Daniel E. Rosner

Effects of interface kinetics, capillarity and solute diffusion on bubble growth rates in highly supersaturated liquids

The growth of an isolated, stationary bubble in an isothermal liquid supersaturated with an atomically or molecularly dissolved gas is treated theoretically, with emphasis on departures from “parabolic” growth produced by: (i) finite rate exsolution kinetics (ii) nonzero surface tension and (iii) nonzero initial bubble size. A convenient moment (integral) method is introduced, which takes full account of interface movement, self-induced radial velocities in the solvent and time-dependent vapor density in the bubble. In the thin solute boundary layer limit, shown to be relevant to highly supersaturated systems, accurate closed form bubble radius-time results are obtained displaying the principal effects of the governing dimensionless parameters. Graphical (radius)2-time curves, included herein for those cases of greatest physicochemical interest, clearly reveal the conditions under which each of the abovementioned phenomena become appreciable and, hence, define the range of validity of previous, more restrictive treatments of bubble growth. Illustrative calculations are included for the recently investigated case of nitrogen degassing of iron melts.

High temperature oxidation of carbon by atomic oxygen

Abstract The true kinetics of the attack of high temperature graphite by both atomic and diatomic oxygen have been studied using microwave discharge-fast flow system techniques. In the surface temperature range 1100°K–2000°K the oxidation probability for O-atom attack 1. (i) exceeds that for O 2 , by factors between 5 and as much as 80, 2. (ii) passes through a maximum in this temperature range, as does the O 2 attack probability on the same surface, and 3. (iii) is independent of oxygen partial pressure (corresponding to a first order reaction), in contrast to the kinetic order of the O 2 /carbon reaction. Several mechanistic implications of these results are briefly discussed.

Enhancement of diffusion-limited vaporization rates by condensation within the thermal boundary layer: 1. The critical supersaturation approximation∗

The general conditions under which condensation within the thermal boundary layer can enhance the diffusion-limited evaporation rates of liquids or solids in cooler environments are examined analytically, based on the notion that condensation occurs where a “critical supersaturation” is achieved. Simple expressions are derived for the expected enhancement in terms of the dimensionless heat of vaporization Λ/RTw the critical supersaturation evaluated at the surface temperature scrit(Tw) ≡ Pv,crit/Pv,eq (Tw), and a parameter governing the temperature dependence of scrit These results clearly display the thermodynamic and transport conditions under which large enhancements can be expected. The facility with which they can be used for absolute predictions and comparison with available data is illustrated for the case of molten iron spheres evaporating into quiescent helium at atmospheric pressure.

Enhancement of diffusion-limited vaporization rates by condensation within the thermal boundary layer 2. Comparison of homogeneous nucleation theory with the critical supersaturation model

Abstract The validity of the critical supersaturation model (CSM) for predicting mass transfer effects of nonequilibrium fog formation in thermal boundary layers is examined by comparing CSM predictions with those of a more complete application of homogeneous nucleation theory to a simple flow with molecular transport. Expressions for the nucleation kinetics and droplet growth are combined with the steady one-dimensional conservation equations and suitably transformed to allow a digital computer solution of the vaporization of a hot condensed phase into a cold gaseous medium. Using a one dimensional film model of the thermal boundary layer, predictions of boundary layer profiles and the effects of nonequilibrium fog formation are obtained and, as anticipated by the CSM, the gross effect of fog formation is to significantly enhance the steady state vaporization rate. Our numerical calculations for methyl alcohol evaporation/condensation confirm the conceptual and computational utility of the critical supersaturation model for this class of problems, provided critical supersaturation predictions are based on large volumetric nucleation rates. Consistent with our purposes, the present investigation is limited to binary gas mixtures with (i) a Lewis number of unity and (ii) both mixture constituents of equal molecular weight. Since methyl alcohol vapor-air mixtures conform well to these restrictions, and are of interest in both research and technology, illustrative numerical results are given for this system.

Chemiluminescent titration of F(g) with Cl2(g) and microwave production of atomic fluorine

Chemiluminescent titration of atomic fluorine with Cl2 in a low pressure (133 Pa) flow apparatus has been investigated to establish the accuracy of this titration method and the efficiency of F atom production in a microwave discharge. Up to 90 % dissociation of F2(0.5–10 % in Ar) is achieved by a 100 W Evenson-type cavity 2450 MHz discharge when the microwave power exceeds 2500 kJ mol–1 F and discharge residence time exceeds 0.7 ms. Heterogeneous F atom loss on the fluorine-passivated Al2O3 discharge tube walls occurs with a recombination probability, γF≈ 2 × 10–4.Heterogeneous Cl atom recombination does not interfere with the chemiluminescent F/Cl2 titration in glass apparatus since, in the presence of fluorine, γCl(pyrex) < 8 × 10–5. However, homogeneous three-body recombination to form ClF and/or Cl2 produces errors in the titration endpoint which exceed 10 % if the product of F atom partial pressure, total pressure and the mean residence time between titrant addition and chemiluminescent intensity measurement exceeds 160 Pa2 s at 300 K.

Chemical energy accommodation at catalyst surfaces. Flow reactor studies of the association of nitrogen atoms on metals at high temperatures

The fate of the energy release in highly exoergic surface-catalysed chemical reactions is of considerable fundamental interest and influences catalyst volatilization/sintering, the aerodynamic heating of hypersonic glide vehicles subject to bombardment by atomic nitrogen and atomic oxygen, etc. To provide the first available high temperature data (T > 800 K) on what fraction (β) of the equilibrium (bond) dissociation energy is delivered to the catalyst per atom association event, a coaxial filament flow reactor (CFFR) has been developed, well-suited to both precise atom mass balance and isothermal calorimetric measurements. Experimental results for the chemical energy accommodation (CEA) coefficient β, and the corresponding N-atom recombination probabilities, γ, are presented for the metals Pt, Ir, Rh, Pd, Co, W and Re at temperatures up to 2600 K. Catalyst energy deposition can be an order of magnitude less than the equilibrium reaction energy. However, since this is not true at all surface temperatures, simple rankings of β-values for metals (at, say, room temperature) or correlations based only on one or two relevant system parameters (e.g. bulk Debye temperature) are of limited application. Alternatively, for N/Re, N/W a Langmuir-type mass-action analysis of the operative elementary steps, combined with a simple postulate (viz. Rideal-produced molecules leave excited whereas Langmuir—Hinshelwood (LH) produced molecules do not) provides a semi-quantitative understanding of β-trends in terms of the adatom binding energy, the equilibrium bond dissociation energy of the product molecule and an elementary Rideal reaction probability. However, high β-values can be observed at low temperatures if the system admits LH-reaction, or Rideal-formed excited molecules are rapidly quenched prior to desorption. We postulate that low catalyst energy deposition occurs at high temperatures (N/Pt, N/Ir) if LH-reaction occurs prior to the complete accommodation of the reactant (atom) chemisorption energy.

Fog formation conditions near cool surfaces

Abstract A simple criterion incorporating nonequilibrium phenomena is developed for predicting the onset of fog formation due to homogeneous nucleation during vapor (or solute) condensation on cold surfaces. Surface temperatures and/or free stream vapor concentrations leading to incipient fogging are related to available critical supersaturation data. Illustrative results for initially unsaturated water vapor-air mixtures at 25°C reveal that surface temperatures about 60°C below the dew point will always produce mists within the thermal boundary layer.

Combustion of zirconium droplets in oxygen/rare gas mixtures—kinetics and mechanism

To help understand the combustion mechanism of molten zirconium, time-resolved luminosity traces of freely falling submillimeter droplets have been obtained. These data and prior photographic, spectroscopic, gravimetric, and related observations on flash-heated (laser or xenon lamp) specimens in subatmospheric pressure oxygen/rare gas mixtures are shown to be consistent with a model in which the reaction rate is initially limited by the true kinetics of a gas/liquid interface reaction, later becomes limited by external oxygen transport to the droplet through a film of carrier gas and/or vaporization products, and finally is limited by internal diffusion of oxygen to the Zr-rich droplet core.

Influence of the turbulent diffusion boundary layer on the apparent kinetics of surface catalysed reactions in external flow systems

Abstract Steep gradients of reactant concentration in the immediate vicinity of solid catalysts in forced-flow systems cause the apparent chemical kinetics of surface catalysed reactions to differ from the true interfacial kinetics. In the present paper the magnitude of this falsification is investigated quantitatively for the case of turbulent incompressible flow within the diffusion boundary layer, using the uniform activity catalytic flat plate as an example. Corresponding results for laminar diffusion layers are included for comparison. Several distinct computational techniques are briefly discussed for diffusional Prandtl numbers Pr ≡ ν/ D of order unity as well as for the asymptotic extreme Pr → ∞. While the accuracy of predictions which completely neglect the effect of upstream reaction history on the local transfer coefficient is found to be better than in the corresponding laminar boundary layer case, their accuracy degenerates as the diffusional Prandtl number is increased (contrary to the fully laminar case). Using a rational improvement of the Frank-Kamenetskiĭ quasi-stationary approximation, results are given for all pertinent non-dimensional reaction rate coefficients over the entire range from reaction rate to diffusion-control for half-order, first-order and second-order irreversible, surface-catalysed reactions.

Effects of the stefan-nusselt flow on the apparent kinetics of heterogeneous chemical reactions in forced convection systems

Abstract The effect of the interfacial mass velocity normal to surfaces undergoing heterogeneous reaction on the apparent kinetics of such reactions is quantitatively investigated. A simple algebraic model is developed which enables all pertinent non-dimensional reaction-rate coefficients to be obtained over the entire range from reaction rate (“chemical”) control to diffusion control for one-step irreversible heterogeneous reactions of arbitrary kinetic order. Illustrative results are presented for the case of turbulent boundary layers on flat surfaces undergoing first-order reaction. The effect of this interfacial flow (the Stefan-Nusselt flow) is found to be significant whenever the reaction rate is not completely chemically controlled and the quantity [In (1 + Bdiff)]/Bdiff departs appreciably from unity, where Bdiff is a diffusion-controlled dimensionless mass-transfer parameter obtainable a priori in terms of the reactant mass fraction in the feed and the reaction stoichiometry. The Stefan-Nusselt flow is found to 1. (i) destroy the time-honored notion that diffusional limitations ultimately cause all surface reactions to masquerade as first order reactions 2. (ii) introduce a connection between the profile drag on reacting surfaces and the true kinetics of the reaction 3. (iii) leave unaltered the form of a potentially useful relation between the power required to maintain a reacting surface at a prescribed temperature and the true kinetics of the chemical reaction at that temperature. Applications of the theory to specific heterogeneous reactions (e.g. oxidation, chlorination, chemical vapor plating) are facilitated by the compilation of representative values of the mass-transfer parameter Bdiff The errors committed by neglecting the Stefan-Nusselt flow are discussed for two cases of current interest, viz. the high temperature oxidation of graphite and molybdenum in air. The results of the theory are presented and discussed in such a way as to emphasize their generality as well as the physicochemical conditions under which simple computational procedures are likely to be acceptable.