a versatile and scalable method for sorting colloidal 2D nanomaterials according to their size of thickness difference. Establishing such density gradient ultracentrifugation method not only achieves monodispersed nanosheets and provides new opportunities for investigation on size dependent properties of 2D materials, but also makes the surface modification possible by introducing “reaction zones” during sedimentation of the colloids. - Highlights: • Density gradient ultracentrifugation was applied on size separation of 2D material. • Isopycnic separation was applied on separation of low density materials. • Rate-zonal separation was applied on separation of large density materials. • Size separation lead to investigation on size dependent properties of 2D material. • Mechanism was investigated by introducing “reaction zones” in the gradient.

77 NANOSCIENCE AND NANOTECHNOLOGY↗