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NASA NTRS1985

Coalescence of two pressure waves associated with stream interactions

An MHD unsteady 1-D model is used to simulate the interaction and coalescence of two pressure waves in the outer heliosphere. Each of the two pressure waves was a compression region bounded by a shock pair. Computer simulation using Voyager data as input demonstrates the interaction and coalescence process involving one pressure wave associated with a fast stream and the other pressure wave without a fast stream. The process produced a significant change in the magnetic field and plasma signatures. The propagation of the forward and reverse shocks first widened the radial dimension of the shock compression region with increasing heliocentric distances. The shocks belonging to two neighboring compression regions eventually collided and two compression regions began to overlap with each other. This type of interaction is a dominant dynamical process in the outer heliosphere, and significantly and irreversible alters the structure of the medium.

Whang, Y. C.↗

NASA NTRS1985

The coalescence instability in solar flares

The nonlinear coalescence instability of current carrying solar loops can explain many of the characteristics of the solar flares such as their impulsive nature, heating and high energy particle acceleration, amplitude oscillations of electromagnetic and emission as well as the characteristics of two-dimensional microwave images obtained during a flare. The plasma compressibility leads to the explosive phase of loop coalescence and its overshoot results in amplitude oscillations in temperatures by adiabatic compression and decompression. It is noted that the presence of strong electric fields and super-Alfvenic flows during the course of the instability play an important role in the production of nonthermal particles. A qualitative explanation on the physical processes taking place during the nonlinear stages of the instability is given.

Tajima, T.↗

NASA NTRS1986

Explosive coalescence of magnetic islands

Simulation results from both the EM collisionless particle code and the MHD particle code reveal an explosive reconnection process associated with nonlinear evolution of the coalescence instability. The explosive coalescence is a self-similar process of magnetic collapse, and ensuing amplitude oscillations in the magnetic and electrostatic energies and temperatures are modeled by an equation of motion for the scale factor in the Sagdeev potential. This phenomenon may explain the rapid energy release of a certain class of solar flares during their impulsive phase.

Tajima, T.↗

NASA NTRS1990

Modeling of collision and coalescence of droplets during microgravity processing of Zn-Bi immiscible alloys

A population balance model is presented for the coarsening of the dispersed phase of liquid-liquid two-phase mixtures in microgravity due to gravity sedimentation and Marangoni migration, which lead to the collision and coalescence of droplets. The model is used to predict the evolution of the size distribution of the dispersed phase in a liquid-phase miscibility gap system, Zn-Bi, which has been used in a number of experimental microgravity processing studies in which significant phase segregation has been observed. The analysis shows that increasing the temperature gradient, gravity level, volume fraction of the dispersed phase, initial average drop radius, initial standard deviation of droplet radii, or the temperature coefficient of the interfacial tension leads to an increase in the rate of droplet growth due to collision and coalescence. Comparison of the distribution evolutions for unimodal and bimodal initial distributions shows that the latter yield significantly more rapid droplet growth. Finally, it is shown that droplet growth can be dramatically reduced with antiparallel orientation of the gravity vector and the temperature gradient, provided that the relative magnitude of these two vectors is properly chosen.

Davis, R. H.↗

NASA NTRS1990

Rheological properties, shape oscillations, and coalescence of liquid drops with surfactants

A method was developed to deduce dynamic interfacial properties of liquid drops. The method involves measuring the frequency and damping of free quadrupole oscillations of an acoustically levitated drop. Experimental results from pure liquid-liquid systems agree well with theoretical predictions. Additionally, the effects of surfactants is considered. Extension of these results to a proposed microgravity experiment on the drop physics module (DPM) in USML-1 are discussed. Efforts are also underway to model the time history of the thickness of the fluid layer between two pre-coalescence drops, and to measure the film thickness experimentally. Preliminary results will be reported, along with plans for coalescence experiments proposed for USML-1.

Apfel, R. E.↗

NASA NTRS1991

Coincidence probabilities for spacecraft gravitational wave experiments - Massive coalescing binaries

Massive coalescing binary systems are candidate sources of gravitational radiation in the millihertz frequency band accessible to spacecraft Doppler tracking experiments. This paper discusses signal processing and detection probability for waves from coalescing binaries in the regime where the signal frequency increases linearly with time, i.e., 'chirp' signals. Using known noise statistics, thresholds with given false alarm probabilities are established for one- and two-spacecraft experiments. Given the threshold, the detection probability is calculated as a function of gravitational wave amplitude for both one- and two-spacecraft experiments, assuming random polarization states and under various assumptions about wave directions. This allows quantitative statements about the detection efficiency of these experiments and the utility of coincidence experiments. In particular, coincidence probabilities for two-spacecraft experiments are insensitive to the angle between the directions to the two spacecraft, indicating that near-optical experiments can be done without constraints on spacecraft trajectories.

Tinto, Massimo↗

NASA NTRS1992

Modeling of coalescence, agglomeration, and phase segregation in microgravity processing of bimetallic composite materials

The overall objective of this research is to develop models to predict drop-size-distribution evolutions due to droplet collisions and coalescence during processing within the miscibility gap of bimetallic liquid-phase-miscibility-gap materials. The individual and collective action of gravitational and nongravitational mechanisms on the relative motion and coalescence of drops are considered.

Davis, Robert H.↗

NASA NTRS1992

Molecular structure of the coalescence of liquid interfaces

When two bodies of liquid merge, their interfaces must also rupture and rearrange into one. Virtually no information is available concerning the small-scale dynamics of this process. Molecular dynamics simulations of coalescence in systems of about 10,000 Lennard-Jones particles have been performed, arranged so as to mimic laboratory experiments on dense liquids. The coalescence event begins when molecules near the boundary of one liquid body thermally fluctuate into the range of attraction of the other, forming a string of mutually attracting molecules. These molecules gradually thicken into a tendril, which continues to thicken as the bodies smoothly combine in a zipper-like merger.

Koplik, Joel↗

NASA NTRS1993

Collective effects of temperature gradients and gravity on droplet coalescence

The interaction and coalescence of small spherical drops in dilute, homogeneous dispersions are considered theoretically under conditions, where drop motion results from gravity settling and thermocapillary migration acting simultaneously. A trajectory analysis is used to predict pairwise collision rates, and population dynamics equations are solved to predict the time evolution of the droplet size distribution. The rate of droplet collisions and growth may be reduced dramatically by antiparallel alignment of the gravitational and thermocapillary velocities. For such antiparallel alignment with the gravitational relative velocity exceeding the thermocapillary relative velocity for two widely separated drops, there is a 'collision-forbidden region' in parameter space. This occurs because the gravitational relative velocity decays more rapidly with decreasing separation distance between the drops than does the thermocapillary relative velocity, and so the resultant relative velocity along the line-of-centers from these two sources combined becomes zero at a finite separation and the drops are unable to collide. As a result, small drops which initially collide and coalesce due to thermocapillary motion will only grow until they reach a critical size for which the oppositely directed gravitational motion balances the thermocapillary motion.

Zhang, Xiaoguang↗

NASA NTRS1994

The Flow Induced by the Coalescence of Two Initially Stationary Drops

The coalescence of two initially stationary drops of different size is investigated by solving the unsteady, axisymmetric Navier-Stokes equations numerically, using a Front-Tracking/Finite Difference method. Initially, the drops are put next to each other and the film between them ruptured. Due to surface tension forces, the drops coalesce rapidly and the fluid from the small drop is injected into the larger one. For low nondimensional viscosity, or Ohnesorge number, little mixing takes place and the small drop fluid forms a blob near the point where the drops touched initially. For low Ohnesorge number, on the other hand, the small drop forms a jet that penetrates far into the large drop. The penetration depth also depends on the size of the drops and shows that for a given fluid of sufficiently low viscosity, there is a maximum penetration depth for intermediate size ratios.

Nobari, M. R.↗

NASA NTRS1994

Phase segregation due to simultaneous migration and coalescence

Ground-based modeling and experiments have been performed on the interaction and coalescence of drops leading to macroscopic phase separation. The focus has been on gravity-induced motion, with research also initiated on thermocapillary motion of drops. The drop size distribution initially shifts toward larger drops with time due to coalescence, and then a back towards smaller drops due to the larger preferentially settling out. As a consequence, the phase separation rate initially increases with time and then decreases.

Davis, Robert H.↗

NASA NTRS1994

Computations of drop collision and coalescence

Computations of drops collision and coalescence are presented. The computations are made possible by a recently developed finite difference/front tracking technique that allows direct solutions of the Navier-Stokes equations for a multi-fluid system with complex, unsteady internal boundaries. This method has been used to examine the boundaries between the various collision modes for drops of equal size and two examples, one of a 'reflective' collision and another of a 'grazing' collision is shown. From drops of unequal size, coalescence can result in considerable mixing between the fluid from the small and the large drop. This problem is discussed and one example showed. In many cases it is necessary to account also for heat transfer along with the fluid mechanics. We show two preliminary results where we are using extensions of the method to simulate such a problem. One example shows pattern formation among many drops moving due to thermal migration, the other shows unstable evolution of a solidification front.

Tryggvason, Gretar↗

NASA NTRS1994

Hydrodynamic instability and coalescence of binary neutron stars

We study the importance of hydrodynamic effects on the evolution of coalescing binary neutron stars. Using an approximate energy functional constructed from equilibrium solutions for polytropic binary configuration, we incorporate hydrodynamic effects into the calculation of the orbital decay driven by gravitational wave emission. In particular, we follow the transition between the quasi-static, secular decay of the orbit at large separation and the rapid dynamical evolution of confirgurations approaching contact. We show that a purely Newtonian hydrodynamic instability can significantly accelerate the coalescence at small separation. Such an instability occurs in all close binary configurations containing sufficiently incompressible stars. Calculations are performed for various neutron star masses, radii, and spins. The influence of the stiffness of the equation of state is also explored by varying the effective polytopic index. Typically, we find that the radial infall velocity just prior to contact is about 10% of the tangential orbital velocity. Once the stability limit is reached, the final evolution only takes another orbit. Post-Newtonian effects can move the stability limit to a larger binary separation, and may induce an even larger radial velocity. We also consider the possibiltiy of mass transfer form one neutron star to the other. We show that stable mass transfer is unlikely except when the mass of one of the components is very small (M is less than or approximately 0.4 solar mass) and the viscosity is high enough to maintain corotation. Otherwise, either the two stars come into contact or the dynamical instability sets in before a Roche limit can be reached.

Lai, Dong↗

NASA NTRS1995

Hydrodynamics of coalescing binary neutron stars: Ellipsoidal treatment

We employ an approximate treatment of dissipative hydrodynamics in three dimensions to study the coalescence of binary neutron stars driven by the emission of gravitational waves. The stars are modeled as compressible ellipsoids obeying a polytropic equation of state; all internal fluid velocities are assumed to be linear functions of the coordinates. The hydrodynamics equations then reduce to a set of coupled ordinary differential equations for the evolution of the principal axes of the ellipsoids, the internal velocity parameters, and the binary orbital parameters. Gravitational radiation reaction and viscous dissipation are both incorporated. We set up exact initial binary equilibrium configurations and follow the transition from the quasi-static, secular decay of the orbit at large separation to the rapid dynamical evolution of the configurations just prior to contact. A hydrodynamical instability resulting from tidal interactions significantly accelerates the coalescence at small separation, leading to appreciable radial infall velocity and tidal lag angles near contact. This behavior is reflected in the gravitational waveforms and may be observable by gravitational wave detectors under construction. In cases where the neutron stars have spins which are not aligned with the orbital angular momentum, the spin-induced quadrupole moment can lead to precession of the orbital plane and therefore modulation of the gravitational wave amplitude even at large orbital radius. However, the amplitude of the modulation is small for typical neutron star binaries with spins much smaller than the orbital angular momentum.

Lai, Dong↗

NASA NTRS1997

Gamma-Ray Bursts and Relativistic MHD around Coalescing Neutron Stars

In this proposal we performed the first relativistic hydrodynamic simulations of the binary neutron stars near coalescence. Calculations were performed in three spatial dimensions and were supplemented with magnetohydrodynamic simulations of the magnetic reconnection as the neutron star fluid responds to the relativistic forces of the binary. The ultimate goal of the proposed work was to develop a theoretical model for the temporal and spectral evolution of cosmological gamma-ray bursts produced during the magnetic reconnection. This is the first time such hydrodynamic calculations were performed and some surprising results were obtained. The neutrons stars were observed to compress and heat in the simulations. They could even collapse to black holes many orbits before coalescence. The question then arose as to whether this strange phenomenon could power a gamma-ray burst. The bulk of computing effort in this proposal was therefore devoted to an analysis of the implications of this possible new gamma-ray burst paradigm. The initial focus of the work performed under this proposal was therefore to utilize (3+1) dimensional and spherical numerical general relativistic hydrodynamics to study the origin, evolution, and parametric sensitivity of the collapse instability. We derived modified conditions of hydrostatic equilibrium for stars in the curved space of quasi-static orbits. We followed the magnetic field evolution for approximately one orbit (10 msec). The magnetic field energy was observed to exponentiate with an e-folding time of about 1 msec. Thus, the field should build up very quickly to a magnitude such that reconnection and back reaction of the fluid inhibits further growth.

Mathews, Grant J.↗

NASA NTRS2002

Event Rate for LISA Gravitational Wave Signals from Black Hole-Massive Black Hole Coalescences

Bender, Peter L.↗

NASA NTRS2002

Event Rate for LISA Gravitational Wave Signals from Black Hole-Massive Black Hole Coalescences

Earlier work under a previous grant had been mainly on investigating the event rate for coalescences of white dwarfs or neutron stars with massive black holes (MBHs) in galactic nuclei. Under the new grant, two studies were undertaken. One was an approximate extension of the earlier study to stellar mass black holes as the lighter object, with masses in the range of roughly 3 to 20 solar mass rather than about 1 solar mass. The other was an improved estimate of the confusion noise due to galactic binaries against which the signals from BH-MBH coalescences would have to be detected. In the earlier work, the mass of the white dwarfs (WDs) and neutron stars (NSs) was assumed to be about the same as that of the evolved stars in the density cusp around the galactic center MBH. However, with the BH mass being substantially larger, the sinking down of pHs toward the center (mass segregation) became important, and was included in the model. A single representative mass of 7 solar mass was used. The other main difference involved what happened after the compact object got scattered in close enough to the MBH to start losing appreciable energy and angular momentum by gravitational radiation. For WDs or NSs, it had been found in most cases that the object would be perturbed considerably by other stars in the cusp before much energy had been lost. Thus the angular momentum would either increase enough so that gravitational radiation would be cut off, or would decrease enough so that the WD or NS would plunge into the MBH in just a few revolutions. The latter event would mean that the signal-to noise ratio would not have time to build up, and the event would not be detectable. The ratio of gradual energy loss events to plunges was found to be roughly one to a few percent, and thus substantially decreased the expected rate of detectable events.

Bender, Peter L.↗

NASA NTRS2002

Non-Coalescence in Microgravity: Science and Technology

In this project we examine non-coalescence and non-wetting phenomena driven by either thermocapillary convection or forced motion of one surface relative to the other. In both cases, the non-coalescence or non-wetting is enabled by the existence of a lubricating layer of gas that exists to keep the two surfaces in question from coming into contact with one another. Recent progress has been made on several fronts: 1) measurement of the vibrational modes of pinned droplets; 2) development of an apparatus for the measurement of the frictional forces associated with a non-wetting droplet sliding over a solid surface; 3) measurements of the failure modes for non-wetting droplets and the influence of static electric charge on failure-, and 4) numerical simulation of a two-dimensional non-wetting droplet revealing a possible explanation for why the phenomenon has not been able to be observed using water as the droplet liquid. Issue 1) above is of relevance to the use of non-wetting droplets as positioning mechanisms and vibration dampers in a microgravity environment; issue 2) relates to the use of non-wetting droplets as nearly 'frictionless' bearings in low-load applications. Understanding of the failure modes identified in 3) is of importance to any potential application and the numerical simulations conducted under 4) allow us to obtain information about these systems that is currently not available through experimentation Each of these topics will be discussed briefly during the presentation.

Neitzel, G. Paul↗