Scale-up Analysis of Continuous Cross-flow Atomic Layer Deposition Reactor Designs

This paper presents the development of a non-dimensional model of a continuous cross-flow atomic layer deposition (ALD) reactor with temporally separated precursor pulsing and a structured model-based methodology for scaling up the substrate dimensions. The model incorporates an ALD gas–surface reaction kinetic mechanism for the deposition of thin ZnO films from Zn(C2H5)2 and H2O precursors that was experimentally validated in our previous work (Holmqvist et al., 2012, 2013a). In order to maintain dynamic similarity, a scaling analysis was applied based on the dimensionless numbers, appearing in non-dimensionalized momentum and species mass conservation equations, that describe the convective laminar flow, mass transfer and heterogeneous reaction. The impact on these dimensionless numbers and, more importantly, the impact on the limit-cycle deposition rate and its relative uniformity was thoroughly investigated when linearly scaling up the substrate dimensions. In the scale-up procedure, the limit-cycle precursor utilization was maximized by means of dynamic optimization, while ensuring that identical deposition profiles were obtained in the scaled-up system. The results presented here demonstrated that the maximum precursor yields were promoted at higher substrate dimensions. Limit-cycle dynamic solutions to the non-dimensionalized model, computed with a collocation discretization in time, revealed that it is a combination of the degree of precursor depletion in the flow direction and the magnitude of the pressure drop across the reactor chamber that governs the extent of the deposition profile non-uniformity. A key finding of this study is the identification of optimal scaling rules for maximizing precursor utilization in the scaled-up system while maintaining fixed absolute growth rate and its relative uniformity

Dynamic parameter estimation of atomic layer deposition kinetics applied to in situ quartz crystal microbalance diagnostics

This paper presents the elaboration of an experimentally validated model of a continuous cross-flow atomic layer deposition (ALD) reactor with temporally separated precursor pulsing encoded in the Modelica language. For the experimental validation of the model, in situ quartz crystal microbalance (QCM) diagnostics was used to yield submonolayer resolution of mass deposition resulting from thin film growth of ZnO from Zn(C2H5)2 and H2O precursors. The ZnO ALD reaction intrinsic kinetic mechanism that was developed accounted for the temporal evolution of the equilibrium fractional surface concentrations of precursor adducts and their transition states for each half-reaction. This mechanism was incorporated into a rigorous model of reactor transport, which comprises isothermal compressible equations for the conservation of mass, momentum and gas-phase species. The physically based model in this way relates the local partial pressures of precursors to the dynamic composition of the growth surface, and ultimately governs the accumulated mass trajectory at the QCM sensor. Quantitative rate information can then be extracted by means of dynamic parameter estimation. The continuous operation of the reactor is described by limit-cycle dynamic solutions and numerically computed using Radau collocation schemes and solved using CasADi's interface to IPOPT. Model predictions of the transient mass gain per unit area of exposed surface QCM sensor, resolved at a single pulse sequence, were in good agreement with experimental data under a wide range of operating conditions. An important property of the limit-cycle solution procedure is that it enables the systematic approach to analyze the dynamic nature of the growth surface composition as a function of process operating parameters. Especially, the dependency of the film growth rate per limit-cycle on the half-cycle precursor exposure dose and the process temperature was thoroughly assessed and the difference between ALD in saturating and in non-saturating film growth conditions distinguished

On the modelling of drop behaviour in siphon riser tubes in paper drying cylinders

A theoretical model has been developed for the drop behaviour in siphon riser tubes in paper drying cylinders. Analytical solutions to the equations are presented for the systems air-water at atmospheric pressure and saturated steam-water. Numerical simulations are performed for a large number of input data. Calculated drop trajectories indicate that the drops travel only a small part of the riser tube length before they are deflected to the frontside of the riser tube. For the system air-water the drop radial velocity when hitting the tube does not exceed 50% of the gas velocity, while with the system steam-water the radial velocity can be up to 90% of the gas velocity. The azimuthal drop velocities are in the range 2-10 m/s. The condensate slip relative to the cylinder results in an initial backward motion of the drops before they are accelerated to the frontside. Thus, part of the drops will hit the backside wall resulting, in the formation of a liquid film. This film will also be subjected to the coriolis force resulting in a liquid redistribution to the frontside wall. A criterion for cylinder flooding to occur, based on the fundamental differential equations, is presented. Good agreement with experimental data is presented for the system air-water in a 1.5 m model cylinder

Product engineering by the paper dryer

The design of product properties is the main task for all process industries. The quality parameters, transport phenomena and mechanical parameters are closely coupled and all these phenomena must thus be taken into account at the same time to understand the development of product properties. In this work the importance of transport phenomena for paper quality parameters in the paper dryer will be discussed. This includes topics such as the distribution of water, different structure models, shrinkage, temperature, moisture and pressure gradients

Drying of paper : A review 2000–2018

Drying of paper during 2000–2018 is reviewed. The review includes new drying processes, multi-cylinder dryers, tissue and impingement drying, TAD-drying, infrared drying and energy use for drying of paper. It includes general aspects of infrared dryers but not drying of coated papers. Paper quality aspects, paper shrinkage and paper isotherms are not included. Impingement drying has been the most successful new technology with several applications while others such as impulse drying has not been commercialized mainly due to problems with paper quality parameters. One promising development is the introduction of steel instead of cast iron cylinders with increased heat transfer reducing the number of cylinders. Future research should focus on modeling the internal transport phenomena and to couple these phenomena to paper shrinkage and quality parameters. The influence of the fabric for the drying process needs more attention, understanding the drying process for new components such as microfibrillar cellulose in the stock and reducing energy use and increasing the amount of renewable energies for drying of paper

Extraction of cadmium from phosphoric acid solutions with amines. Part III. A thermodynamic extraction model

A thermodynamic model for cadmium extraction from phosphoric-hydrochloric acid mixtures has been developed. The model enables calculations of cadmium extraction as well as coextraction of phosphoric and hydrochloric acids to be made. In the aqueous phase Bromley's model for the activity coefficients is adopted. In the organic phase simple expressions for the non-ideal behaviour of phosphoric acid are used. The model is capable of calculating cadmium extraction from 0.02 M up to 6.7 M H3PO4 and chloride concentrations between 0.005 and 0.10 M HCl. For high amine concentrations the prediction for cadmium extraction is too high, indicating that high concentrations of phosphoric acid in the organic phase affect the activity coefficient for the extracted cadmium complex significantly. The thermodynamic constant for the extraction equilibrium has been determined as log K11 = 10.23