Constant Gradient Research Articles

Heat transfer and entropy generation analysis of ternary nanofluid

Abstract In light of the rising demand for improved heat transfer in thermal systems, this work offers a unique technique for boosting heat transfer capacity and reducing entropy generation using a ternary nanofluid. Moreover, constant pressure gradient, magnetic field, Joule heating, and thermal radiation also contribute to the flow dynamics. The 2D mathematical model is solved numerically using a finite difference method and the simulations are done in MATLAB. The obtained results show that ternary nanoparticles not only increase the thermal rates but are also helpful in maintaining the irreversibility of a system. It is also observed that the heat transfer of the base fluid increased by 7.5%, 8.3%, and 8.5% on adding TiO2, CuO-TiO2, and MgO-CuO-TiO2 nanoparticles, respectively.

A hybrid lattice Boltzmann and finite difference method for two-phase flows with soluble surfactants

A hybrid method is developed to simulate two-phase flows with soluble surfactants. In this method, the interface and bulk surfactant concentration equations of diffuse-interface form, which include source terms to consider surfactant adsorption and desorption dynamics, are solved in the entire fluid domain by the finite difference method, while two-phase flows are solved by a lattice Boltzmann color-gradient model, which can accurately simulate binary fluids with unequal densities. The flow and interface surfactant concentration fields are coupled by a modified Langmuir equation of state, which allows for surfactant concentration beyond critical micelle concentration. The capability and accuracy of the hybrid method are first validated by simulating three numerical examples, including the adsorption of bulk surfactants onto the interface of a stationary droplet, the droplet migration in a constant surfactant gradient, and the deformation of a surfactant-laden droplet in a simple shear flow, in which the numerical results are compared with theoretical solutions and available literature data. Then, the hybrid method is applied to simulate the buoyancy-driven bubble rise in a surfactant solution, in which the influence of surfactants is identified for varying wall confinement, density ratio, Eotvos number and Biot number. It is found that surfactants exhibit a retardation effect on the bubble rise due to the Marangoni stress that resists interface motion, and the retardation effect weakens as the Eotvos or Biot number increases. We further show that the weakened retardation effect at higher Biot numbers is attributed to a decreased non-uniform effect of surfactants at the interface. By comparing with the Cahn-Hilliard phase-field method, we also show that the present method conserves the mass for each fluid, improves numerical stability especially at high density ratio and Eotvos number, and does not need the selection of free parameters, thus breaking the limitations of the existing method.

Additive manufacturing of gradient porous Si/SiC ceramic parts: Quasi-static behaviors and mechanical properties

Porous silicon carbide (SiC) ceramic exhibits low density, high toughness, which endow it with an indispensable role in engineering applications. However, the manufacturing, designing, and making full use of the rich pore structure of gradient porous SiC ceramic to improve its mechanical performance still face many challenges. Herein, the manufacture of gradient porous Si/SiC ceramic part is realized for the first time, and the influence of gradient structural on mechanical properties is deeply analyzed. The results indicate that the porous Si/SiC ceramics with constant gradient transition rate is characterized by step-by-step destruction and can carry larger strains than the porous Si/SiC ceramics with non-constant gradient transition rate. Meanwhile, reducing the gradient span can improve the strength, but it is easy to lead to brittle damage. In particular, gradient porous Si/SiC ceramics with constant gradient transition rate and 30 % gradient span can exhibit both good strength and toughness. The compressive strength can reach 11.71 MPa, and the equivalent elastic modulus can reach 2.28 GPa. Finally, a laminar material prediction model for mechanical properties is presented. This paper presents an effective fabrication method for gradient porous ceramic parts and provides a feasible means for the design and prediction of mechanical properties.

Selective enhancement of 1H signal from water and oil in porous media at low field with Overhauser DNP.

In porous media MR studies, discriminating between oil and water presents a challenge because MR lifetimes are often similar and spectra overlap. Low saturations might suggest an experimental strategy of increasing the static field for increased sensitivity, but susceptibility effects are exacerbated at higher field. Overhauser dynamic nuclear polarization, effective at low static field, was employed with water and oil-soluble nitroxide to selectively enhance water and oil signals. We employ a home-built 2MHz ceramic magnet to achieve selective enhancement of water and oil, in bulk, and in a rock core. For imaging, we employ a 705kHz ceramic magnet with a 4 gauss/cm constant gradient configuration to image the hyperpolarized signal. A rock core flooding experiment was undertaken to highlight the advantages of Overhauser enhancement. A simple phase cycling technique may be employed to cancel the thermally polarized 1H signal to isolate the enhanced signal of interest.

Mixed Convection Flow of a Viscous Dissipative and Heat Generating/Absorbing Fluid Through a Slit Microchannel

This paper is aimed at investigating the consequences of viscous dissipation and super-hydrophobicity on a magnetized mixed convection flow of an electrically conducting fluid across an up facing microchannel influenced by a transverse magnetic field. The plates were alternatively heated and incorporated with heat source/sink effect. The modeled governing equations have been obtained using a semi-analytical (regular perturbation) method. Various line graphs have been plotted to demonstrate the behavior of key parameter dictating the flow. It was found out that the thermal gradient and fluid velocity are significantly enhanced for mounting values of mixed convection Gre, Brickman number Br, Darcy porous number K and heat source S parameters in the superhydrophobic microchannel for constant pressure gradient Г. On the other hand, the velocity deteriorates for increasing levels of magnetic field M and heat sink S factors. Further, the comparison of this present analysis with previously published literature for limiting cases when Г=S=0 and Gre=1 showcased an excellent concurrence, thereby confirming the accuracy and validity of this present investigation. The findings from this research will find relevance in engineering, technological and industrial processes such as for solar collectors, nuclear reactors cooled during emergency shutdown, nuclear power plants, gas turbines and the various propulsion devices for aircraft, missiles, satellites and space vehicles.

Couette flow of micropolar fluid in a channel filled with anisotropic porous medium

This paper presents a mathematical model for the flow of micropolar fluid in a horizontal channel filled with an anisotropic porous medium, bounded by two parallel plates—where the upper plate is stationary, and the lower plate moves at a constant velocity. The flow, driven by both a constant pressure gradient and the movement of the lower plate, is governed by the Darcy-Brinkman equation. Using no-slip and no-spin boundary conditions, we analytically derive expressions for the velocity, microrotational velocity, and stress distributions. The study provides a graphical analysis of the flow behavior influenced by key parameters such as the Darcy number, porous medium anisotropy, anisotropy angle, and the micropolar fluid’s material parameters. Furthermore, the effects of the material parameters and Darcy number on shear stress and couple stress are thoroughly investigated. The findings have applications in modeling fluid flow in striated or fractured rock formations.

Entropy analysis of mixed convective electro-magnetohydrodynamic couple-stress hybrid nanofluid flow with variable electrical conductivity in a porous channel

The paper presents a novel study to examine the irreversibility of quadratically mixed convective electro-magnetohydrodynamic (EMHD) flow of a couple-stress hybrid nanofluid (CSHNF) with variable properties in a vertical porous channel. The channel walls are exposed to an applied electric field effect and a uniform transverse magnetic field. The hybrid nanofluid considered is an ethylene glycol (C 2 H 6 O 2) base mixed with multi-walled carbon nanotubes (MWCNT) and silver (Ag) nanoparticles (NPs), assuming the base fluid and nanoparticles to be in a state of thermal equilibrium following the Tiwari-Das nanofluid model. The potential applications of the study can be in microfluidics to nanofluidics, particularly in developing cooling technologies, EMHD pumps, high-end microelectromechanical systems (MEMS), and lab-on-a-chip (LOC) devices used in bioengineering. A constant pressure gradient acting in the flow direction and the buoyancy effect under the quadratic Boussinesq approximation drive the flow. The governing momentum and energy equations are nondimensionalized using pertinent dimensionless parameters and solved by the semi-analytical homotopy analysis method (HAM). The entropy generation and the Bejan numbers are derived to examine the irreversibilities in the system. To investigate the rate of shear stresses and heat transfer, skin friction coefficients and Nusselt numbers on the channel walls are determined. The analysis emphasizes the influence of nanoparticle concentration and electromagnetic field on the flow dynamics, temperature distribution, and system irreversibilities in the presence of porous media. It reveals the enhancement of fluid velocity and temperature degradation for higher concentrations. In contrast, both reduce for higher magnetic and electrical strength. With the enhancement of electrical joule heating and quadratic convection, a higher entropy generation rate is attained with a low rate of heat transfer irreversibility. However, it reduces with higher nanoparticle concentration, electrical strength, porosity, and variable electrical conductivity parameters under the dominance of heat transfer irreversibility.

Estimate of in-band eddy current effect in space gravitational wave detection

Abstract In space detection of gravitational waves (GWs), the presence of a low-frequency varying magnetic field will generate eddy currents in the test mass, resulting in a varying magnetic moment. This magnetic moment will couple with a constant magnetic field gradient, producing residual acceleration within the frequency band of GW detection, causing the test mass to deviate from the free-falling mode. However, this effect has not yet been studied clearly in the noise budget for TianQin and LISA Pathfinder since the constant DC magnetic susceptibility was applied to quantify the varying magnetic moment. This paper utilizes the parameter of alternating current (AC) magnetic susceptibility to define this process, and further analyzes and evaluates the effect. In a general magnetic field environment, the contribution of this effect to TianQin acceleration noise reaches 20\% from 0.1 mHz to 3 mHz. The contribution to LISA noise is less than 10\% from $10^{-4}$ to 0.1 Hz, and less than 10\% below $10^{-4}$ Hz. This effect does not have a potential limit on LISA low-frequency science down to 20 $\mu$Hz [Phys. Rev. Lett. 120, 061101 (2018)].

Investigation of the impact of transient pressure gradients on turbulent channel flow dynamics

AbstractThe effect of transient pressure gradients, or transient pumping in turbulent channel flow configuration, is investigated. Employing a cost‐efficient reduced‐order stochastic method known as one‐dimensional turbulence (ODT) modeling, simulations explore different signal shapes for the modulation of the prescribed pressure gradient forcing, including sinusoidal modulation, step‐like modulation, and piecewise sinusoidal beating. Various cycle periods and active pumping times are investigated. The simulations are conducted at a frictional Reynolds number of and a molecular Prandtl number of . The study adopts a passive scalar formulation to investigate heat transfer properties. The study quantifies the effects of transient pressure gradients on heat transfer rate, drag, and pumping power. Preliminary ODT predictions suggest that all transient cases exhibit lower heat transfer rates and a higher pumping power requirement than the constant pressure gradient case, with the step‐like modulation yields superior skin‐friction drag and heat transfer rate reductions relative to other signals.

Estimating the In Situ Stratification via Remotely Sensed Internal Wave Speeds

Abstract This work tests a methodology for estimating the ocean stratification gradient using remotely sensed, high temporal and spatial resolution field measurements of internal wave propagation speeds. The internal wave (IW) speeds were calculated from IW tracks observed using a shore-based, X-band marine radar deployed at a field site on the south-central coast of California. An inverse model, based on the work of Kar and Guha, utilizes the linear internal wave dispersion relation, assuming a constant vertical density gradient is the basis for the inverse model. This allows the vertical gradient of density to be expressed as a function of the internal wave phase speed, local water depth, and a background average density. The inputs to the algorithm are the known cross-shore bathymetry, the background ocean density, and the remotely sensed cross-shore profiles of IW speed. The estimated density gradients are then compared to the synchronously measured vertical density profiles collected from an in situ instrument array. The results show a very good agreement offshore in deeper water (∼50–30 m) but more significant discrepancies in shallow water (20–10 m) closer to shore. In addition, a sensitivity analysis is conducted that relates errors in measured speeds to errors in the estimated density gradients. Significance Statement The propagation speed of ocean internal waves inherently depends on the vertical structure of the water density, which is termed stratification. In this work, we evaluate and test with real field observations a technique to infer the ocean density stratification from internal wave propagation speeds collected from remote sensing images. Such methods offer a way to monitor ocean stratification without the need for extensive in situ measurements.

Identifying the mixed and forced convection flow with transverse magnetic field

AbstractOptimal control of the steady, laminar, magnetohydrodynamics (MHD) mixed convection flow of an electrically conducting fluid is considered under the effect of the transverse magnetic field in a square duct. The viscous and Joule dissipations are included and the flow is driven by a constant pressure gradient. The triple nonlinear set of momentum, induction, and energy equations are solved in dimensionless form by using the mixed finite element method (FEM) with the implementation of Newton's method for nonlinearity with the discretize‐then‐linearize approach. Accordingly, FEM solutions are obtained for various values of the problem parameters to ensure the efficiency of the underlying scheme. This study aims to investigate the problem of controlling the steady flow by using the physically significant parameters of the problem as control variables in the case of a mixed convection flow. In this respect, classification of the type of convection, forced or free, is achieved by controlling the Grashof number (Gr). Besides, single and pairwise controls with Hartmann number (M), Prandtl number (Pr), and magnetic Reynolds number (Rm) are also used to regain the prescribed fluid behaviors and required magnetic field. Control simulations are conducted with the sequential‐least‐squares‐programming (SLSQP) algorithm in the optimization.

Investigation of micropolar dusty fluid flow in a rotational frame with magnetic field: A meshless radial basis function pseudospectral approach

AbstractRotational flow has numerous applications across a wide range of fields, including industrial processes for mixing, pumping, and processing materials, geophysical fluid dynamics for studying the Earth's atmosphere and oceans, aerospace engineering for designing and testing aircraft and spacecraft, medical imaging for creating detailed images of the human body, and environmental engineering for studying the transport of pollutants in water and air. In rotational flow, pumping power is an important parameter that measures the amount of energy required to maintain the flow of the fluid in a rotating frame. It is significant because the presence of the Coriolis force and other rotational effects can substantially alter the fluid dynamics, making it difficult to maintain a steady flow. The present study deals with the flow of micropolar dusty fluid in a rotating frame under the influence of the magnetic field, applied transversely to the flow in a horizontal channel. The fluid is induced to flow between two parallel plates by the movement of the upper plate and a constant pressure gradient. A meshless radial basis function pseudospectral approach is employed to derive a set of partial differential equations that determine the primary and secondary velocity profiles of the fluid, as well as the particle and microrotation velocities and temperature distribution. The pumping power required to sustain the flow in the absence of a pressure gradient is also calculated based on these velocity profiles. The findings provide valuable insights into the behavior of micropolar dusty fluids in a rotational channel and can potentially inform the design of industrial processes involving such fluids.

Microbial mechanisms for higher hydrogen production in anaerobic digestion at constant temperature versus gradient heating

BackgroundClean energy hydrogen (H2) produced from abundant lignocellulose is an alternative to fossil energy. As an essential influencing factor, there is a lack of comparison between constant temperatures (35, 55 and 65 °C) and gradient heating temperature (35 to 65 °C) on the H2 production regulation potential from lignocellulose-rich straw via high-solid anaerobic digestion (HS-AD). More importantly, the microbial mechanism of temperature regulating H2 accumulation needs to be investigated.ResultsConstant 65 °C led to the lowest lignin residue (1.93%) and the maximum release of cellulose and hemicellulose, and the highest H2 production (26.01 mL/g VS). H2 production at 35 and 55 °C was only 14.56 and 24.13 mL/g VS, respectively. In order to further explore the potential of ultra-high temperature (65 °C), HS-AD was performed by gradient heating conditions (35 to 65 °C). However, compared to constant 65 °C, gradient heating conditions led to higher lignin residue (2.49%) and lower H2 production (13.53 mL/g VS) than gradient heating conditions (47.98%). In addition, metagenomic analysis showed the cellulose/hemicellulose hydrolyzing bacteria and genes (mainly Thermoclostridium, and xynA, xynB, abfA, bglB and xynD), H2-producing bacteria and related genes (mainly Thermoclostridium, and nifD, nifH and nifK), and microbial movement and metabolic functions were enriched at 65 °C. However, the enrichment of two-component systems under gradient heating conditions resulted in a lack of highly-enriched ultra-high-temperature cellulose/hemicellulose hydrolyzing genera and related genes but rather enriched H2 consumption genera and genes (mainly Acetivibrio, and hyaB and hyaA) resulting in a weaker H2 production.ConclusionsThe lignin degradation process does not directly determine H2 accumulation, which was actually regulated by bacteria/genes contributing to H2 production/consumption. In addition, it is temperature that enhances the hydrolysis process of lignin rather than lignin-degrading enzymes, bacteria and genes by promoting microbial material transfer and metabolism. In terms of temperature, one of the key parameters of HS-AD for H2 production, we developed an important regulatory strategy, enriched the theoretical basis of temperature regulation for H2 production to further expanded the research horizon in this field.ABqfqNejHM5MQBNj5XnjcNVideo

Design and test of an X -band constant gradient structure

A light source project named very compact inverse Compton scattering gamma-ray source (VIGAS) is under development at Tsinghua University. VIGAS aims to generate monochromatic high-energy gamma rays by colliding 350-MeV electron beams with 400-nm laser photons within a 12-m beamline. To produce a high-energy electron beam in such a compact space, the system consists of an S-band high-brightness injector and six X-band high-gradient accelerating structures. The goal of the X-band structure is to operate at a high gradient of 80 MV/m. Therefore, we adopts the constant gradient traveling wave approach, where the iris from the first cell to the end cell is tapered. The structure has 72 cells, including 70 cells and 2 couplers, so we named it XT72. The frequency of XT72 is selected to 11.424 GHz, and the 2π/3 mode is adopted. In this paper, we present a comprehensive study covering the detailed design, fabrication, rf tuning, and high-power test results of the first XT72. Additionally, we compare the performance of this structure to that of the previous constant impedance structure. Our results demonstrate that the XT72 is capable of operating at an 80−MV/m gradient with a lower breakdown rate. This advancement paves the way for the development of VIGAS project and contributes to the wider application of X-band room-temperature high-gradient structures in compact accelerator facilities. Published by the American Physical Society 2024

Hydromagnetic Non-Newtonian Nanofluid Flow Past Linealy Stretching Convergent-Divergent Conduit with Chemical Reaction

This paper investigates hydromagnetic non-Newtonian nanofluid flow past linearly stretching convergent-divergent conduit with chemical reaction using spectral ralaxation method. The fluid considered here is electrically conducting and is subjected to a constant pressure gradient and variable magnetic field. The two non-parallel walls are assumed not to intersect and the angle between the inclined walls is <i>θ</i>. The governing equations are continuity equation, momentum equation, species concentration, induction equation and energy equation. On modelling, the resulting partial differential equations are non-linear and are first transformed into system of ordinary differential equations through similarity transformation. The resulting boundary value problem is solved numerically using Spectral Relaxation Method. The results obtained after varying Hartman number, Unsteadiness parameter, Reynolds number, Solutal and Thermal Grashof number on velocity, concentration, temperature and induction profiles are represented in form of graphs. Some of the application of this study are, when extracting the energy from earth crust that varies in length between five to ten kilometres and temperature in between 500° and 1000°, nano-fluids are employed to cool the machinery and equipment working under high friction and high temperature. This present study considers nanofluid acting as a coolant of such equipment as well as acting as a lubricant thus reducing the rate of wear and tear of the equipment. The copper-water increases the thermophysical properties thus increasing heat transfer coefficient and hence increasing cooling rate.

Characterizing magnetohydrodynamic effects on developed nanofluid flow in an obstructed vertical duct under constant pressure gradient

Abstract This research endeavors to conduct an examination of the thermal characteristics within the duct filled with the copper nanoparticles and water as base fluid. In exhaust systems, like car exhausts, chimneys, and kitchen hoods, duct flows are crucial. These systems safely discharge odors, smoke, and contaminants into the atmosphere after removing them from enclosed places. The study focuses on a laminar flow regime that is both hydrodynamically and thermally developed, with a specified constraints at any cross-sectional plane. To address this, we employ the finite volume method as it stands as a judicious choice, offering a balance between computational efficiency and solution accuracy. Notably, we have observed that the deceleration of flow induced by elevated Rayleigh numbers can be effectively regulated by the application of an appropriately calibrated external magnetic field. The prime parameters of the problem with ranges are: pressure gradient ( 1 ≤ p 0 ≤ 100 ) (1\le {p}_{0}\le 100) , Hartmann number ( 0 ≤ Ha ≤ 50 ) (0\le \text{Ha}\le 50) , Rayleigh number ( 1 , 000 ≤ Ra ≤ 40 , 000 ) (1,000\le \text{Ra}\le 40,000) , and magnetic parameter ( 0 ≤ M ≤ 50 ) (0\le M\le 50) . Furthermore, our analysis reveals that the Nusselt number exhibits a nearly linear correlation with the nanoparticle volume fraction parameter, a trend observed across a range of Rayleigh numbers and magnetic parameter values. We have noted that a mere 20% nanoparticle volume fraction can result in up to 62% rise in the Nusselt number while causing an almost 50% decrease in the factor f Re. This research framework serves as a robust foundation for understanding the intricate interplay between magnetic influences and thermal-hydraulic behavior within the delineated system.

Beam energy spectra in the presence of cell-to-cell phase advance errors

The parameters of the accelerating structures of linear accelerators have a strong influence on the beam parameters such as the mean energy and the energy spread. One of the most common types the accelerating structures is based on disk loaded waveguides. Imperfections in such structure parameters may be critical for subsequent beam dynamics. We analytically study the influence of the errors of the cell-to-cell phase advance on the beam energy spread and the mean energy on the example of the constant gradient structure. Derived expressions were applied to the case of a large number of accelerating structures, which is relevant for GeV linacs, to obtain accelerated beam parameters in terms of the probabilistic analysis for several values of the injected beam duration.

Rheological study of water-based Cu nanofluid between two corrugated curved walls under constant pressure gradient

Nanofluids have captured the attention of scientists due to their superior thermophysical properties compared to ordinary liquids. Consequently, nanofluids serve as suitable cooling agents applicable to systems requiring swift response to thermal changes, such as vehicle engines. Therefore, the current article scrutinizes the characteristics of heat transfer on the pressure-driven flow of magnetized nanofluid between two curved corrugated surfaces in the presence of heat generation/absorption. Copper oxide nanoparticles (Cu) have been combined with pure water to form a nanofluid called Cu/H2O. The geometry of the channel is represented mathematically in an orthogonal curvilinear coordinate system. The corrugation grooves are described by sinusoidal functions with phase differences between the corrugated curved walls. The boundary perturbation method is used to find the analytical solution for the velocity field, temperature field, and volumetric flow rate taking the corrugation amplitude as the perturbation parameter. The impact of dissimilar parameters such as the curvature parameter (0.5≤k≤10), wave number (1≤α≤3), magnetic parameter (1≤M≤5), and wave amplitude (0.1≤ε≤0.8) on the flow fields are analyzed through graphs and discussed in detail. The results show that the peak of the velocity increases with the radius of curvature and the width of the channel for a constant pressure gradient. If we increase the magnetic parameter from 1 to 4, the velocity profile at the specified point decreases by 30 %. If we increase the heat source/sink parameter from 2 to 5, the temperature profile at the specified point increases by approximately 17 %. The flow rate is increased by the corrugations for any phase difference between the corrugated curved walls depending on the corrugation wavenumber and the channel radius of curvature.

A study on the pressure‐driven flow of magnetized non‐Newtonian Casson fluid between two corrugated curved walls of an arbitrary phase difference

AbstractPressure‐driven movement is a fundamental concept with numerous applications in various industries, scientific disciplines, and fields of engineering. Its proper execution is vital for promoting revolutionary innovations and providing solutions in numerous sectors. Therefore, this article scrutinizes the pressure‐driven flow of magnetized Casson fluid between two curved corrugated walls. The geometry of the channel is represented mathematically in an orthogonal curvilinear coordinate system. The corrugation grooves are described by sinusoidal functions with phase differences between the corrugated curved walls. The boundary perturbation method is used to find the analytical solution for the velocity field and volumetric flow rate, taking the corrugation amplitude as the perturbation parameter. The results show that the peak of the velocity increases with the radius of curvature and the width of the channel for a constant pressure gradient. The velocity exhibited a declining trend due to an increase in the Casson fluid parameter. For a sufficiently large corrugation wavenumber, the flow rate decreases, and the phase difference becomes irrelevant. However, the reduction in flow can be minimized by decreasing the channel radius of curvature. In general, a smooth curved channel will give the maximum flow rate for a large corrugation wavenumber. The model can be used to simulate blood flow in arteries with varying geometries and magnetic fields, aiding in the study of cardiovascular diseases and the design of medical devices like stents.

The Diffusion Exchange Ratio (DEXR): A minimal sampling of diffusion exchange spectroscopy to probe exchange, restriction, and time-dependence.

Water exchange is increasingly recognized as an important biological process that can affect the study of biological tissue using diffusion MR. Methods to measure exchange, however, remain immature as opposed to those used to characterize restriction, with no consensus on the optimal pulse sequence(s) or signal model(s). In general, the trend has been towards data-intensive fitting of highly parameterized models. We take the opposite approach and show that a judicious sub-sample of diffusion exchange spectroscopy (DEXSY) data can be used to robustly quantify exchange, as well as restriction, in a data-efficient manner. This sampling produces a ratio of two points per mixing time: (i) one point with equal diffusion weighting in both encoding periods, which gives maximal exchange contrast, and (ii) one point with the same total diffusion weighting in just the first encoding period, for normalization. We call this quotient the Diffusion EXchange Ratio (DEXR). Furthermore, we show that it can be used to probe time-dependent diffusion by estimating the velocity autocorrelation function (VACF) over intermediate to long times (~ 2-500 ms). We provide a comprehensive theoretical framework for the design of DEXR experiments in the case of static or constant gradients. Data from Monte Carlo simulations and experiments acquired in fixed and viable ex vivo neonatal mouse spinal cord using a permanent magnet system are presented to test and validate this approach. In viable spinal cord, we report the following apparent parameters from just 6 data points: , , , and , which correspond to the exchange time, restricted or non-Gaussian signal fraction, an effective spherical radius, and permeability, respectively. For the VACF, we report a long-time, power-law scaling with , which is approximately consistent with disordered domains in 3-D. Overall, the DEXR method is shown to be highly efficient, capable of providing valuable quantitative diffusion metrics using minimal MR data.