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At least 37 records · Page 2

Comparative study of machine learning techniques for post-combustion carbon capture systems

Computational analysis of countercurrent flows in packed absorption columns, often used in solvent-based post-combustion carbon capture systems (CCSs), is challenging. Typically, computational fluid dynamics (CFD) approaches are used to simulate the interactions between a solvent, gas, and column's packing geometry while accounting for the thermodynamics, kinetics, heat, and mass transfer effects of the absorption process. These simulations can then be used explain a column's hydrodynamic characteristics and evaluate its CO 2 -capture efficiency. However, these approaches are computationally expensive, making it difficult to evaluate numerous designs and operating conditions to improve efficiency at industrial scales. In this work, we comprehensively explore the application of statistical ML methods, convolutional neural networks (CNNs), and graph neural networks (GNNs) to aid and accelerate the scale-up and design optimization of solvent-based post-combustion CCSs. We apply these methods to CFD datasets of countercurrent flows in absorption columns with structured packings characterized by several geometric parameters. We train models to use these parameters, inlet velocity conditions, and other model-specific representations of the column to estimate key determinants of CO 2 -capture efficiency without having to simulate additional CFD datasets. We also evaluate the impact of different input types on the accuracy and generalizability of each model. We discuss the strengths and limitations of each approach to further elucidate the role of CNNs, GNNs, and other machine learning approaches for CO 2 -capture property prediction and design optimization.

97 MATHEMATICS AND COMPUTING

Droplet burning at zero G

Questions of the importance and feasibility of performing experiments on droplet burning at zero gravity in Spacelab were studied. Information on the physics and chemistry of droplet combustion, with attention directed specifically to the chemical kinetics, heat and mass transfer, and fluid mechanics of the phenomena involved, are presented. The work was divided into three phases, the justification, the feasibility, and the conceptual development of a preliminary design. Results from the experiments performed revealed a few new facts concerning droplet burning, notably burning rates in excess of theoretical prediction and a phenomenon of flash extinction, both likely traceable to accumulation of carbon produced by gas-phase pyrolysis in the fuel-rich zone enclosed by the reaction surface. These experiments also showed that they were primarily due to timing difficulties.

Williams, F. A.

Integration of the fundamental knowledge on solvent-packing interactions into the multiscale framework for column scale design and optimization

The interfacial area, also known as the effective mass transfer area, is a key factor for determining the mass transfer for carbon dioxide (CO 2 ) capture via the chemical absorption process in a packed column, and thus the overall capture efficiency of the packed column. Most of the widely used empirical and semi-empirical models for interfacial area were derived indirectly through absorption mass transfer with simplifications based on fast chemical kinetics. This report presents the comprehensive unique multiscale approach to develop a surrogate model for effective mass transfer area in structured packed columns that accounts local hydrodynamics as well as variation in physical properties, and changes in solid surface characteristics.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH

Accretion onto a Supermassive Black Hole Binary before Merger

While supermassive binary black holes (SMBBHs) inspiral toward merger they may also accrete matter from a surrounding disk. To study the dynamics of this system requires simultaneously describing the evolving spacetime and the magnetized plasma. We present the first relativistic calculation simulating two equal-mass, nonspinning black holes as they inspiral from a 20 M (G = c = 1) initial separation almost to merger. Our results imply important observational consequences: for instance, the accretion rate $\dot{M}$ onto the black holes first decreases and then plateaus, dropping by only a factor of ~3 despite the rapid inspiral. An estimated bolometric light curve follows the same profile, suggesting some merging SMBBHs may be significantly luminous past the predicted circumbinary disk decoupling. The minidisks are nonstandard: Reynolds, not Maxwell, stresses dominate, and they oscillate between two states. In one part of the cycle, "sloshing" streams transfer mass between minidisks, carrying kinetic energy at a rate sometimes as high as the peak minidisk bolometric luminosity. We also discover that episodic accretion drives time-varying minidisk tilts. These complex dynamics all contribute to unique cyclical behavior in the light curves of late-time inspiraling SMBBHs. The poloidal magnetic flux on the black holes is roughly constant at a dimensionless level $\phi$ ~ 2–3, but doubles just before merger; for significant black hole spin, this flux predicts powerful jets with variability driven by binary dynamics, another potentially unique electromagnetic signature. This simulation is the first to employ our multipatch infrastructure PATCHWORK MHD, decreasing the computational expense to ~3% of conventional single-grid methods' cost.

79 ASTRONOMY AND ASTROPHYSICS

Intumescent coating modeling

A thermal response mathematical model for an intumescent coating system is developed. The model predicts indepth temperature profiles of the solid as a function of the fundamental kinetic, mass, and heat-transfer properties of the original coating system. In the model, swelling is based on an empirical function of the paint's weight loss. The model is used to describe the effectiveness of the coating for thermal protection. Using the thermal response time at the backface of the material as a criterion, a sensitivity analysis is made with respect to variation in individual properties, such as total expansion, to provide a guide for designing improved intumescing agents. The sensitivity analysis shows that total expansion and rate of expansion, along with other material properties, are important parameters for providing thermal protection. Finally, backface temperature histories are predicted and compared to experimental data obtained from a representative fire environment. Predicted temperatures agree within a maximum error of plus or minus 20%.

Cagliostro, D. E.

Opportunities and challenges in process modeling and simulation of electrochemical systems

Electrochemical technologies have garnered intense interest in both academic research and industrial applications due to their potential to increase energy efficiency and reduce carbon footprint. However, electrochemical process fundamentals have been absent from the chemical process simulators available to millions of chemical engineers worldwide. To expedite process research and development of electrochemical technologies in the chemical industry, it is imperative that essential electrochemical process fundamentals be incorporated into process simulators to support modeling and simulation of electrochemical processes. Here, this study examines three process fundamentals key to the research and development of electrochemical processes: electrochemical reaction kinetics, electrolyte thermodynamics, and heat and mass transfer. It further illustrates application of these process fundamentals with a case study modeling an electrochemical process for the conversion of acrylonitrile to adiponitrile. The modeling example highlights the roles of applied voltage on reaction rates, and electron flow rates on the performance of electrochemical processes. It suggests that the applied voltage and electron flow rates are two unique concepts that should be included in simulators for electrochemical processes.

09 BIOMASS FUELS

Remobilizing the Interfaces of Thermocapillary Driven Bubbles Retarded by the Adsorption of a Surfactant Impurity on the Bubble Surface

Thermocapillary migration is a method for moving bubbles in space in the absence of buoyancy. A temperature gradient is applied to the continuous phase in which a bubble is situated, and the applied gradient impressed on the bubble surface causes one pole of the drop to be cooler than the opposite pole. As the surface tension is a decreasing function of temperature, the cooler pole pulls at the warmer pole, creating a flow which propels the bubble in the direction of the warmer fluid. A major impediment to the practical use of thermocapillarity to direct the movement of bubbles in space is the fact that surfactant impurities which are unavoidably present in the continuous phase can significantly reduce the migration velocity. A surfactant impurity adsorbed onto the bubble interface is swept to the trailing end of the bubble. When bulk concentrations are low (which is the case with an impurity), diffusion of surfactant to the front end is slow relative to convection, and surfactant collects at the back end of the bubble. Collection at the back lowers the surface tension relative to the front end setting up a reverse tension gradient. For buoyancy driven bubble motions in the absence of a thermocapillarity, the tension gradient opposes the surface flow, and reduces the surface and terminal velocities (the interface becomes more solid-like). When thermocapillary forces are present, the reverse tension gradient set up by the surfactant accumulation reduces the temperature tension gradient, and decreases to near zero the thermocapillary velocity. The objective of our research is to develop a method for enhancing the thermocapillary migration of bubbles which have been retarded by the adsorption onto the bubble surface of a surfactant impurity, Our remobilization theory proposes to use surfactant molecules which kinetically rapidly exchange between the bulk and the surface and are at high bulk concentrations. Because the remobilizing surfactant is present at much higher concentrations than the impurity, it adsorbs to the bubble much faster than the impurity when the bubble is formed, and thereby prevents the impurity from adsorbing onto the surface. In addition the rapid kinetic exchange and high bulk concentration maintain a saturated surface with a uniform surface concentrations. This prevents retarding surface tension gradients and keeps the velocity high. In our first report last year, we detailed experimental results which verified the theory of remobilization in ground based experiments in which the steady velocity of rising bubbles was measured in a continuous phase consisting of a glycerol/water mixture containing a polyethylene glycol surfactant C12E6 (CH3(CH2)11(OCH2CH2)6OH). In our report this year, we detail our efforts to describe theoretically the remobilization observed. We construct a model in which a bubble rises steadily by buoyancy in a continuous (Newtonian) viscous fluid containing surfactant with a uniform far field bulk concentration. We account for the effects of inertia as well as viscosity in the flow in the continuous phase caused by the bubble motion (order one Reynolds number), and we assume that the bubble shape remains spherical (viscous and inertial forces are smaller than capillary forces, i e. small Weber and capillary numbers). The surfactant distribution is calculated by solving the mass transfer equations including convection and diffusion in the bulk, and finite kinetic exchange the bulk and the surface. Convective effects dominate diffusive mass transfer in the bulk of the liquid (high Peclet numbers) except in a thin boundary layer near the surface. A finite volume method is used to numerically solve the hydrodynamic and mass transfer equations on a staggered grid which accounts specifically for the thin boundary layer. We present the results of the nondimensional drag as a function of the bulk concentration of surfactant for different rates of kinetic exchange, from which we develop criteria for the concentration necessary to develop a prescribed degree of remobilization. The criteria compare favorably with the experimental results.

Palaparthi, Ravi

Surfactant Facilitated Spreading of Aqueous Drops on Hydrophobic Surfaces

Microgravity technologies often require aqueous phases to spread over nonwetting hydrophobic solid surfaces. Surfactants facilitate the wetting of water on hydrophobic surfaces by adsorbing on the water/air and hydrophobic solid/water interfaces and lowering the surface tensions of these interfaces. The tension reductions decrease the contact angle, which increases the equilibrium wetted area. Hydrocarbon surfactants; (i.e., amphiphiles with a hydrophobic moiety consisting of an extended chain of (aliphatic) methylene -CH2- groups attached to a large polar group to give aqueous solubility) are capable of reducing the contact angles on surfaces which are not very hydrophobic, but do not reduce significantly the contact angles of the very hydrophobic surfaces such as parafilm, polyethylene or self assembled monolayers. Trisiloxane surfactants (amphiphiles with a hydrophobe consisting of methyl groups linked to a trisiloxane backbone in the form of a disk ((CH3)3-Si-O-Si-O-Si(CH3)3) and an extended ethoxylate (-(OCH2CH2)a-) polar group in the form of a chain with four or eight units) can significantly reduce the contact angle of water on a very hydrophobic surface and cause rapid and complete (or nearly complete) spreading (termed superspreading). The overall goal of the research described in this proposal is to establish and verify a theory for how trisiloxanes cause superspreading, and then use this knowledge as a guide to developing more general hydrocarbon based surfactant systems which superspread. We propose that the trisiloxane surfactants superspread because their structure allows them to strongly lower the high hydrophobic solid/aqueous tension when they adsorb to the solid surface. When the siloxane adsorbs, the hydrophobic disk parts of the molecule adsorb onto the surface removing the surface water. Since the cross-sectional area of the disk is larger than that of the extended ethoxylate chain, the disks can form a space-filling mat on the surface which removes a significant amount of the surface water. In this presentation, we report the results of measurements of the molecular packing and rates of kinetic exchange of the trisiloxane surfactants at the air/water interface in order to confirm our picture of trisiloxane packing, and provide additional insight into the superspreading process. We used the pendant bubble technique as a Langmuir trough to measure the trisiloxane equation of state which relates the tension to the surface concentration. From these measurements we obtain accurate values for the maximum packing density. We find that trisiloxanes with 4 and 8 ethoxylate groups have the same maximum packing concentration, indicating that the maximum packing is controlled by the cross section of the head group. For trisiloxanes with larger than eight ethoxylates, the maximum packing increases with ethoxylate number, indicating that the disposition of the ethoxylate chain (i.e., its effective size) is controlling. This supports our picture of superspreading: The superspreading ability of trisiloxanes decreases considerably for trisiloxanes with larger than eight ethoxylates; the packing measurements indicate that for the higher ethoxylate number trisiloxanes, the compact nonpolar head groups are pushed apart by the ethoxylate chain. They leave spaces of surface water on adsorption and do not lower the solid tension as much as their lower chain analogues. Finally the report measurements of the dynamic tension reduction accompanying the adsorption of trisiloxanes onto an initially clean interface using the pendant bubble technique, and we obtain from these relaxations, the equation of state and a mass transfer model, the rate constants for kinetic exchange. We find that the rate constants for desorption of trisiloxanes are generally much slower than for analogous aliphatic polyethoxylate surfactants with identical ethoxylate chain lengths. When an aqueous drop of a superspreader solution is placed on a hydrophobic surface and begins to spread, the lower desorption rates allows the tension at the drop center to remain reduced relative to the tension of the expanding periphery, thus strengthening Marangoni forces which can assist the spreading. Marangoni forces can be especially significant in the case of superspreaders because their maximum equilibrium reduction in tension is several dynes/cm lower than for aliphatic surfactants.

Kumar, Nitin

Interpenetrating 3D Electrodes for High-Rate Alkaline Water Splitting

Mass transfer is critical for the reaction kinetics and efficiency of alkaline water splitting (AWS). For AWS to operate at high current densities (hundreds of mA/cm 2 ), the device architecture must ensure a large catalytic surface area, rapid ion diffusion, and minimal solution and charge transfer resistances. Effective electrodes should also facilitate gas bubble detachment and release. 3D-printed electrodes have shown promise, but stacking them increases the ion diffusion length and solution resistance. Here we demonstrate a new device architecture with interpenetrating gyroid electrodes, providing a large ion-accessible surface area and gas diffusion channels. This design significantly reduces the interelectrode distance, lowering ion diffusion length and solution resistance. Simulations show faster ion diffusion and higher current density in the interpenetrating configuration compared with separate electrodes. This improved performance, especially at low temperatures and high current densities, highlights a promising strategy for enhancing AWS and other electrochemical systems limited by slow ion diffusion.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH

Bridging the Gap in Carbon Free Iron Making: How Hydrogen Affects the Reduction of Iron Ore between 900 and 1590 °C

Hydrogen-based reduction of iron ore for iron and steel production has emerged as a promising alternative to coal and natural gas. Unlike other hydrogen-based iron ore reduction studies, this research focuses on a wide temperature range across 900–1590 °C, encompassing reduction in solid, mixed, and liquid (slag) phases. For a 20 min exposure to hydrogen, the reduction degree increased monotonically from ∼35% at 900 °C to >90% at 1550 °C, except between 1100 °C and 1400 °C, where it stagnated ∼60%. This experimental work challenges the widely accepted notion that higher temperatures enhance the reduction process. Instead, it reveals an overlooked kinetic bottleneck, suggesting complex thermodynamic and mass transfer limitations influenced by phase transformations, diffusion barriers, and microstructural changes. Density functional theory-based molecular dynamics simulations indicate that oxygen diffusivity in BCC iron is 3.88 × 10 –5 cm 2 /s which is ∼5–10 times higher than that in FCC iron. This study reports that this stagnant reduction degree in the mixed solid–liquid phase is due to competition of multiple mechanisms, such as surface- and bulk-diffusion, pore collapse mechanisms, and crystallographic transitions.

08 HYDROGEN

Droplet Combustion Experiment (DCE)

The first space-based experiments were performed on the combustion of free, individual liquid fuel droplets in oxidizing atmospheres. The fuel was heptane, with initial droplet diameters ranging about from 1 mm to 4 mm. The atmospheres were mixtures of helium and oxygen, at pressures of 1.00, 0.50 and 0.25 bar, with oxygen mole fractions between 20% and 40%, as well as normal Spacelab cabin air. The temperatures of the atmospheres and of the initial liquid fuel were nominally 300 K. A total of 44 droplets were burned successfully on the two flights, 8 on the shortened STS-83 mission and 36 on STS-94. The results spanned the full range of heptane droplet combustion behavior, from radiative flame extinction at larger droplet diameters in the more dilute atmospheres to diffusive extinction in the less dilute atmospheres, with the droplet disappearing prior to flame extinction at the highest oxygen concentrations. Quasisteady histories of droplet diameters were observed along with unsteady histories of flame diameters. New and detailed information was obtained on burning rates, flame characteristics and soot behavior. The results have motivated new computational and theoretical investigations of droplet combustion, improving knowledge of the chemical kinetics, fluid mechanics and heat and mass transfer processes involved in burning liquid fuels.

Haggard, John B., Jr.

Multiphase computational fluid dynamics modeling of reacting flows in absorption columns for carbon capture

First-principles derived computational fluid dynamics (CFD) simulations have been proposed as a fundamental tool for investigating solvent-based CO 2 absorption in packed columns due to their ability to accurately represent the underlying nonlinear, multiscale dynamics. Numerous studies have previously utilized such CFD simulations to investigate hydrodynamics of columns with structured and random packings by assessing the key hydrodynamic metrics such as the interfacial and wetted areas. While mapping such metrics for different conditions is essential to the optimization of absorption columns, it is not sufficient, as the CO 2 capture rate depends also on the coupled, nonlinear dynamics from the underlying chemical reaction kinetics, thermodynamics, and heat-transfer rates. In this work, we present detailed CFD simulation results augmented by incorporating the effects of interfacial physical mass transfer of CO 2 , heat release from chemical reaction kinetics, and thermophysical property variations from resulting temperature gradients. We demonstrate the applicability of the proposed approach in numerically assessing the performance of packed columns by evaluating key hydrodynamic quantities, CO 2 absorption rates, and temperature rise in a reference column with packings that are structurally similar to the Sulzer Mellapak™ 250.Y packing, for different solvent inflow velocities and temperatures. Predictions from simulation results are found to be consistent with the trends in experimental observations from the literature, suggesting that the predictive capabilities of the simulation framework can be leveraged to guide the future development of absorber-column designs and optimized process flowsheets.

Absorption columns

Scanning Electrochemical Microscopy for Kinetic Investigations in Viscous Deep Eutectic Solvents: Identifying Practical Approach Curves and Deviations from Electron Transfer Models

Determining heterogeneous electrochemical electron transfer (ET) kinetics in electrolytes with a wide range of physical properties is of great interest for achieving high-performance redox flow batteries. Among such electrolytes, concentrated hydrogen-bonded electrolytes (CoHBEs), including deep eutectic solvents (DESs), have recently garnered significant attention. Unfortunately, traditional Tafel analysis using macroelectrodes often encounters issues with mass transfer limitations in CoHBEs with high viscosities, thereby restricting kinetic analysis to a narrow potential window. Here, in this work, we introduce a methodology for evaluating ET kinetics in viscous DES using the scanning electrochemical microscopy (SECM). We first determined practical solutions to SECM tip positioning in ethaline DES, which yield pseudopositive feedback responses. Lattice Boltzmann method (LBM) simulations helped us rationalize the impact of the fluid and concentration fields, as well as tip geometry, tip approach velocity v, and the solvent viscosity ηs, on the shape of the approach curves. In addition to successfully recreating approach curves over a variety of conditions, we found that approaching a conductor ensured a practical point where the normalized tip response (Ni T = 2) converged at L = 0.7 within ∼10% error regardless of tip velocity. With positioning capabilities at hand, we investigated the kinetics of Fe 3+ /Fe 2+ redox couple in aqueous and the ethaline media. The experimental kinetic results were interpreted using the Butler–Volmer (BV) and Marcus–Hush–Chidsey (MHC) models. For ethaline, a nonideal kinetic behavior was observed, potentially attributed to solvent dynamics within DESs or to the interplay of chloride anions in the charge transfer process.

electrodes

CFD Modeling of Phase Change and Pressure Drop during Violent Sloshing of Cryogenic Fluid in a Small-Scale Tank

This paper presents the development of a two-phase CFD model that is used to study sloshing of a cryogenic fluid (LN2) undergoing phase change generated by lateral acceleration and its effects on the ensuing heat and mass transfer and pressure drop in a small-scale tank. In this model the interface is captured using the volume-of-fluid (VOF) method [1]. Kinetic-theory based Schrage relation [2] is used for calculating phase change mass transfer at the liquid-vapor interface. Computational results are compared to the data provided by a non-isothermal sloshing experiment with phase change conducted by the University of Tokyo and JAXA in 2018 using liquid Nitrogen in a transparent tank. The effect of different thicknesses of a liquid temperature stratification layer created at the interface on the pressure drop during sloshing was studied experimentally. CFD results for interface movement and tank pressure are presented and compared in this paper to experimental data for the cases with the smallest and largest liquid temperature stratification thickness.

phase change

Modelling of Laser-Enhanced Chemical Vapor Deposition

Research is directed at development of a detailed model of mass and heat transfer and chemical reaction in the pyrolysis of silane for the growth of thin amorphous silicon substrates incorporating laser heating of the gas phase above the film. The model will be the basis for evaluation of the relative importances of the decomposition of SiH4 in the vapor phase, mass transfer of the intermediate species, e.g., SiH2, and the evolution of hydrogen gas. Plans are also underway for developing a model for homogeneous nucleation of Si in the vapor phase to model the rate limitations observed at high gas-phase temperatures and high partial pressures of silane. Work was concentrated on an almost one-dimensional model for the coupling of the CO2 laser beam for heat transfer of the vapor phase with simple kinetic models for SiH4 decomposition and subsequent absorption of Si vapor on the substrate. Mass transfer in the vapor phase is assumed to be solely by diffusion. The role of convection in the vapor phase caused by the large changes in density in and around the center of the laser beam will be analyzed to evaluate the potential of microgravity experiments for increasing the uniformity of the film and the deposition rate.

Brown, R. A.

Impact of Small-Alkane Solvents on Polyolefin Hydrogenolysis over a Ruthenium Catalyst

Selective catalytic hydrogenolysis of polyolefins is a promising route to convert plastic waste into valuable liquid products, such as lubricants, waxes, and surfactants. However, the high viscosity of polymer melts imposes mass transfer limitations on this reaction. Solvents can mitigate these challenges, but their effects on reaction kinetics and product selectivity remain underexplored. Here, we systematically explore the effects of small n-alkanes and cycloalkanes on the hydrogenolysis of polyethylene and polypropylene over a Ru/TiO 2 catalyst. Using kinetic measurements and isotopic labeling, we show that n-octane at high mass fractions alters the mechanism from direct hydrogenation to solvent-mediated hydrogen transfer, reducing the rate of C–C bond cleavage. Longer alkanes further inhibit reactivity due to stronger surface binding. 1,4-Dimethylcyclohexane suppresses methane formation, favoring heavier products, while decalin likely forms surface-bound aromatics that poison the catalyst. Overall, alkane solvents modulate product selectivity and reduce the yield of methane byproduct, allowing for ∼35–40% selectivity to valuable C 20 -C 30 alkane products. This work highlights the complex impact of polymer–alkane mixtures on hydrogenolysis kinetics relevant to the design of commercial-scale plastic waste valorization processes.

Catalysts

Effects of Dissolution Regimes on Flow Channelization and Solute Transport in 3D Fracture Networks: Insights From Graph‐Based Reactive Transport Modeling

We investigate how mineral dissolution reshapes flow pathways and solute transport in three‐dimensional discrete fracture networks using a computationally efficient graph‐based reactive transport model. The DFNs are inspired by field‐site observations of fractured carbonate and represent realistic connectivity and structural heterogeneity. Flow is simulated with the Reynolds equation, and dissolution follows first‐order kinetics with diffusive limitations captured through an effective mass‐transfer coefficient. By systematically varying two key dimensionless parameters, the effective Damköhler number (Da), governing reaction versus advection rates, and a transport parameter (Da), analogous to the Thiele modulus, distinct flow channelization regimes emerge: mildly channelized at low G, highly channelized at intermediate Da, and extreme wormhole formation at high Da and low G. Eulerian and Lagrangian analyses, including breakthrough curves, particle tortuosity, dispersivity, and flow channeling indicators quantitatively characterize the progression of dissolution‐driven network restructuring. Across all regimes, initial fracture heterogeneity persists. The results underscore how the interplay between this initial structure, advection, reaction, and diffusion critically shapes subsurface flow pathways, with implications for applications ranging from groundwater remediation to enhanced geothermal systems.

54 ENVIRONMENTAL SCIENCES

Physiological Response of Plants Grown on Porous Ceramic Tubes

This research involves the manipulation of the root-zone water potential for the purposes of discriminating the rate limiting step in the inorganic nutrient uptake mechanism utilized by higher plants. This reaction sequence includes the pathways controlled by the root-zone conditions such as water tension and gradient concentrations. Furthermore, plant based control mechanisms dictated by various protein productions are differentiated as well. For the nutrients limited by the environmental availability, the kinetics were modeled using convection and diffusion equations. Alternatively, for the nutrients dependent upon enzyme manipulations, the uptakes are modeled using Michaelis-Menten kinetics. In order to differentiate between these various mechanistic steps, an experimental apparatus known as the Porous Ceramic Tube - Nutrient Delivery System (PCT-NDS) was used. Manipulation of the applied suction pressure circulating a nutrient solution through this system imposes a change in the matric component of the water potential. This compensates for the different osmotic components of water potential dictated by nutrient concentration. By maintaining this control over the root-zone conditions, the rate limiting steps in the uptake of the essential nutrients into tomato plants (Lycopersicon esculentum cv. Cherry Elite) were differentiated. Results showed that the uptake of some nutrients were mass transfer limited while others were limited by the enzyme kinetics. Each of these were adequately modeled with calculations and discussions of the parameter estimations provided.

Tsao, David