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At least 91 records · Page 5

Periodic solutions to systems of reaction-diffusion equations

Necessary and sufficient conditions are derived for the existence of temporally periodic 'dissipative structure' solutions in weak diffusion with the reaction rate terms dominant in a generic system of reaction-diffusion differential equations. The enumerator index i of the equations denotes the density or concentration of the ith participating molecular or biological species, and D sub i is the diffusivity constant for the ith species while Q sub i (c), an algebraic function of the n-tuple c, expresses the local rate of production of the ith species due to chemical reactions or biological interactions.

Rosen, G.↗

Water Recovery from Bioreactor Mixed Liquors Using Forward Osmosis with Polyelectrolyte Draw Solutions

This paper reports on the use of forward osmosis (FO) with polyelectrolyte draw solutions to recover water from bioreactor mixed liquors. The work was motivated by the need for new regenerative water purification technologies to enable long-duration space missions. Osmotic membrane bioreactors may be an option for water and nutrient recovery in space if they can attain high water flux and reverse solute flux selectivity (RSFS), which quantifies the mass of permeated water per mass of draw solute that has diffused from the draw solution into a bioreactor. Water flux was measured in a direct flow system using wastewater from a municipal wastewater treatment plant and draw solutions prepared with two polyelectrolytes at different concentrations. The direct flow tests displayed a high initial flux (>10 L/m2/h) that decreased rapidly as solids accumulated on the feed side of the membrane. A test with deionized water as the feed revealed a small mass of polyelectrolyte crossover from the draw solution to the feed, yielding an RSFS of 80. Crossflow filtration experiments demonstrated that steady state flux above 2 L/m2·h could be maintained for 70 h following an initial flux decline due to the formation of a foulant cake layer. This study established that FO could be feasible for regenerative water purification from bioreactors. By utilizing a polyelectrolyte draw solute with high RSFS, we expect to overcome the need for draw solute replenishment. This would be a major step towards sustainable operation in long-duration space missions.

Calen R Raulerson↗

Transport of solar flare protons: Comparison of a new analytic model with spacecraft measurements

An analytic solution was obtained to the complete Fokker-Planck equation including the effects of convection, interplanetary deceleration and acceleration, corotation, and anisotropic diffusion. The solution yields a time to maximum for the particle flux of about 10 h and an exponential decay time of about 5 h. Several solar flare particle events were observed with the solar and galactic cosmic ray experiment on OGO-6. Comparisons of the calculated time dependence of the fluxes with these observations of 1 to 70 MeV protons show that the model adequately describes both the rise and decay times.

Lupton, J. E.↗

Shadowing and the role of small diffusivity in the chaotic advection of scalars

Using techniques from shadowing theory, the solution of the scalar advection-diffusion equation is studied. It is shown that, under certain circumstances, the effect of small scalar diffusivity is to smooth the zero-diffusivity solution by averaging local fine-scaled structure against a Gaussian. The method of study depends on shadowing and thus fails for nonuniformly stretching systems, its failure suggesting the ways in which the effects of asymptotically small molecular diffusion can become nonlocal in chaotic fluid flows.

Klapper, I.↗

Effect of Gravity Level on the Particle Shape and Size During Zeolite Crystal Growth

A microscopic diffusion model is developed to represent solute transport in the boundary layer of a growing zeolite crystal. This model is used to describe the effect of gravity on particle shape and solute distribution. Particle dynamics and crystal growth kinetics serve as the boundary conditions of flow and convection-diffusion equations. A statistical rate theory is used to obtain the rate of solute transport across the growing interface, which is expressed in terms of concentration and velocity of solute species. Microgravity can significantly decrease the solute velocity across the growing interface compared to its earth-based counterpart. The extent of this reduction highly depends on solute diffusion constant in solution. Under gravity, the flow towards the crystal enhances solute transport rate across the growing interface while the flow away from crystals reduces this rate, suggesting a non-uniform growth rate and thus an elliptic final shape. However, microgravity can significantly reduce the influence of flow and obtain a final product with perfect spherical shape. The model predictions compare favorably with the data of space experiment of zeolites grown in space.

Song, Hong-Wei↗

Coherent pulses in the diffusive transport of charged particles`

We present exact solutions to the diffusive transport of charged particles following impulsive injection for a simple model of scattering. A modified, two-parameter relaxation-time model is considered that simulates the low rate of scattering through perpendicular pitch-angle. Scattering is taken to be isotropic within each of the foward- and backward-pointing hemispheres, respectively, but, at the same time, a reduced rate of sccattering is assumed from one hemisphere to the other one. By applying a technique of Fourier- and Laplace-transform, the inverse transformation can be performed and exact solutions can be reached. By contrast with the first, and so far only exact solutions of Federov and Shakov, this wider class of solutions gives rise to coherent pulses to appear. The present work addresses omnidirectional densities for isotropic injection from an instantaneous and localized source. The dispersion relations are briefly discussed. We find, for this particular model, two diffusive models to exist up to a certain limiting wavenumber. The corresponding eigenvalues are real at the lowest wavenumbers. Complex eigenvalues, which are responsible for coherent pulses, appear at higher wavenumbers.

Kota, J.↗

Investigation of compositional segregation during unidirectional solidification of solid solution semiconducting alloys

Compositional segregation of solid solution semiconducting alloys in the radial direction during unidirectional solidification was investigated by calculating the effect of a curved solid liquid interface on solute concentration at the interface on the solid. The formulation is similar to that given by Coriell, Boisvert, Rehm, and Sekerka except that a more realistic cylindrical coordinate system which is moving with the interface is used. Analytical results were obtained for very small and very large values of beta with beta = VR/D, where V is the velocity of solidification, R the radius of the specimen, and D the diffusivity of solute in the liquid. For both very small and very large beta, the solute concentration at the interface in the solid C(si) approaches C(o) (original solute concentration) i.e., the deviation is minimal. The maximum deviation of C(si) from C(o) occurs for some intermediate value of beta.

Wang, J. C.↗

Interfacial geometry and D-variation effects in two-phase systems

Numerical solutions of the governing diffusion equation for two-phase concentration dependent diffusion coefficients are examined. Solutions were also calculated for planar, cylindrical, and spherical geometries to compare the effect of interface geometries with those caused by concentration-dependent diffusion coefficients, and two methods of averaging D were considered to determine the best averaging method for different types of D-variations. The effects of interface-location criteria on mass conservation and convergence of interface location, diffusion coefficient variation in the alpha and beta-phases of a two-phase binary alloy system, effect of D(alpha) variation in a cylindrical couple on beta-phase thickness, and geometry and D-variation effects on the degree of homogenization were determined. It is concluded that typical D(alpha)-variations can have a greater influence on the kinetics of interdiffusion than the geometry.

Tenney, D. R.↗

Ar Atmosphere: Implications for Structure and Composition of Mercury's Crust

We examine the possibilities of sustaining an argon atmosphere by diffusion from the upper 10 km of crust, and alternatively by effusion from a molten or previously molten area at great depth . Ar-40 in the atmospheres of the planets is a measure of potassium abundance in the interiors since Ar-40 is a product of radiogenic decay of K-40 by electron capture with the subsequent emission of a 1.46 eV gamma-ray. Although the Ar-40 in the earth's atmosphere is expected to have accumulated since the late bombardment, Ar-40 in surface-bounded exospheres is eroded quickly by photoionization and electron impact ionization. Thus, the argon content in the exospheres of the Moon, Mercury and probably Europa is representative of current effusion rather than accumulation over the lifetime of the body. Argon content will be a function of K content, temperature, grain size distribution, connected pore volume and possible seismic activity. Although Mercury and the Moon differ in many details, we can train the solutions to diffusion equations to predict the average lunar atmosphere. Then these parameters can be varied for Hermean conditions. Assuming a lunar crustal potassium abundance of 300 ppm, the observed argon atmosphere requires equilibrium between the argon production in the upper 9 Km of the moon (1.135 x 10(exp -3) cm(exp -3) s(exp -1)) and its loss. Hodges et al. conclude that this loss rate and the observed time variability requires argon release through seismic activity, tapping a deep argon source. An important observation is that the extreme surface of the Moon is enhanced in argon rather than depleted, as one would expect from outgassing of radiogenic argon. Manka and Michel concluded that ion implantation explains the surface enhancement of Ar-40. About half of the argon ions produced in the lunar atmosphere would return to the surface, where they would become embedded in the rocks. Similarly, at Mercury we expect the surface rocks to be enhanced in Ar-40 wherever the magnetosphere has been open over time. Thus the measurement of surface composition will reveal the long-term effects of solar wind-magnetosphere interaction. Additional information is contained in the original extended abstract.

Killen, R. M.↗

Development of a New Membrane Casting Apparatus for Studying Macrovoid Defects in Low-G

A new membrane-casting apparatus is developed for studying macrovoid defects in polymeric membranes made by the wet- and dry-casting process in low-gravity. Macrovoids are large (10-50 micron), open cavities interspersed among the smaller pores in the substructure under the gelled skin surface layer of the cast membrane. Although their occurrence is considered endemic to the wet- and dry-casting process since they can lead to compaction or skin rupture in the membrane process, recent studies suggest several useful applications such as transdermal and osmotic drug delivery systems, miniature bioreactors, etc. However, lack of knowledge about the macrovoid formation mechanism is an obstacle to further development of applications using them. An on-going debate is the role of the surface-tension-driven solutocapillary convection during macrovoid formation. The rapid growth of macrovoids within 1-5 seconds and the high polymer concentration in and near macrovoids make it difficult to explain the mechanism of macrovoid growth by diffusion alone, which is the widely accepted hypothesis proposed by Reuvers et al. The hypothesis advanced by our research group can explain this rapid growth via a mechanism that involves diffusion from the casting solution in the meta-stable region to the macrovoid enhanced by solutocapillary convection induced by the steep nonsolvent concentration gradient in the vicinity of the macrovoid. Since macrovoid growth is hypothesized to be the interplay of a solutocapillary-induced driving force counteracted by viscous drag and buoyancy, eliminate the latter provides a means for testing this hypothesis. Moreover, free convection mass transfer in the nonsolvent immersion bath used to cause phase-separation in membrane casting complicates developing a model for both the wet-casting process and macrovoid growth. The low-g environment minimizes gravitationally induced free convection thereby permitting a tractable solution to the ternary diffusion equations that characterize membrane formation. NASA's Parabolic Flight Research Aircraft provides a small window of low-g (approximately 25 s) that can be used to study macrovoid development in both wet- and dry-cast membranes if an appropriate casting apparatus is used. This casting apparatus should be able to cast the membrane in both low- and high-g in a manner so that essential one-dimensional mass transfer conditions are achieved to insure lateral uniformity in the membrane. The apparatus used in previous research on membrane casting in low-gravity was operated with the plunger driven mechanism. The spring-loaded plunger pushes the bottom block containing the polymer casting solution well directly under the absorbent chamber located in the upper stationary block. However, membranes made via this casting apparatus often displayed lateral nonuniformities that precluded obtaining quantitative information on the macrovoid growth process. Thus, it was necessary to determine the reason for these structural irregularities observed in the low-g casting apparatus. Both experimental as well as computer simulation studies of the low-g casting apparatus established that the impulsive action of the plunger caused the undesired structural nonuniformities. The simulation results showed that the width-to-depth aspect ratio of the shallow well that contains the casting solution in this apparatus was not an important factor in minimizing this problem. Even for a 40:1 (width : depth) aspect ratio, any convection induced by the horizontal motion of the interface of the casting solution will be damped out within 6.25x10(exp 4) seconds. However, the experimental studies revealed that the impulsive motion of the plunger caused a 'sloshing' of the casting solution that had to be eliminated. Therefore, the plungerdriven mechanism was changed to a cam-driven mechanism that did not cause any impulsive motion of the casting solution. Other refinements to this new membrane-casting apparatus include provision for removing the membranes from the casting wells in a less destructive manner. This was accomplished by using a slit geometry for the casting well that permitted disassembly for removal of the cast membrane. The materials used in the construction of this casting apparatus were chosen to insure wetting at the side walls and to maintain precise control of the thickness of the polymer solution in the casting well. An additional provision in this new casting apparatus is the ability to carry out both wet- as well as dry-casting. As such, this apparatus permitted the first studies of the wet-casting of polymeric membranes in low-g. Both wet- and dry-casting experiments on NASA's KC-135 research aircraft employing this new membrane-casting apparatus are scheduled in July 2002. The morphology of the resulting membranes will be characterized using an environmental scanning electron microscope (ESEM). The results of these low-g studies will be reported later.

Lee, Hanyong↗

Analysis of heat transfer for a normally impinging liquid-metal slot jet

A two-dimensional liquid-metal slot jet that is impinging normally against a uniformly heated flat plate is analyzed. The distributions of wall temperature and heat-transfer coefficient are obtained as functions of position along the plate. The liquid-metal assumptions are made that the jet is inviscid and that molecular condition is dominating heat diffusion. The solution is obtained by mapping the jet flow region into a potential plane where it occupies a strip of uniform width. The energy equation is transformed into potential coordinates, and an exact solution obtained in the strip region. Conformal mapping is then used to transform the solution into the physical plane.

Siegel, R.↗

Cosmic Ray Hysteresis as Evidence for Time-dependent Diffusive Processes in the Long Term Solar Modulation

A simple one-dimensional time-dependent diffusion-convection model for the modulation of cosmic rays is presented. This model predicts that the observed intensity at a given time is approximately equal to the intensity given by the time independent diffusion convection solution under interplanetary conditions which existed a time iota in the past, (U(t sub o) = U sub s(t sub o - tau)) where iota is the average time spent by a particle inside the modulating cavity. Delay times in excess of several hundred days are possible with reasonable modulation parameters. Interpretation of phase lags observed during the 1969 to 1970 solar maximum in terms of this model suggests that the modulating region is probably not less than 10 a.u. and maybe as much as 35 a.u. in extent.

Ogallagher, J. J.↗

Crystal growth experiment MA-028

The crystal growth experiment assessed a novel process for growing single crystals of insoluble substances by allowing two or more reactant solutions to diffuse toward each other through a region of pure solvent in zero g. The experiment was entirely successful and yielded crystals of about the expected size, quality, and number. Photographs were taken in orbit to record the progress of the crystal growth.

Lind, M. D.↗

Experiment MA-028 crystal growth

A crystal growth experiment is reported on orbital space flights. The experiment was performed during the Apollo-Soyuz Test Project. The Crystal Growth Experiment assessed a novel process for growing single crystals of insoluble substances by allowing two or more reactant solutions to diffuse toward each other through a region of pure solvent in zero gravity. The experiment was entirely successful and yielded crystals of about the expected size, quality, and number.

Lind, D. M.↗