Deterministic analyses applied to both velocity and concentration fluctuation data obtained in a region extremely close to air-water interface in a free-surface, unbaffled stirred tank allow estimation of the length and the velocity scales of individual eddies taking part in gas absorption. The mass transfer prediction by this method is superior to that by a statistical method using an integral length scale in the low-turbulence flow employed in this work. Eddy velocities are generally lower in the diffusion boundary layer zone compared with the bulk zone. Small eddies are generally associated with low velocity scales whereas large eddies occur at high velocity scales. SCOPEIn earlier gas absorption models such as Higbie's (1935) penetration theory or Danckwerts' (1951) surface renewal theory, the fluid mechanics contribution is represented by a single parameter such as the exposure time or the surface renewal rate. In more recent models (Fortescue and Pearson, 1967; Lamont and Scott, 1970;Theofanous et al., 1976), attempts have been made to describe the convective diffusion in eddies near the gas-liquid interface in more realistic terms. These models contain statistically measurable length and velocity scales instead of a single parameter.Experimentally, however, the investigation of mass transfer in individual eddies has not been possible. In the conventional method, the mean length and velocity scales are obtained independently from a sufficiently long data record of velocity fluctuations by using a suitable statistical method. These scales are then combined to give a single exposure time for the whole system. The major disadvantage of this approach is that in the process of the statistical averaging, the information on the length and velocity scales of individual eddies is lost. As a result, the eddy exposure time distribution cannot be obtained, the mass transfer predictions are often poor, and there is always a question as to which size eddy controls the mass transfer.In the present study, we propose a direct analysis of the velocity or concentration fluctuation data by using a pseudosteady, two-dimensional single-eddy model to extract the length and velocity scales of individual eddies. This deterministic analysis readily enables estimations of the eddy exposure time distribution and the contribution of each eddy toward the overall mass transfer. The analysis is applied to both the velocity and concentration fluctuation data measured extremel) close to the air-water interface in a free-surface, unbaf fled stirred tank. CONCLUSION AND SIGNIFICANCEThe predictions of mass transfer coefficients by deterministic analyses of both the velocity and concentration fluctuation data obtained at 90 pm depth from the air-water interface agree well with the experimental values obtained from local concentration profile measurements. The predictions by the statistical method employing the integral length scale are always lower due to underestimation of the length scale. The eddy

Pirt's maintenance model has been widely accepted for the effects of growth rate and maintenance on growth yield. However, the interpretation of parameters in Pirt's model as biological constants is difficult for energy-sufficient culture growth. In this study, a mechanistic model for the growth energetics of energy-sufficient chemostat cultures is proposed and verified with literature data. In the model, the overutilization of the energy substrate in energy-sufficient culture growth is attributed to the defective regulation of the energy substrate metabolism and energy uncoupling. The model also uses an "energy surplus" concept to collectively represent the effects of energy excessiveness. The proposed model provides a better quantitative understanding of the maximum growth yield and maintenance of energy-sufficient cultures. It also explains the glucose concentration effect reported in the literature.

to draw definite conclusions, these results suggest that the steady-state concentration of arsine entering the reactor may be somewhat reduced due to absorption effects in the molecular sieve column.A possible area for further investigation is the effect of lowering the temperature of the molecular sieves to a point where dopant impurities may be more effectively absorbed. However arsine absorption effects are also expected to be more pronounced at lower temperatures. (The condensation temperature of arsine in the 4% mixture is ca. -113~ (12). We have not attempted to pursue this approach. Also, we have not examined other molecular sieve structures. ConclusionWe have grown InGaAs samples by hydride VPE using a column of Type 4A molecular sieves in the arsine line. These samples did not differ significantly either in background carrier concentration or in Hall mobility from corresponding samples grown using untreated arsine. We therefore conclude that these molecular sieves are not effective at room temperature in removing dopant impurities from the 4% arsine-hydrogen mixture used. AcknowledgmentsWe wish to thank C. M. Stiles for SEM measurements and R.F. Kopf for Hall effect measurements. We also thank J. Long, D. Coblentz, and J. L. Zilko for helpful discussions and W. D. Johnston, Jr. and M. A. DiGiuseppe for advice and encouragement.

Radio-frequency (rf) methane and methane/hydrogen plasmas are used extensively for the deposition of hard-coating of diamond-like carbon films. 1 The prediction of the deposition of thin carbon films in nanoscale is a technological challenge. The discharge in typical reactors being essentially two dimensional, a two-dimensional modeling of the glow discharge physics is essential to identify the axial and radial variations of the species and their fluxes. Multidimensional discharge modeling for a polyatomic gas like methane is challenging in terms of computational effort and time. A methane discharge contains a number of positive and negative ions and radicals. The gas phase chemistry and surface deposition models need to be coupled with the discharge physics model to predict the radial and axial variations of radicals. The radical and ion fluxes to the cathode are required for the prediction of the diamond-like carbon film deposition rate on the wafer. The motivation of the present research is to develop a comprehensive plasma model for the prediction of the deposition of thin diamond-like carbon film under reactor operating conditions.Capacitively coupled rf discharges are extensively used in the semiconductor industry for etching and deposition processes, and their use is important for ultralarge-scale integration (ULSI) device fabrications. Recently, diamond-like carbon (DLC) film deposition has been investigated for its potential applications as a low dielectric constant material for the back end of the line interconnect structures in ULSI circuits. 2 A number of one-dimensional fluid models for rf discharges has been developed in the last decade. Recently, some of these models have been extended to two-dimensions to capture both the axial and radial variations of plasma properties.Considerable research has been performed for modeling monatomic gas discharges in capacitively coupled reactors. By using three moments of the Boltzmann equation, one-and two-dimensional rf He discharges 3 were simulated for plasma density, electric field, mean energy, and ionization rates. A two-dimensional fluid model for an rf Ar discharge in a cylindrical chamber 4 was presented where self-induced dc bias was computed using a trial-and-error method. An asymmetric axial ion density profile was predicted that peaked toward the smaller, powered electrode. The electron energy in the presheath region in front of the powered electrode was several electron-volts higher than that in the bulk plasma. The off-axis maximum in electron density was observed in a two-dimensional Ar discharge model with metastable neutral transport. 5 An Ar discharge model for the Gaseous Electronics Conference reference reactor 6 also predicted an off-axis maximum for plasma density. The electron and ion current densities on the powered electrode were observed to increase radially outward. A three-moment approach 7 for both electrons and ions to model the two-dimensional rf Ar discharge was used to predict the electron density, potential and electron-excitat...

Fermentation stoichiometry can be derived from macroscopic balancesIz2 or from metabolic pathway balances .3*4 The pathway balance methods, although more complicated, are more powerful than the macroscopic balance methods. In applying stoichiometry to fermentation processes, a system is overdetermined if the number of process measurements is greater than the number of measurements required to define the system. In such a system, because of the presence of measurement errors, fermentation stoichiometry is usually not satisfied exactly. Unless some optimal adjustment of measurement data is made, the measurement errors may lead to erroneous state estimates or false conclusions. ' There are numerous studies on statistical analysis of measurement data as summarized by Wang and Stephanopoulos.' Among them is the method of maximum likelihood estimation by Madron et aL6 for reactors with parallel reactions. This method was successfully applied to macroscopic balance stoichiometry.' The objective of this study is to develop a method for applying Madron's statistical method to pathway stoichiometry for analyzing bioreactor data. THEORYAs shown by Papoutsakis and the stoichiometry of each pathway reaction can be written when the metabolic pathway information is known. The overall reaction then can be expressed as a linear combination of all pathway reactions. If there are J linearly independent pathway reactions among I species, the pathway reactions can be written as where a,, is the stoichiometric coefficient of the ith species in the jth pathway reaction. Species considered in the pathway reactions include nonaccumulating intermediates of the metabolic pathways, as well as reactants and products of the overall reaction. Equation (1) can also be written in a matrix form:* To whom correspondence should be addressed. where A is the matrix (all) and S the vector of species s, .The number of moles of species i produced in the overall reaction (called "flow i" in the following text), n, , is thus given by