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NASA NTRS2016

Exercise Effects on the Brain and Sensorimotor Function in Bed Rest

Long duration spaceflight microgravity results in cephalad fluid shifts and deficits in posture control and locomotion. Effects of microgravity on sensorimotor function have been investigated on Earth using head down tilt bed rest (HDBR). HDBR serves as a spaceflight analogue because it mimics microgravity in body unloading and bodily fluid shifts. Preliminary results from our prior 70 days HDBR studies showed that HDBR is associated with focal gray matter (GM) changes and gait and balance deficits, as well as changes in brain functional connectivity. In consideration of the health and performance of crewmembers we investigated whether exercise reduces the effects of HDBR on GM, functional connectivity, and motor performance. Numerous studies have shown beneficial effects of exercise on brain health. We therefore hypothesized that an exercise intervention during HDBR could potentially mitigate the effects of HDBR on the central nervous system. Eighteen subjects were assessed before (12 and 7 days), during (7, 30, and ~70 days) and after (8 and 12 days) 70 days of 6-degrees HDBR at the NASA HDBR facility in UTMB, Galveston, TX, US. Each subject was randomly assigned to a control group or one of two exercise groups. Exercise consisted of daily supine exercise which started 20 days before the start of HDBR. The exercise subjects participated either in regular aerobic and resistance exercise (e.g. squat, heel raise, leg press, cycling and treadmill running), or aerobic and resistance exercise using a flywheel apparatus (rowing). Aerobic and resistance exercise intensity in both groups was similar, which is why we collapsed the two exercise groups for the current experiment. During each time point T1-weighted MRI scans and resting state functional connectivity scans were obtained using a 3T Siemens scanner. Focal changes over time in GM density were assessed using voxel based morphometry (VBM8) under SPM. Changes in resting state functional connectivity was assessed using both a region of interest (ROI, or seed-to-voxel) approach as well as a whole brain intrinsic connectivity (i.e., voxel-to-voxel) analysis. For the ROI analysis we selected 11 ROIs of brain regions that are involved in sensorimotor function (i.e., L. Insular C., L. Putamen, R. Premotor C., L.+R. Primary Motor C., R. Vestibular C., L. Posterior Cingulate G., R. Cerebellum Lobule V + VIIIb + Crus I, and the R. Superior Parietal G.) and correlated their time course of brain activation during rest with all other voxels in the brain. The whole brain connectivity analysis tests changes in the strength of the global connectivity pattern between each voxel and the rest of the brain. Functional mobility was assessed using an obstacle course. Vestibular contribution to balance was measured using Neurocom Sensory Organization Test 5. Behavioral measures were assessed pre-HDBR, and 0, 8 and 12 days post-HDBR. Linear mixed models were used to test for effects of time, group, and group-by-time interactions. Family-wise error corrected VBM revealed significantly larger increases in GM volume in the right primary motor cortex in bed rest control subjects than in bed rest exercise subjects. No other significant group by time interactions in gray matter changes with bed rest were observed. Functional connectivity MRI revealed that the increase in connectivity during bed rest of the left putamen with the bilateral midsagittal precunes and the right cingulate gyrus was larger in bed rest control subjects than in bed rest exercise subjects. Furthermore, the increase in functional connectivity with bed rest of the right premotor cortex with the right inferior frontal gyrus and the right primary motor cortex with the bilateral premotor cortex was smaller in bed rest control subjects than in bed rest exercise subjects. Functional mobility performance was less affected by HDBR in exercise subjects than in control subjects and post HDBR exercise subjects recovered faster than control subjects. The group performance differences and GM changes were not related. Exercise in HDBR partially mitigates the adverse effect of HDBR on functional mobility, particularly during the post-bed rest recovery phase. In addition, exercise appears to result in differential brain structural and functional changes in motor regions such as the primary motor cortex, the premotor cortex and the putamen. Whether these central nervous system changes are related to motor behavioral changes including gait and balance warrants further research.

Koppelmans, V.↗

NASA NTRS2009

In-flight Assessment of Lower Body Negative Pressure as a Countermeasure for Post-flight Orthostatic Intolerance

Introduction. We investigated the efficacy of combining fluid loading with sustained lower body negative pressure (LBNP) to reverse orthostatic intolerance associated with weightlessness during and immediately after Space Shuttle missions. Methods. Shuttle astronauts (n=13) underwent 4 hours of LBNP at -30 mm(Hg) and ingested water and salt ( soak treatment) during flight in two complementary studies. In the first study (n=8), pre-flight heart rate (HR) and blood pressure (BP) responses to an LBNP ramp (5-min stages of -10 mm(Hg) steps to -50 mm(Hg) were compared to responses in-flight one and two days after LBNP soak treatment. In the second study (n=5), the soak was performed 24 hr before landing, and post-flight stand test results of soak subjects were compared with those of an untreated cohort (n=7). In both studies, the soak was scheduled late in the mission and was preceded by LBNP ramp tests at approximately 3-day intervals to document the in-flight loss of orthostatic tolerance. Results. Increased HR and decreased BP responses to LBNP were evident early in-flight. In-flight, one day after LBNP soak, HR and BP responses to LBNP were not different from pre-flight, but the effect was absent the second day after treatment. Post-flight there were no between-group differences in HR and BP responses to standing, but all 5 treatment subjects completed the 5-minute stand test whereas 2 of 7 untreated cohort subjects did not. Discussion. Exaggerated HR and BP responses to LBNP were evident within the first few days of space flight, extending results from Skylab. The combined LBNP and fluid ingestion countermeasure restored in-flight LBNP HR and BP responses to pre-flight levels and provided protection of post-landing orthostatic function. Unfortunately, any benefits of the combined countermeasure were offset by the complexity of its implementation, making it inappropriate for routine application during Shuttle flights.

Charles, J. B.↗

NASA NTRS1973

Fluid dynamic aspects of cardiovascular behavior during low-frequency whole-body vibration

The behavior of the cardiovascular system during low frequency whole-body vibration, such as encountered by astronauts during launch and reentry, is examined from a fluid mechanical viewpoint. The vibration characteristics of typical manned spacecraft and other vibration environments are discussed, and existing results from in vivo studies of the hemodynamic aspects of this problem are reviewed. Recent theoretical solutions to related fluid mechanical problems are then used in the interpretation of these results and in discussing areas of future work. The results are included of studies of the effects of vibration on the work done by the heart and on pulsatile flow in blood vessels. It is shown that important changes in pulse velocity, the instantaneous velocity profile, mass flow rate, and wall shear stress may occur in a pulsatile flow due to the presence of vibration. The significance of this in terms of changes in peripheral vascular resistance and possible damage to the endothelium of blood vessels is discussed.

Nerem, R. M.↗

NASA NTRS1991

Effects of leading-edge flap oscillation on unsteady delta wing flow and rock control

The isolated and interdisciplinary problems of unsteady fluid dynamics and rigid-body dynamics and control of delta wings with and without leading-edge flap oscillation are considered. For the fluid dynamics problem, the unsteady, compressible, thin-layer Navier-Stokes (NS) equations, which are written relative to a moving frame of reference, are solved along with the unsteady, linearized, Navier-displacement (ND) equations. The NS equations are solved for the flowfield using an implicit finite-volume scheme. The ND equations are solved for the grid deformation, if the leading-edge flaps oscillate, using an ADI scheme. For the dynamics and control problem, the Euler equation of rigid-body rolling motion for a wing and its flaps are solved interactively with the fluid dynamics equations for the wing-rock motion and subsequently for its control. A four-stage Runge-Kutta scheme is used to explicitly integrate the dynamics equation.

Kandil, Osama A.↗

NASA NTRS1955

Fifty Years of Boundary-Layer Theory and Experiment

The year 1954 marked the 50th anniversary of the Prandtl boundary-layer theory from which we may date the beginning of man's understanding of the dynamics of real fluids. A backward look at this aspect of the history of the last 50 years may be instructive. This paper (1) attempts to compress the events of those 50 years into a few thousand words, to tell in this brief space the interesting story of the development of a new concept, its slow acceptance and growth, its spread from group to group within its country of origin, and its diffusion to other countries of the world. The original brief paper of Prandtl (2) was presented at the Third International Mathematical Congress at Heidelberg in 1904 and published in the following year. It was an attempt to explain the d'Alembert paradox, namely, that the neglect of the small friction of air in the theory resulted in the prediction of zero resistance to motion. Prandtl set himself the task of computing the motion of a fluid of small friction, so small that its effect could be neglected everywhere except where large velocity differences were present or a cumulative effect of friction occurred This led to the concept of boundary layer, or transition layer, near the wall of a body immersed in a fluid stream in which the velocity rises from zero to the free-stream value. It is interesting that Prandtl used the term Grenzsehicht (boundary layer) only once and the term Ubergangsschicht (transition layer) seven times in the brief article. Later writers also used Reibungsschicht (friction layer), but most writers today use Grenzschicht (boundary layer).

Dryden, Hugh L.↗

NASA NTRS1996

Clinical aspects of the control of plasma volume at microgravity and during return to one gravity

Plasma volume is reduced by 10-20% within 24-48 h of exposure to simulated or actual microgravity. The clinical importance of microgravity induced hypovolemia is manifested by its relationship with orthostatic intolerance and reduced maximal oxygen uptake (VO2max) after return to one gravity (1G). Since there is no evidence to suggest that plasma volume reduction during microgravity is associated with thirst or renal dysfunctions, a diuresis induced by an immediate blood volume shift to the central circulation appears responsible for microgravity-induced hypovolemia. Since most astronauts choose to restrict their fluid intake before a space mission, absence of increased urine output during actual space flight may be explained by low central venous pressure (CVP) which accompanies dehydration. Compelling evidence suggests that prolonged reduction in CVP during exposure to microgravity reflects a "resetting" to a lower operating point, which acts to limit plasma volume expansion during attempts to increase fluid intake. In ground based and space flight experiments, successful restoration and maintenance of plasma volume prior to returning to an upright posture may depend upon development of treatments that can return CVP to its baseline IG operating point. Fluid-loading and lower body negative pressure (LBNP) have not proved completely effective in restoring plasma volume, suggesting that they may not provide the stimulus to elevate the CVP operating point. On the other hand, exercise, which can chronically increase CVP, has been effective in expanding plasma volume when combined with adequate dietary intake of fluid and electrolytes. The success of designing experiments to understand the physiological mechanisms of and development of effective counter measures for the control of plasma volume in microgravity and during return to IG will depend upon testing that can be conducted under standardized controlled baseline conditions during both ground-based and space flight investigations.

Review, Tutorial↗

NASA NTRS2014

Focal Gray Matter Plasticity as a Function of Long Duration Head-down Tilt Bed Rest

Long duration spaceflight (i.e., 22 days or longer) has been associated with changes in sensorimotor systems, resulting in difficulties that astronauts experience with posture control, locomotion, and manual control. The microgravity environment is an important causal factor for spaceflight induced sensorimotor changes. Whether these sensorimotor changes may be related to structural and functional brain changes is yet unknown. However, increased intracranial pressure that by itself has been related to microgravity-induced bodily fluid shifts: [1] has been associated with white matter microstructural damage, [2] Thus, it is possible that spaceflight may affect brain structure and thereby cognitive functioning. Long duration head-down tilt bed rest has been suggested as an exclusionary analog to study microgravity effects on the sensorimotor system, [3] Bed rest mimics microgravity in body unloading and bodily fluid shifts. In consideration of the health and performance of crewmembers both in- and post-flight, we are conducting a prospective longitudinal 70-day bed rest study as an analog to investigate the effects of microgravity on brain structure, and [4] Here we present results of the first eight subjects.

Koppelmans, Vincent↗

NASA NTRS2017

Implementation of a Body Force Model in OVERFLOW for Propulsor Simulations

We present an implementation of a propulsor model based on body force method into the OVERFLOW computational fluid dynamics code to model turbofan engines and propulsors of similar type. The model estimates the forces imparted on the fluid by the blade camber surfaces as a body force source terms in the momentum and energy equations over grids that represent the rotor and stator of a fan stage. We tested the implementation on three cases: 1) Source Diagnostics Test (SDT) fan with R4 rotors, which has extensive test data on aerodynamic performance and rotor wake surveys, 2) A stand-alone Aeronaut TF8000 propulsor which is an off-the-shelf propulsor used on model aircraft and 3) The D8 aircraft model with TF8000 propulsors placed in a wind tunnel. Despite missing some of the features in the velocity profiles near the endwalls (i.e. hub and casing surfaces), the OVERFLOW simulations with body force model predicted area-averaged flow speed and total pressure rise through the SDT propulsor within a few percent of the LDV (Laser Doppler Velocimetry) measurements. In the case of TF8000 propulsor on the D8 airframe, the model under-predicted mechanical power coefficient by several percent of the wind tunnel test results when the horizontal force balance condition over the airframe is targeted by tuning rotor speed. By investigating the upstream influence of the rotor swirl, it was found out that the induced swirl velocity effects upstream were relatively small and they rapidly vanished before reaching one fan diameter upstream of the fan face. The body force model provided insights on aerothermodynamics and aeromechanics of boundary layer ingesting propulsor; these insights could not be obtained by using the uniform pressure jump model.

Propulsor↗

NASA NTRS2004

Shock Re-equilibration of Fluid Inclusions

Fluid inclusions (microscopic volumes of fluid trapped within minerals as they precipitate) are extremely common in terrestrial minerals formed under a wide range of geological conditions from surface evaporite deposits to kimberlite pipes. While fluid inclusions in terrestrial rocks are nearly ubiquitous, only a few fluid inclusion-bearing meteorites have been documented. The scarcity of fluid inclusions in meteoritic materials may be a result of (a) the absence of fluids when the mineral was formed on the meteorite parent body or (b) the destruction of fluid inclusions originally contained in meteoritic materials by subsequent shock metamorphism. However, the effects of impact events on pre-existing fluid inclusions trapped in target and projectile rocks has received little study. Fluid inclusions trapped prior to the shock event may be altered (re-equilibrated) or destroyed due to the high pressures, temperatures, and strain rates associated with impact events. By examining the effects of shock deformation on fluid inclusion properties and textures we may be able to better constrain the pressure-temperature path experienced by terrestrial and meteoritic shocked materials and also gain a clearer understanding of why fluid inclusions are rarely found in meteorite samples.

Madden, M. E. Elwood↗

NASA NTRS2013

Generalized Fluid System Simulation Program, Version 6.0

The Generalized Fluid System Simulation Program (GFSSP) is a finite-volume based general-purpose computer program for analyzing steady state and time-dependant flow rates, pressures, temperatures, and concentrations in a complex flow network. The program is capable of modeling real fluids with phase changes, compressibility, mixture thermodynamics, conjugate heat transfer between solid and fluid, fluid transients, pumps, compressors and external body forces such as gravity and centrifugal. The thermo-fluid system to be analyzed is discretized into nodes, branches, and conductors. The scalar properties such as pressure, temperature, and concentrations are calculated at nodes. Mass flow rates and heat transfer rates are computed in branches and conductors. The graphical user interface allows users to build their models using the 'point, drag, and click' method; the users can also run their models and post-process the results in the same environment. The integrated fluid library supplies thermodynamic and thermo-physical properties of 36 fluids, and 24 different resistance/source options are provided for modeling momentum sources or sinks in the branches. This Technical Memorandum illustrates the application and verification of the code through 25 demonstrated example problems.

Majumdar, A. K.↗

NASA NTRS1993

A continuum theory of a lubrication problem with solid particles

The governing equations for a two-dimensional lubrication problem involving the mixture of a Newtonian fluid with solid particles at an arbitrary volume fraction are developed using the theory of interacting continuua (mixture theory). The equations take the interaction between the fluid and the particles into consideration. Provision is made for the possibility of particle slippage at the boundaries. The equations are simplified assuming that the solid volume fraction varies in the sliding direction alone. Equations are solved for the velocity of the fluid phase and that of the solid phase of the mixture flow in the clearance space of an arbitrary shaped bearing. It is shown that the classical pure fluid case can be recovered as a special case of the solutions presented. Extensive numerical solutions are presented to quantify the effect of particulate solid for a number of pertinent performance parameters for both slider and journal bearings. Included in the results are discussions on the influence of particle slippage on the boundaries as well as the role of the interacting body force between the fluid and solid particles.

Dai, Fuling↗

NASA NTRS1996

Cardiovascular Deconditioning and Venous Air Embolism in Simulated Microgravity in the Rat

Astronauts conducting extravehicular activities undergo decompression to a lower ambient pressure, potentially resulting in gas bubble formation within the tissues and venous circulation. Additionally, exposure to microgravity produces fluid shifts within the body leading to cardiovascular deconditioning. A lower incidence of decompression illness in actual spaceflight compared with that in ground-based altitude chamber flights suggests that there is a possible interaction between microgravity exposure and decompression illness. The purpose of this study was to evaluate the cardiovascular and pulmonary effects of simulated hypobaric decompression stress using a tail suspension (head-down tilt) model of microgravity to produce the fluid shifts associated with weightlessness in conscious, chronically instrumented rats. Venous bubble formation resulting from altitude decompression illness was simulated by a 3-h intravenous air infusion. Cardiovascular deconditioning was simulated by 96 h of head-down tilt. Heart rate, mean arterial blood pressure, central venous pressure, left ventricular wall thickening and cardiac output were continuously recorded. Lung studies were performed to evaluate edema formation and compliance measurement. Blood and pleural fluid were examined for changes in white cell counts and protein concentration. Our data demonstrated that in tail-suspended rats subjected to venous air infusions, there was a reduction in pulmonary edema formation and less of a decrease in cardiac output than occurred following venous air infusion alone. Mean arterial blood pressure and myocardial wall thickening fractions were unchanged with either tail-suspension or venous air infusion. Heart rate decreased in both conditions while systemic vascular resistance increased. These differences may be due in part to a change or redistribution of pulmonary blood flow or to a diminished cellular response to the microvascular insult of the venous air embolization.

Robinson, R. R.↗

NASA NTRS1999

Vortex Reconnection or Breakdown Subsequent to Perpendicular Collision With A Solid Body

This paper analytically examines the unsteady fluid dynamics of a vortex filament subsequent to a normal collision of the vortex with a solid body. In particular, the breakdown or reconnection phenomena, post-collision, for a vortex filament is studied. The paper does not investigate the collision dynamics process itself. The derived exact solution is based upon the laminar viscous form of the Helmholtz equations.

Young, Larry A.↗

NASA NTRS2020

Tin Abundances Require that Chassignites Originated from Multiple Magmatic Bodies Distinct from Nakhlites

Meteorites from Mars lack field context but chemical and chronologic studies have revealed remarkable links between nakhlites and chassignites. A widely held consensus is that nakhlites and chassignites originated from a large, single differentiated flow or shallow intrusive [1-5]. An Ar-Ar study assumed multiple flows based on resolvable age differences between meteorites [6], but did not address the possibility of differential cooling in a large, shallowly emplaced intrusion [1]. REE abundances in pyroxenes from nakhlites and Chassigny led [7] to argue for derivation of these rocks from distinct magmas. Volatile abundances (F, Cl, OH) in chlorapatites indicated that the entire suite of nakhlites and chassignites experienced hydrothermal interaction with a single fluid supporting a single body origin [4]. The discovery of a new chassignite, NWA 8694, extended the Mg# range from 80-54, providing a closer link to nakhlites but revealed the petrological difficulty of fractionating a single body of liquid to yield a series of olivine cumulates with such a large Mg# range [8]. When mafic magmas are emplaced into the crust, crustal assimilation can impart distinct elemental signatures if the country rock has experienced sedimentary or hydrothermal processing [9]. In this work, we used Sn abundances of nakhlites and chassignites to show that these rocks were crystallized from distinct magma batches, providing vital contextual clues to their origin.

Humayun, M.↗

NASA NTRS1985

Homeostasis in Primates in the Hyperdynamic Environment

The influence of chronic centrifugation upon the homestatic regulation of the circadian timekeeping system was examined. The interactions of body temperature regulation and the behavioral state of arousal were studied by evaluating the influence of cephalic fluid shifts induced by lower body positive air pressure (LBPP), upon these systems. The small diurnal squirrel monkey (Saimiri sciureus) was used as the non-human primate model. Results show that the circadian timekeeping system of these primates is functional in the hyperdynamic environment, however, some of its components appear to be regulated at different homeostatic levels. The LBPP resulted in an approximate 0.7 C decrease in DBT (p 0.01). However, although on video some animals appeared drowsy during LBPP, sleep recording revealed no significant changes in state of arousal. Thus, the physiological mechanisms underlying this lowering of body temperature can be independent of the arousal state.

Fuller, C. A.↗

NASA NTRS2008

Flow Components in a NaK Test Loop Designed to Simulate Conditions in a Nuclear Surface Power Reactor

A test loop using NaK as the working fluid is presently in use to study material compatibility effects on various components that comprise a possible nuclear reactor design for use on the lunar surface. A DC electromagnetic (EM) pump has been designed and implemented as a means of actively controlling the NaK flow rate through the system and an EM flow sensor is employed to monitor the developed flow rate. These components allow for the matching of the flow rate conditions in test loops with those that would be found in a full-scale surface-power reactor. The design and operating characteristics of the EM pump and flow sensor are presented. In the EM pump, current is applied to a set of electrodes to produce a Lorentz body force in the fluid. A measurement of the induced voltage (back-EMF) in the flow sensor provides the means of monitoring flow rate. Both components are compact, employing high magnetic field strength neodymium magnets thermally coupled to a water-cooled housing. A vacuum gap limits the heat transferred from the high temperature NaK tube to the magnets and a magnetically-permeable material completes the magnetic circuit. The pump is designed to produce a pressure rise of 5 psi, and the flow sensor's predicted output is roughly 20 mV at the loop's nominal flow rate of 0.5 GPM.

Polzin, Kurt A.↗

NASA NTRS2022

A Record of Low-Temperature Asteroidal Processes of Amoeboid Olivine Aggregates from the Kainsaz Co3.2 Chondrite

Amoeboid olivine aggregates (AOAs) from the Kainsaz CO3.2 chondrite were analyzed using transmission electron microscopy in order to gain a more complete understanding of thermal metamorphism on the parent body and the role of fluids during metamorphic heating. The Kainsaz AOAs are dominated by strongly zoned, fine-grained, olivine grains (Fa2-31) with heterogeneous Fe enrichments along the grain boundaries, which are interpreted as the result of 26Fe2+-Mg2+ interdiffusion with the matrix during thermal metamorphism. However, our diffusion calculations show that such AOA olivine zoning and compositions cannot be produced by a simple diffusional exchange during metamorphic heating, unlike chondrule olivine zoning and compositions. In addition, fine-grained ferroan olivine overgrowths occur heterogeneously in crystallographic continuity with olivines on the AOA exteriors. The overgrowths (Fa33-36) are compositionally distinct from the underlying AOA olivines and are not fully equilibrated with the matrix olivines (Fa~20-55).The ferroan olivine overgrowths likely formed by precipitation from fluids in an epitaxial relationship with forsteritic olivine on the edges of AOAs. Texturally and compositionally diverse chromite grains are also observed along olivine grain boundaries, in olivine grains, and in pore spaces between olivine grains. They share a similar crystallographic orientation relationships with adjacent olivine, suggestive of their formation by exsolution and/or epitaxial growth. Collectively, these observations provide evidence for the mobilization of Fe, Mg, Si, Cr, and Al in the presence of fluids along olivine grain boundaries and into olivine grains during thermal metamorphism. We conclude that in Kainsaz AOAs, the strong zonation development in individual olivine grains and the formation of ferroan olivine overgrowths and chromite grains were a fluid-driven process that occurred at relatively low temperatures (<500°C), during the cooling history of the CO3 chondrite parent body, following the peak of thermal metamorphism.

Amoeboid olivine aggregates↗

NASA NTRS1991

Rotating reactor studies

Undesired gravitational effects such as convection or sedimentation in a fluid can sometimes be avoided or decreased by the use of a closed chamber uniformly rotated about a horizontal axis. In a previous study, the spiral orbits of a heavy or buoyant particle in a uniformly rotating fluid were determined. The particles move in circles, and spiral in or out under the combined effects of the centrifugal force and centrifugal buoyancy. A optimization problem for the rotation rate of a cylindrical reactor rotated about its axis and containing distributed particles was formulated and solved. Related studies in several areas are addressed. A computer program based on the analysis was upgraded by correcting some minor errors, adding a sophisticated screen-and-printer graphics capability and other output options, and by improving the automation. The design, performance, and analysis of a series of experiments with monodisperse polystyrene latex microspheres in water were supported to test the theory and its limitations. The theory was amply confirmed at high rotation rates. However, at low rotation rates (1 rpm or less) the assumption of uniform solid-body rotation of the fluid became invalid, and there were increasingly strong secondary motions driven by variations in the mean fluid density due to variations in the particle concentration. In these tests the increase in the mean fluid density due to the particles was of order 0.015 percent. To a first approximation, these flows are driven by the buoyancy in a thin crescent-shaped depleted layer on the descending side of the rotating reactor. This buoyancy distribution is balanced by viscosity near the walls, and by the Coriolis force in the interior. A full analysis is beyond the scope of this study. Secondary flows are likely to be stronger for buoyant particles, which spiral in towards the neutral point near the rotation axis under the influence of their centrifugal buoyancy. This is because the depleted layer is thicker and extends all the way around the reactor.

Roberts, Glyn O.↗