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NASA NTRS1995

Image analysis used to count and measure etched tracks from ionizing radiation

We have developed techniques to use digitized scanning electron micrographs and computer image analysis programs to measure track densities in lunar soil grains and plastic dosimeters. Tracks in lunar samples are formed by highly ionizing solar energetic particles and cosmic rays during near surface exposure on the Moon. The track densities are related to the exposure conditions (depth and time). Distributions of the number of grains as a function of their track densities can reveal the modality of soil maturation. We worked on two samples identified for a consortium study of lunar weathering effects, 61221 and 67701. They were prepared by the lunar curator's staff as polished grain mounts that were etched in boiling 1 N NaOH for 6 h to reveal tracks. We determined that backscattered electron images taken at 10 percent contrast and approximately 50 percent brightness produced suitable high contrast images for analysis. We used the NIH Image program to cut out areas that were unsuitable for measurement such as edges, cracks, etc. We ascertained a gray-scale threshold of 25 to separate tracks from background. We used the computer to count everything that was two pixels or greater in size and to measure the area to obtain track densities. We found an excellent correlation with manual measurements for track densities below 1 x 10(exp 8) cm(exp -2). For track densities between 1 x 10(exp 8) cm(exp -2) to 1 x 10(exp 9) cm(exp -2) we found that a regression formula using the percentage area covered by tracks gave good agreement with manual measurements. We determined the track density distributions for 61221 and 67701. Sample 61221 is an immature sample, but not pristine. Sample 67701 is a submature sample that is very close to being fully mature. Because only 10 percent of the grains have track densities less than 10(exp 9) cm(exp -2), it is difficulty to determine whether the sample matured in situ or is a mixture of a mature and a submature soil. Although our analysis of plastic dosimeters is at an early stage of development, results are encouraging. The dosimeter was etched in 6.25 N NaOH at 70 deg C for 16 h. We took 200x secondary electron images of the sample and used the NIH Image software to count and measure major and minor diameters of the etched tracks. We calculated the relative track etch rate from a formula that relates it to the major and minor diameters. We made a histogram of the number of tracks versus their relative etch rate. The relative track etching rate is proportional to the linear energy transfer of the particle. With appropriate calibration experiments, the histogram could be used to calculate the radiation dose.

Blanford, George E.↗

NASA NTRS1994

Early time evolution of negative ion clouds and electron density depletions produced during electron attachment chemical release experiments

Two-dimensional electrostatic particle-in-cell simulations are used to study the early time evolution of electron depletions and negative ion clouds produced during electron attachment chemical releases in the ionosphere. The simulation model considers the evolution in the plane perpendicular to the magnetic field and a three-species plasma that contains electrons, positive ions, and also heavy negative ions that result as a by-product of the electron attachment reaction. The early time evolution (less than the negative ion cyclotron period) of the system shows that a negative charge surplus initially develops outside of the depletion boundary as the heavy negative ions move across the boundary. The electrons are initially restricted from moving into the depletion due to the magnetic field. An inhomogenous electric field develops across the boundary layer due to this charge separation. A highly sheared electron flow velocity develops in the depletion boundary due to E x B and Delta-N x B drifts that result from electron density gradients and this inhomogenous electric field. Structure eventually develops in the depletion boundary layer due to low-frequency electrostatic waves that have growth times shorter than the negative ion cyclotron period. It is proposed that these waves are most likely produced by the electron-ion hybrid instability that results from sufficiently large shears in the electron flow velocity.

Scales, W. A.↗

NASA NTRS2001

Robust Strategy for Rocket Engine Health Monitoring

Monitoring the health of rocket engine systems is essentially a two-phase process. The acquisition phase involves sensing physical conditions at selected locations, converting physical inputs to electrical signals, conditioning the signals as appropriate to establish scale or filter interference, and recording results in a form that is easy to interpret. The inference phase involves analysis of results from the acquisition phase, comparison of analysis results to established health measures, and assessment of health indications. A variety of analytical tools may be employed in the inference phase of health monitoring. These tools can be separated into three broad categories: statistical, rule based, and model based. Statistical methods can provide excellent comparative measures of engine operating health. They require well-characterized data from an ensemble of "typical" engines, or "golden" data from a specific test assumed to define the operating norm in order to establish reliable comparative measures. Statistical methods are generally suitable for real-time health monitoring because they do not deal with the physical complexities of engine operation. The utility of statistical methods in rocket engine health monitoring is hindered by practical limits on the quantity and quality of available data. This is due to the difficulty and high cost of data acquisition, the limited number of available test engines, and the problem of simulating flight conditions in ground test facilities. In addition, statistical methods incur a penalty for disregarding flow complexity and are therefore limited in their ability to define performance shift causality. Rule based methods infer the health state of the engine system based on comparison of individual measurements or combinations of measurements with defined health norms or rules. This does not mean that rule based methods are necessarily simple. Although binary yes-no health assessment can sometimes be established by relatively simple rules, the causality assignment needed for refined health monitoring often requires an exceptionally complex rule base involving complicated logical maps. Structuring the rule system to be clear and unambiguous can be difficult, and the expert input required to maintain a large logic network and associated rule base can be prohibitive.

Santi, L. Michael↗

NASA NTRS1992

Development of a full-scale transmission testing procedure to evaluate advanced lubricants

Experimental tests were performed on the OH-58A helicopter main rotor transmission in the NASA Lewis 500-hp Helicopter Transmission Test Stand. The testing was part of a joint Navy/NASA/Army lubrication program. The objective of the program was to develop a separate lubricant for gearboxes and demonstrate an improved performance in life and load-carrying capacity. The goal of the experiments was to develop a testing procedure to fail certain transmission components using a MIL-L-23699 base reference oil, then run identical tests with improved lubricants and demonstrate performance. The tests were directed at failing components that the Navy has had problems with due to marginal lubrication. These failures included mast shaft bearing micropitting, sun gear and planet bearing fatigue, and spiral bevel gear scoring. A variety of tests were performed and over 900 hours of total run time accumulated for these tests. Some success was achieved in developing a testing procedure to produce sun gear and planet bearing fatigue failures. Only marginal success was achieved in producing mast shaft bearing micropitting and spiral bevel gear scoring.

Lewicki, David G.↗

NASA NTRS1984

The growth, propagation and decay of global scale Rossby waves during FGGE

A portrait of the evolution of global scale Rossby waves for the FGGE year is presented. Emphasis is placed on the temporal evolution of the amplitude and phase of Hough mode projections, rather than on characteristics of the time spectra of these waves. On the basis of previous work, it was felt that it would be adequate to consider the 500 mb level in isolation from the others, and that the Hough functions (which are vector functions of the horizontal wind components and the height field) were good approximations to the "true' eigenfunctions. Thus, the first steps of the analysis consisted of projecting the 500 mb height and wind data (obtained from the ECMWF analyses) onto Hough functions for each synoptic time. The seasonal cycle and time mean were removed separately for each season, and all remaining eastward propagating components removed on a seasonal basis; all remaining westward propagating components were retained.

Lindzen, R. S.↗

NASA NTRS1987

Diffuse infrared emission of the galaxy: Large scale properties

A quantitative analysis of Infrared Astronomy Satellite (IRAS) data in the galactic plane shows that: about 66% of the power radiated in the 100 micron band comes from the diffuse medium, the other 33% coming from well identified luminous sources. The diffuse emission has almost constant colors throughout the Galaxy, similar to the local cirrus colors. The sources have a much lower 12 micron/25 micron and a much high 60 micron/100 micron emission ratio than the diffuse component, giving a very striking anticorrelation in the color-color diagrams. The separation between one narrow and a second broader component shows that the molecular component does not provide much more than one half of the diffuse emission in the molecular ring: this implies a 4 pi nuI(nu) emissivity at 100 microns for the atomic component of about 2.4 x 10 to the minus 30th watts per H atom, 10 times higher than the emissivity of the molecular component at the same galactocentric radius. The atomic component emissivity measures the interstellar radiation field density. The temperature distribution of the 2 components is discussed comparing IRAS data with measures of the 900 micron emission of the galactic plane, which appears to be dominated by cold dust in the narrow component.

Puget, J. L.↗

NASA NTRS1989

Dynamical evolution of domain walls in an expanding universe

Whenever the potential of a scalar field has two or more separated, degenerate minima, domain walls form as the universe cools. The evolution of the resulting network of domain walls is calculated for the case of two potential minima in two and three dimensions, including wall annihilation, crossing, and reconnection effects. The nature of the evolution is found to be largely independent of the rate at which the universe expands. Wall annihilation and reconnection occur almost as fast as causality allows, so that the horizon volume is 'swept clean' and contains, at any time, only about one, fairly smooth, wall. Quantitative statistics are given. The total area of wall per volume decreases as the first power of time. The relative slowness of the decrease and the smoothness of the wall on the horizon scale make it impossible for walls to both generate large-scale structure and be consistent with quadrupole microwave background anisotropy limits.

Press, William H.↗

NASA NTRS1991

Simultaneous Solar Maximum Mission (SMM) and Very Large Array (VLA) observations of solar active regions

Very Large Array observations at 20 cm wavelength can detect the hot coronal plasma previously observed at soft x ray wavelengths. Thermal cyclotron line emission was detected at the apex of coronal loops where the magnetic field strength is relatively constant. Detailed comparison of simultaneous Solar Maximum Mission (SMM) Satellite and VLA data indicate that physical parameters such as electron temperature, electron density, and magnetic field strength can be obtained, but that some coronal loops remain invisible in either spectral domain. The unprecedent spatial resolution of the VLA at 20 cm wavelength showed that the precursor, impulsive, and post-flare components of solar bursts originate in nearby, but separate loops or systems of loops.. In some cases preburst heating and magnetic changes are observed from loops tens of minutes prior to the impulsive phase. Comparisons with soft x ray images and spectra and with hard x ray data specify the magnetic field strength and emission mechanism of flaring coronal loops. At the longer 91 cm wavelength, the VLA detected extensive emission interpreted as a hot 10(exp 5) K interface between cool, dense H alpha filaments and the surrounding hotter, rarefield corona. Observations at 91 cm also provide evidence for time-correlated bursts in active regions on opposite sides of the solar equator; they are attributed to flare triggering by relativistic particles that move along large-scale, otherwise-invisible, magnetic conduits that link active regions in opposite hemispheres of the Sun.

Willson, Robert F.↗

NASA NTRS2001

A Hybrid Numerical Method for Turbulent Mixing Layers

A hybrid method has been developed for simulations of compressible turbulent mixing layers. Such mixing layers dominate the flows in exhaust systems of modern day aircraft and also those of hypersonic vehicles currently under development. The method configurations in which a dominant structural feature provides an unsteady mechanism to drive the turbulent development in the mixing layer. The hybrid method uses a Reynolds-averaged Navier-Stokes (RANS) procedure to calculate wall bounded regions entering a mixing section, and a Large Eddy Simulation (LES) procedure to calculate the mixing dominated regions. A numerical technique was developed to enable the use of the hybrid RANS-LES method on stretched, non-Cartesian grids. Closure for the RANS equations was obtained using the Cebeci-Smith algebraic turbulence model in conjunction with the wall-function approach of Ota and Goldberg. The wall-function approach enabled a continuous computational grid from the RANS regions to the LES region. The LES equations were closed using the Smagorinsky subgrid scale model. The hybrid RANS-LES method is applied to a benchmark compressible mixing layer experiment. Preliminary two dimensional calculations are used to investigate the effects of axial grid density and boundary conditions. Vortex shedding from the base region of a splitter plate separating the upstream flows was observed to eventually transition to turbulence. The location of the transition, however, was much further downstream than indicated by experiments. Actual LES calculations, performed in three spatial directions, also indicated vortex shedding, but the transition to turbulence was found to occur much closer to the beginning of the mixing section. which is in agreement with experimental observations. These calculations demonstrated that LES simulations must be performed in three dimensions. Comparisons of time-averaged axial velocities and turbulence intensities indicated reasonable agreement with experimental data.

Georgiadis, Nicholas J.↗

NASA NTRS2021

Compact, Self-Aligned Focusing Schlieren System

A novel compact, self-aligned focusing Schlieren system is presented that eliminates the need for a separate source grid and cutoff grid. A single grid element serves to both generate a projected source grid onto a retroreflective background, and to act as the cutoff grid for the reflected light. This is made possible by manipulating the polarization of the light through the system. The use of only a single grid element eliminates the need to create a cutoff grid that is perfectly matched and scaled to the source grid, and removes the need to align the source and cutoff grids to each other. The sensitivity to density objects is adjustable with the use of a polarizing prism. Images obtained with this system show similar operation to existing focusing Schlieren systems, but with much reduced complexity and setup time. Images taken with acrylic windows placed nor-mal to the optical axis further demonstrate the system’s utility for wind tunnel measurements.

Focusing Schlieren↗

NASA NTRS1976

Drive tube 60009 - A chemical study of magnetic separates of size fractions from five strata

Each bulk soil and both the magnetic and nonmagnetic components of the 90-150 micron and below 20 micron fractions of five soils from drive tube 60009 were analyzed. Samples were analyzed for FeO, Na2O, Sc, Cr, Co, Ni, Hf, Ta, Th, La, Ce, Sm, Eu, Tb, Yb, and Lu by neutron activation analysis. Several samples were fused and analyzed for major elements by electron microprobe analysis. Compositional variations are not systematically related to depth. The compositions of the five soils studied are well explained by a two-component mixing model whose end members are a submature Apollo 16-type soil and an extremely immature anorthositic material similar to 60025. There is evidence that the anorthositic component had received a small amount of exposure before these soils were mixed. After mixing, the soils received little exposure suggesting mixing and deposition on a rapid time scale.

Blanchard, D. P.↗

NASA NTRS2012

Effect of Population III Multiplicity on Dark Star Formation

We numerically study the mutual interaction between dark matter (DM) and Population III (Pop III) stellar systems in order to explore the possibility of Pop III dark stars within this physical scenario. We perform a cosmological simulation, initialized at z approx. 100, which follows the evolution of gas and DM. We analyze the formation of the first mini halo at z approx. 20 and the subsequent collapse of the gas to densities of 10(exp 12)/cu cm. We then use this simulation to initialize a set of smaller-scale 'cut-out' simulations in which we further refine the DM to have spatial resolution similar to that of the gas. We test multiple DM density profiles, and we employ the sink particle method to represent the accreting star-forming region. We find that, for a range of DM configurations, the motion of the Pop III star-disk system serves to separate the positions of the protostars with respect to the DM density peak, such that there is insufficient DM to influence the formation and evolution of the protostars for more than approx. 5000 years. In addition, the star-disk system causes gravitational scattering of the central DM to lower densities, further decreasing the influence of DM over time. Any DM-powered phase of Pop III stars will thus be very short-lived for the typical multiple system, and DM will not serve to significantly prolong the life of Pop III stars.

Stacy, Athena↗

NASA NTRS2014

Testing Mars Exploration Rover-Inspired Operational Strategies for Semi-Autonomous Rovers on the Moon Ii: the GeoHeuristic Operational Strategies Test in Alaska

We used MER-derived semi-autonomous rover science operations strategies to determine best practices suitable for remote semi-autonomous lunar rover geology. Two field teams studied two glacial moraines as analogs for potential ice-bearing lunar regolith. At each site a Rover Team commanded a human rover to execute observations based on common MER sequences; the resulting data were used to identify and characterize targets of interest. A Tiger Team followed the Rover Team using traditional terrestrial field methods, and the results of the two teams were compared. Narrowly defined goals that can be addressed using cm-scale or coarser resolution may be met sufficiently by the operational strategies adapted from MER survey mode. When reconnaissance is the primary goal, the strategies tested are necessary but not sufficient. Further, there may be a set of optimal observations for such narrowly defined, hypothesis-driven science goals, such that collecting further data would result in diminishing returns. We confirm results of previous tests that indicated systematic observations might improve efficiency during strategic planning, and improve science output during data analysis. This strategy does not markedly improve the rate at which a science team can ingest data to feed back into tactical decision-making. Other methods should be tested to separate the strategic and tactical processes, and to build in time for data analysis.

MER↗

NASA NTRS2016

MarCO: Interplanetary Mission Development on a CubeSat Scale

Shortly after JPL’s Interior Exploration using Seismic Investigations, Geodesy and Heat Transport (InSight) mission launches, separates, and commences its cruise phase, two CubeSats will deploy from the launch vehicle’s upper stage and begin independent flight to Mars (Fig. 1). During InSight’s entry, descent, and landing (EDL) sequence, these twin Mars Cube One (MarCO) spacecraft will fly 3,500 km above the Martian surface, recording and relaying InSight UHF radio data to the Deep Space Network (DSN) on Earth1. MarCO is a twin CubeSat mission developed by the NASA Jet Propulsion Laboratory (JPL) to accompany the InSight (Interior Exploration using Seismic Investigations, Geodesy and Heat Transport) Mars mission lander. MarCO's primary mission objective is to launch with InSight and independently fly to Mars to serve as a communications relay during InSight's entry, descent, and landing (EDL) phase. MarCO represents a new type of deep space mission: CubeSats at Mars. Building on the development of JPL's first interplanetary CubeSat project, the Interplanetary Nano-Spacecraft Pathfinder in Relevant Environment (INSPIRE), MarCO further refined the approach to hardware, software, and ground architecture development to solve the challenges of quickly building low-budget spacecraft to fly to Mars. The greatest constraint, beyond others typical of CubeSat missions, was time. The duration between MarCO's conception to completion of spacecraft assembly was less than two years - an unprecedented schedule for any planetary mission to date. Through necessity, MarCO has built on previous experience, procedures, systems, and development methodologies, defining a new niche for supporting larger primary missions. The MarCO spacecraft are poised to write a new chapter in deep space exploration. Originally slated to launch and reach Mars in 2016, the InSight mission schedule subsequently slipped to 2018. During the original landing of InSight, Earth would not be in view, and no orbiter around Mars would have been in position to both receive UHF EDL data and simultaneously relay it back to Earth. It was from this obstacle that MarCO was conceived. Regardless of any changes to InSight’s 2018 EDL configuration geometry, MarCO is still expected to fly and serve in the same capacity as originally designed: the first CubeSat mission to Mars. CubeSats have historically been firmly in the domain of universities and small companies. As first conceived, they served as a platform upon which to teach all aspects of the space mission lifecycle. JPL took on this mission type with Interplanetary Nano-Spacecraft Pathfinder in Relevant Environment2 (INSPIRE), moving the concept into a new domain: deep space. Building from the INSPIRE platform and lessons learned, MarCO addressed new challenges in the domain of planetary missions: independent interplanetary flight and navigation, integration with a large-scale mission, long-distance and long-delay communication, short development time, and a small development team. Of these, the greatest constraint was schedule: only 18 months passed from conception of mission concept until delivery of fully assembled and tested flight hardware. Careful selection of mission team, along with extensive use of off-the-shelf equipment, and streamlining automated processes, was essential. This achievement represents the next step in the evolution of CubeSats beyond low-Earth orbit.

Werne, Thomas↗

NASA NTRS1989

Tropical forecasting - Predictability perspective

Results are presented of classical predictability studies and forecast experiments with observed initial conditions to show the nature of initial error growth and final error equilibration for the tropics and midlatitudes, separately. It is found that the theoretical upper limit of tropical circulation predictability is far less than for midlatitudes. The error growth for a complete general circulation model is compared to a dry version of the same model in which there is no prognostic equation for moisture, and diabatic heat sources are prescribed. It is found that the growth rate of synoptic-scale errors for the dry model is significantly smaller than for the moist model, suggesting that the interactions between dynamics and moist processes are among the important causes of atmospheric flow predictability degradation. Results are then presented of numerical experiments showing that correct specification of the slowly varying boundary condition of SST produces significant improvement in the prediction of time-averaged circulation and rainfall over the tropics.

Shukla, J.↗

NASA NTRS1990

Aerothermodynamic measurements on a proposed assured crew return vehicle (ACRV) lifting-body configuration at Mach 6 and 10 in air

A 0.02-scale model of a lifting-body concept for possible application to the Assured Crew Return Vehicle from Space Station Freedom was tested at Mach 6 and 10 in air. Thermal mappings and surface streamline patterns were obtained at angles of attack ranging from 0 to 30 deg and unit Reynolds numbers Re from 2 to 8 x 10 to the 6th/ft. Areas that experienced the highest heating were near the model nose and tip-fin leading edges. The effect of Re on windward centerline heating coefficients was negligible, whereas increases in angles of attack produced increases in heating. At Mach 6 and the highest unit Re, turbulent heat at the windward centerline was three to four times the laminar level. Leeward crossflow separation and vortex reattachment along the centerline are evident across the Re and angle-of-attack ranges tested, indicative of a complex flowfield.

Horvath, Thomas J.↗

NASA NTRS1993

Monitoring issues from a modeling perspective

Recognition that earth's climate and biogeophysical conditions are likely changing due to human activities has led to a heightened awareness of the need for improved long-term global monitoring. The present long-term measurement efforts tend to be spotty in space, inadequately calibrated in time, and internally inconsistent with respect to other instruments and measured quantities. In some cases, such as most of the biosphere, most chemicals, and much of the ocean, even a minimal monitoring program is not available. Recently, it has become painfully evident that emerging global change issues demand information and insights that the present global monitoring system simply cannot supply. This is because a monitoring system must provide much more than a statement of change at a given level of statistical confidence. It must describe changes in diverse parts of the entire earth system on regional to global scales. It must be able to provide enough input to allow an integrated physical characterization of the changes that have occurred. Finally, it must allow a separation of the observed changes into their natural and anthropogenic parts. The enormous policy significance of global change virtually guarantees an unprecedented level of scrutiny of the changes in the earth system and why they are happening. These pressures create a number of emerging challenges and opportunities. For example, they will require a growing partnership between the observational programs and the theory/modeling community. Without this partnership, the scientific community will likely fall short in the monitoring effort. The monitoring challenge before us is not to solve the problem now, but rather to set appropriate actions in motion so as to create the required framework for solution. Each individual piece needs to establish its role in the large problem and how the required interactions are to take place. Below, we emphasize some of the needs and opportunities that could and should be addressed through participation by the theoreticians and modelers in the global change monitoring effort.

Mahlman, Jerry D.↗

NASA NTRS2000

Thermocapillary Flow and Aggregation of Bubbles on a Solid Wall

During the electrolytic evolution of oxygen bubbles forming on a vertically oriented transparent tin oxide electrode, bubbles were found to be mutually attractive. The mechanism of the aggregation had never been explained satisfactorily until Guelcher et al. attributed it to thermocapillary flow. The gradient of surface tension of the liquid at the bubble's surface, which was established because of reaction heat and ohmic heat loss at the electrode wall, drives flow of the liquid adjacent to each bubble; the bubble "pumps" fluid along its surface away from the wall. Fluid flows toward the bubble to conserve mass and entrains nearby bubbles in the flow pattern. The same logic would apply when two bubbles of equal size are adjacent to each other on a warm wall. Each bubble drives thermocapillary flow and hence entrains the other in its flow pattern, which drives the aggregation. Our objective here is to perform experiments where the temperature gradient at the wall is well known and controlled. The theory can be quantitatively tested by studying aggregation of bubble pairs of equal size, and by varying system parameters such as temperature gradient, bubble size and fluid viscosity. The results are then compared with the theory in a quantitatively rigorous manner. We demonstrate that the theory without adjustable parameters is capable of quantitatively modeling the rate of aggregation of two bubbles. The equations governing the thermocapillary flow around a single stationary bubble on a heated or cooled wall in a semi-infinite domain were solved. Both Reynolds number and Marangoni number were much less than unity. The critical result is that liquid in the vicinity of a warm wall flows toward a stationary collector bubble. Consequently the thermocapillary flow around the stationary bubble entrains another bubble toward itself. The bubbles undergo hindered translation parallel to the wall with velocity U while the fluid flow field is described with u. Two velocities were equated by using a wall hindrance parameter q: U = qu [1] which shows the velocity of bubble is proportional to the entraining velocity. The hindrance parameter q can experimentally be measured independently. q can also be calculated by solving the equations of motion for a bubble translating parallel to a solid wall. The experimental cell is cylindrical with an ID of 10 cm and consists of a 1 cm deep main cell filled with silicone oil and flanked by two thermal reservoirs. The upper thermal reservoir was heated and the lower thermal reservoir was cooled so that the bubbles aggregate. Two types of silicone oil (eta = 0.02 and 0.50 Pa s) were used. Two equal sized air bubbles were injected into the cell with a syringe. The center-to-center distance of bubbles was observed through a microscope. Bubble radius ranged from 0.40 mm to 0.65 mm and the temperature gradients along with the cell ranged from 1400 to 5000 K/m. The bubbles aggregated when heat flows from the wall to the fluid. The velocities of bubbles were in the range of 1 - 10 microns/s. The separation r decreased more quickly when the temperature gradient was higher, bubble size was larger, and the oil viscosity was lower. r decreased more rapidly as the bubbles approached each other. Dimensionless time was arbitrarily set to be zero when the dimensionless center-to-center distance between the bubbles was 4. All the bubble trajectories fall onto one line, especially in the range of dimensionless distance from 4 to 3. This means the relative movement of the bubble pair is proportional to the temperature gradient and bubble size and it is inversely proportional to the viscosity of the oil. This result strongly suggests that the thermocapillary flow-based aggregation mechanism is correct. A value of q can be estimated by fitting the scaled data to Eq. [1]. A best fit value of q was obtained as q = 0.26 with a standard deviation of 0.03. Independent experimental results for q for a 0.5 mm radius bubble, give values of q in the range 0.11 to 0.23. The value of q obtained from solving the equations of motion reveals q has values in the range 0.23 - 0.30. Since the full scale of possible values of q is zero to one, the maximum deviation of independently determined values of q from the best fit value was 15% of this full scale. Thus reasonable quantitative agreement between theory and experiment has been obtained.

Kasumi, Hiroki↗