ALBERT

Notes: The phenomenon of aerodynamic enrichment of heavy molecules seeded in supersonic free jets has been known since 1955. But its systematic exploitation in the generation of intensely focused molecular beams has been prevented by the lack of a quantitative and realistic explanation of the observed facts. Here, the aerodynamic focusing of CBr4, W(CO)6, and C2Cl6 molecules seeded in jets of He or H2 is studied experimentally, and found to be most singular under conditions similar to those known to produce sharply focused beams of microscopic spheres suspended in air jets. The gas mixture expands through thin-plate orifice into a vacuum chamber, forming a supersonic free jet. The spacial distribution of the heavy molecules in the jet is measured at varying distances L to the nozzle by scanning a thermocouple probe across a jet diameter. The probe is sufficiently small to interfere negligibly with the flow. The increment DV in the thermocouple voltage resulting from seeding the heavy gas on a given flow of He or H2 is seen to be a sensitive indicator of the local concentration of seed molecules in the jet. The following behavior is observed in terms of the same Stokes number or inertia parameter S that governs the simpler and better understood phenomenon of aerosol focusing. Below S=0.4 for H2 and S=0.2 for He, heavy molecule and aerosol beam widths are practically identical, and the boundary of the jet of heavy molecules is rather sharp. At higher values of S, aerosol beams show further reductionsin cross section, down to less than 10% of a nozzle throat diameter dn. In contrast, the measured heavy species minimal beam widths or waists at a distance L∼dn from the throat are around 0.5dn and 0.35 dn for jets of He and H2, respectively. In units of dn, these widths are several times larger than expected from elementary considerations on the defocusing effects due to Brownian motion (of the order of the square root of the molecular mass ratio between light and heavy molecules). Nonetheless, the thin-plate orifice nozzle yields considerably more concentrated jets of heavy gases than previously seen, with far-field enrichment factors for the seed species close to 50 in thecase of H2 jets. This technique, thus, appears to provide a greatly improved source for intense molecular beams. Aerodynamically focused beams have a sharp distribution of kinetic energies, being ideally suited for cross beam and beam surface studies. But they are not quite so optimal for spectroscopic studies because they require moderate source Reynolds numbers (of order 100), at which the heavy gas undergoes very little translational, rotational, or vibrational cooling.

Notes: The large inertia of heavy molecules suspended in a light carrier gas is exploited in the impingement of seeded free jets against surfaces at near-continuum conditions. It emerges that the kinetic energy at impact can be close to the free stream convective kinetic energy, even at near-continuum densities, i.e., at Knudsen numbers of 10−2 or less. Thus, one can simulate collision energies previously obtained only under molecular beam conditions but with the much higher flux densities characteristic of free jets upstream of the transition to free-molecule flow. The principal design parameter in such "high density seeded free jet'' experiments is the heavy molecule Knudsen number, analogous to the Stokes number governing the inertial impaction of aerosol particles. When the ratio of masses mp/m for the heavy and the light gases is large, the interspecies transfer of momentum and energy is rather slow, and the Stokes number is of the order of mp/m times larger than the light gas Knudsen number. Thus, there is a region in which the light gas still behaves as a continuum fluid while the heavy component penetrates through it under effectively free-molecular conditions. A hydrodynamic theory capable of predicting the distribution of impact energies for such free jets impinging on solid objects at Stokes numbers of order unity is developed.

Notes: Amaranth seeds were germinated at a water activity of about 0.92 for up to 72 hr. Crude protein, true protein and crude fiber were found to increase and fat content to decrease. For 48 hr of germination reactive lysine values did not change. At 72 hr, a slight decrease was observed in lysine and in vitro protein digestibility was similar to the control. During germination Hunter color parameters L were lowered and a and b were enhanced. Germinated seeds showed a pinky color which appeared very attractive for various food uses.

Notes: Particle acceleration in a localized electrostatic wave packet is studied. A weak field regime and a strong field regime are displayed. In the weak field limit a quasilinear relation for the velocity perturbation is derived. When the particles cross the accelerating field several times, a quasilinear equation for the distribution function is established. The theory is illustrated by numerical results from a model of resonance absorption of laser light by a plasma. Finally a model of electron reheating in resonance absorption including collisions is presented, leading to a nearly Maxwellian behavior for the hot component of the electron distribution function, f∼exp−(v/v0)8/3.

Notes: The electric field pattern is studied in the capacitor model of resonance absorption. Hydrodynamic and kinetic theory are used. The electric field is calculated for L(approximately-greater-than)10λD, where L is the density gradient length and λD the Debye length. The effect of collisional damping is studied. One obtains three different regimes. In the intermediate regime, the electric field amplitude is determined by the thermal convection, while the energy absorption is mainly caused by collisional damping.

Notes: New results concerning the mathematical properties of the Fokker–Planck equation describing the electron distribution function are presented. The validity of the approximations obtained by using a finite number of Legendre polynomials to describe the electron distribution function is discussed. It is shown that, due to the Landau form of the electron-ion collision operator, it is sufficient to use two or three Legendre polynomials in problems of interest. The theory is applied to the classical albedo problem as a test, and is also applied to determine the distribution and the heat flux in a heat front typical of laser plasma experiments. It is shown that the heat flux can be expressed as a sort of convolution of the Spitzer–Härm heat flux by a delocalization function. The convolution formula leads in a physically relevant way to the saturation and the delocalization of the heat flux.

Notes: As a result of the increasing inefficiency in the transfer of energy in collisions between species with a decreasing ratio of molecular masses, the Knudsen number range of validity of the Chapman–Enskog (CE) theory for binary gas mixtures decreases linearly with the molecular mass ratio. To remedy the situation, a two-fluid CE theory uniformly valid in the molecular mass ratio is constructed here. The analysis extends previous two-fluid theories to allow for arbitrary potentials of intermolecular interaction and arbitrary mass ratios. The treatment differs from the CE formulation in that the mean velocities and temperatures of the two gases are not required to be identical to lowest order. To first order, the streaming terms of the Boltzmann equation are thus computed in terms of the derivatives of the two-fluid hydrodynamic quantities, rather than the mean mixture properties as in the CE theory. As a result, associated with the nonconservation of momentum and energy for each species alone, two new "driving forces'' appear in the first-order integral equations. The amount of momentum and energy transferred per unit time between the species appear in the theory as free constants, which allow satisfying the constraint that all hydrodynamic information be contained within the lowest-order two-fluid Maxwellians. Simultaneously, this constraint fixes the rate of momentum and energy interchange in terms of the two-fluid hydrodynamic quantities and their gradients. The driving force d12 of the CE theory is directly related to the rate of interspecies momentum transfer, and the corresponding CE functions D1 and D2 appear here unmodified.But the physical interpretation of d12 is very different in the two pictures. On the CE side there is only one momentum equation, while d12 provides constitutive information fixing the diffusion flux (velocity differences) in the mass conservation equation. Here, the similar constitutive information associated to d12 is used to couple two different momentum equations. Although the CE theory captures some of the two-velocity aspects of the problem, no CE analog exists with the functions E1 and E2 associated here with temperature differences, which now require solving new integral equations. Finally, the presence of two velocities and two temperatures leads to four coefficients of viscosity and of thermal conductivity for the two stress tensors and heat flux vectors. Also, two thermal diffusion factors enter now into the expression for d12. Although all these new coefficients arise as portions of the overall CE transport coefficients, their independent optimal determination requires new developments. The corresponding variational formulation is presented here and used to first order to obtain explicit expressions for all two-fluid transport coefficients by means of Sonine polynomials as trial functions.

Notes: The collision integrals describing the rate of exchange of momentum and tensorial energy between the components in a binary mixture of neutral gases with very different atomic masses are determined for arbitrary values of their two temperatures and velocities, for realistic intermolecular potentials, and allowing for large departures of the heavy gas from equilibrium conditions. In the range of interest where the system is perturbed within times of the order of the slow relaxation time characterizing the transfer of energy between unlike molecules, the light gas distribution function is Maxwellian to lowest order, with corrections given asymptotically in powers of the small parameter m/mp formed with the ratio of the species molecular masses. Also, provided that the ratio Tp/T between the temperatures of the two gases remains much smaller than mp/m, the desired collision integrals may be evaluated asymptotically in powers of m/mp in all generality. The computation is carried out in detail for the case when the interaction between atoms is described by a Lennard–Jones potential. A combination of numerical computations with optimal matching of analytical expressions valid for large and small slip velocities leads to a set of compact formulas which hold for the limits of high and low temperatures and to a general approximate expression for all temperatures.