INFLUENCE OF A LEVELNESS DEFECT IN A THRUST BEARING ON THE DYNAMIC BEHAVIOUR OF AN ELASTIC SHAFT

This paper examines the non-linear dynamic behaviour of a flexible shaft. The shaft is mounted on two journal bearings and the axial load is supported by a defective hydrodynamic thrust bearing at one end. The defect is a levelness defect of the rotor. The thrust bearing behaviour must be considered to be non-linear because of the effects of the defect. The shaft is modelled with typical beam finite elements including effects such as the gyroscopic effects. A modal technique is used to reduce the number of degrees of freedom. Results show that the thrust bearing defects introduce supplementary critical speeds. The linear approach is unable to show the supplementary critical speeds which are obtained only by using non-linear analysis.     

Global Analysis of the Flows of Fluids with Pressure-Dependent Viscosities

 To describe the flows of fluids over a wide range of pressures, it is necessary to take into account the fact that the viscosity of the fluid depends on the pressure. That the viscosity depends on the pressure has been verified by numerous careful experiments. While the existence of solutions local-in-time to the equations governing the flows of such fluids are available for small, special data and rather unrealistic dependence of the viscosity on the pressure, no global existence results are in place. Our interest here is to establish the existence of weak solutions for spatially periodic three-dimensional flows that are global in time, for a large class of physically meaningful viscosity-pressure relationships. (Accepted May 1, 2002) Published online November 15, 2002 Communicated by S. S. ANTMAN     

The effect of the counterion on water mobility in reverse micelles studied by molecular dynamics simulations

In this study, mobility and structure of water molecules in Aerosol OT (bis(2-ethylhexyl) sulfosuccinate, AOT) reverse micelles with water content w0 = 5 and Na+, K+, Cs+ counterions have been explored with molecular dynamics (MD) simulations. Using the Faeder/Ladanyi model (J. Phys. Chem. B, 2000, 104, 1033) of the reverse micelle interior, MD simulations were performed to calculate the self-intermediate scattering function, FS(Q,t), for water hydrogen atoms that could be measured in a quasielastic neutron scattering experiment. Separate intermediate scattering functions FRS(Q,t) and FCMS(Q,t) were determined for rotational and translational motion. We find that the decay of FCMS(Q,t) is nonexponential and our analysis of the MD data indicates that this behavior arises from decreased water mobility for molecules close to the interface and from confinement-induced restrictions on the range of translational displacements. Rotational relaxation also exhibits nonexponential decay, which is consistent with relatively rapid restricted rotation and slower rotational relaxation over the full angular range. Rotational relaxation is anisotropic, with the O-H bond short-time rotational mobility considerably higher than that of the molecular dipole. This behavior is related to the decreased density of water-water hydrogen bonds in the vicinity of the interface compared to core or bulk water. We find that the interfacial mobility of water molecules is quite different for the three counterion types, but that the core mobility exhibits weak counterion dependence. Differences in interfacial mobility are strongly correlated with structural features, especially ion-water coordination, and the extent of disruption by the counterions of the water hydrogen bond network.     

New inversion techniques for the triton photoeffect

The photoeffect cross section for a particle in a model potential has been calculated analytically along with five energy-weighted moments. Two sets of orthonormalized polynomials R_n and S_n are developed with the weighting functions $\text{exp}\text{(?x}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{)}$ and $\text{x}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{exp}\text{(?x}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{)}$. respectively. These polynomials are used to invert the calculated moments to get the cross section corresponding to 5, 4, 3 and 2 moments.The cross sections found by S-inversion are in good agreement with the model; those using R-inversion give somewhat poorer agreement.Clare and Lally calculated triton moments and used Laguerre inversion to find the triton cross section. We use their moments with R-inversion and S-inversion. Our resulting cross section agrees reasonably well with Gorbunov's and Faul's measurements of the ³He photoeffect. We find better agreement than that found by Clare and Lally.     

Correlated hyperspherical harmonics

The expansion of the wavefunction for a bound three particle state in the five-dimensional hyperspace of hyperspherical harmonics in some cases suffers bad convergence, especially for weakly bound states. For this reason correlated hyperspherical harmonics are proposed, of which the ordinary hyperspherical harmonics are one special choice. The “best” suited correlated hyperspherical harmonics are chosen from an infinite set of complete orthogonal systems by a Ritz variational calculation.     

Testing the core/shell model of nanoconfined water in reverse micelles using linear and nonlinear IR spectroscopy

A core/shell model has often been used to describe water confined to the interior of reverse micelles. The validity of this model for water encapsulated in AOT/isooctane reverse micelles ranging in diameter from 1.7 to 28 nm (w0 = 2-60) and bulk water is investigated using four experimental observables: the hydroxyl stretch absorption spectra, vibrational population relaxation times, orientational relaxation rates, and spectral diffusion dynamics. The time dependent observables are measured with ultrafast infrared spectrally resolved pump-probe and vibrational echo spectroscopies. Major progressive changes appear in all observables as the system moves from bulk water to the smallest water nanopool, w0 = 2. The dynamics are readily distinguishable for reverse micelle sizes smaller than 7 nm in diameter (w0 = 20) compared to the response of bulk water. The results also demonstrate that the size dependent absorption spectra and population relaxation times can be quantitatively predicted using a core-shell model in which the properties of the core (interior of the nanopool) are taken to be those of bulk water and the properties of the shell (water associated with the headgroups) are taken to be those of w0 = 2. A weighted sum of the core and shell components reproduces the size dependent spectra and the nonexponential population relaxation dynamics. However, the same model does not reproduce the spectral diffusion and the orientational relaxation experiments. It is proposed that, when hydrogen bond structural rearrangement is involved (orientational relaxation and spectral diffusion), dynamical coupling between the shell and the core cause the water nanopool to display more homogeneous dynamics. Therefore, the absorption spectra and vibrational lifetime decays can discern different hydrogen bonding environments whereas orientational and spectral diffusion correlation functions predict that the dynamics are size dependent but not as strongly spatially dependent within a reverse micelle.     

What can you learn from a molecular probe? New insights on the behavior of C343 in homogeneous solutions and AOT reverse micelles

The behavior of C343, a common molecular probe utilized in solvation dynamics experiments, was studied in homogeneous media and in aqueous and nonaqueous reverse micelles (RMs). In homogeneous media, the Kamlet and Taft solvatochromic comparison method quantified solute-solvent interactions from the absorption and emission bands showing that the solvatochromic behavior of the dye depends not only on the polarity of the medium but also on the hydrogen-bonding properties of the solvent. Specifically, in the ground state the molecule displays a bathochromic shift with the polarity polarizability (pi) and the H-bond acceptor (beta) ability of the solvents and a hypsochromic shift with the hydrogen donor ability (alpha) of the media. The carboxylic acid group causes C343 to display greater sensitivity to the beta than to the pi polarity parameter; this sensitivity increases in the excited state, while the dependence on alpha vanishes. This demonstrates that C343 forms a stable H-bond complex with solvents with high H-bond acceptor ability (high beta) and low H-bond donor character (low alpha). Spectroscopy in nonpolar solvents reveals J-aggregate formation. With information from the Kamlet-Taft analysis, C343 was used to explore RMs composed of water or polar solvents/sodium 1,4-bis-2-ethylhexylsulfosuccinate (AOT)/isooctane using absorption, emission, and time-resolved spectroscopies. Sequestered polar solvents included ethylene glycol (EG), formamide (FA), N,N-dimethylformamide (DMF), and N,N-dimethylacetamide (DMA). Dissolved in the AOT RM systems at low concentration, C343 exists as a monomer, and when introduced to the RM samples in its protonated form, C343 remains protonated driving it to reside in the interface rather than the water pool. The solvathochromic behavior of the dye depends the specific polar solvent encapsulated in the RMs, revealing different types of interactions between the solvents and the surfactant. EG and water H-bond with the AOT sulfonate group destroying their bulk H-bonded structures. While water remains well segregated from the nonpolar regions, EG appears to penetrate into the oil side of the interface. In aqueous AOT RMs, C343 interacts with neither the sulfonate group nor the water, perhaps because of intramolecular H-bonding in the dye. DMF and DMA interact primarily through dipole-dipole forces, and the strong interactions with AOT sodium counterions destroy their bulk structure. FA also interacts with the Na+ counterions but retains its H-bond network present in bulk solvent. Surprisingly, FA appears to be the only polar solvent other than water forming a "polar-solvent pool" with macroscopic properties similar to the bulk.     

Quasi-elastic neutron scattering study of dimethyl-sulfoxide-water mixtures: probing molecular mobility in a nonideal solution

The translational and rotational motions of water and dimethyl sulfoxide, [DMSO, (CH(3))(2)SO] have been investigated using quasi-elastic neutron scattering. Water-DMSO mixtures at five DMSO mole fractions, chi(DMSO), ranging from 0 to 0.75, were measured. Hydrogen-deuterium substitution was used to extract independently the water proton dynamics (d-DMSO-H(2)O), the DMSO methyl proton dynamics (h-DMSO-D(2)O) and to obtain background corrections (d-DMSO-D(2)O). The translational diffusion of water slows down significantly compared to bulk water at all chi(DMSO)>0. The rotational time constant for water exhibits a maximum at chi(DMSO)=0.33 that corresponds to the observed maximum of the viscosity of the mixture. Data for DMSO can be analyzed in terms of a relatively slow tumbling of the molecule about its center-of-mass in conjunction with random translational diffusion. The rotational time constant for this motion exhibits some dependence on chi(DMSO), while the translational diffusion constant shows no clear variation for chi(DMSO)>0. The results presented reinforce the idea that due to the stronger associative nature of DMSO, DMSO-water aggregates are formed over the whole composition range, disturbing the tetrahedral natural arrangement of the water molecules. As a consequence adding DMSO to water causes a drastic slowing down of the dynamics of the water molecule, and vice versa.     

1H NMR studies of aerosol-OT reverse micelles with alkali and magnesium counterions: preparation and analysis of MAOTs

Simple procedures and characterization of a series of well-defined precursors are described for preparation of a unique microenvironment in nanoreactors, reverse micelles. The Na(+), K(+), Rb(+), Cs(+), and Mg(2+) surfactants were prepared using liquid-liquid ion exchange using chloride and nitrate salts. The surfactants were characterized using (1)H NMR spectroscopy and a variety of other techniques. (1)H NMR spectroscopy was found to be a sensitive probe for characterization of the size of the nanoreactor as well as its water content. (1)H NMR spectra can be used for detailed characterization of reactions in confined environments when counterion effects are likely to be important. (1)H NMR spectroscopy revealed two separate peaks corresponding to water in Mg(AOT)2 samples; one peak arises from water coordinated to the Mg(2+) ion while the other peak arises from bulk water. The two water signals arise directly from the slow exchange of the water coordinated to Mg(2+) in these microemulsions with water in the water pool, and provide an opportunity to study hydration of Mg(2+). This work thus extends the potential use of MAOT microemulsions for applications such as in green chemistry.