Gas distribution in shallow packed beds

Packed beds have many industrial applications and are increasingly used in the process industries due to their low pressure drop. With the introduction of more efficient packings, novel packing materials (i.e. adsorbents) and new applications (i.e. flue gas desulphurisation); the aspect ratio (height to diameter) of such beds is decreasing. Obtaining uniform gas distribution in such beds is of crucial importance in minimising operating costs and optimising plant performance. Since to some extent a packed bed acts as its own distributor the importance of obtaining uniform gas distribution has increased as aspect ratios (bed height to diameter) decrease. There is no rigorous design method for distributors due to a limited understanding of the fluid flow phenomena and in particular of the effect of the bed base / free fluid interface. This study is based on a combined theoretical and modelling approach. The starting point is the Ergun Equation which is used to determine the pressure drop over a bed where the flow is uni-directional. This equation has been applied in a vectorial form so it can be applied to maldistributed and multi-directional flows and has been realised in the Computational Fluid Dynamics code PHOENICS. The use of this equation and its application has been verified by modelling experimental measurements of maldistributed gas flows, where there is no free fluid / bed base interface. A novel, two-dimensional experiment has been designed to investigate the fluid mechanics of maldistributed gas flows in shallow packed beds. The flow through the outlet of the duct below the bed can be controlled, permitting a rigorous investigation. The results from this apparatus provide useful insights into the fluid mechanics of flow in and around a shallow packed bed and show the critical effect of the bed base. The PHOENICS/vectorial Ergun Equation model has been adapted to model this situation. The model has been improved by the inclusion of spatial voidage variations in the bed and the prescription of a novel bed base boundary condition. This boundary condition is based on the logarithmic law for velocities near walls without restricting the velocity at the bed base to zero and is applied within a turbulence model. The flow in a curved bed section, which is three-dimensional in nature, is examined experimentally. The effect of the walls and the changes in gas direction on the gas flow are shown to be particularly significant. As before, the relative amounts of gas flowing through the bed and duct outlet can be controlled. The model and improved understanding of the underlying physical phenomena form the basis for the development of new distributors and rigorous design methods for them.

A study on the flow characteristics of an industrial radiant tube burner

The thesis presents an experimentally validated modelling study of the flow of combustion air in an industrial radiant tube burner (RTB). The RTB is used typically in industrial heat treating furnaces. The work has been initiated because of the need for improvements in burner lifetime and performance which are related to the fluid mechanics of the com busting flow, and a fundamental understanding of this is therefore necessary. To achieve this, a detailed three-dimensional Computational Fluid Dynamics (CFD) model has been used, validated with experimental air flow, temperature and flue gas measurements. Initially, the work programme is presented and the theory behind RTB design and operation in addition to the theory behind swirling flows and methane combustion. NOx reduction techniques are discussed and numerical modelling of combusting flows is detailed in this section. The importance of turbulence, radiation and combustion modelling is highlighted, as well as the numerical schemes that incorporate discretization, finite volume theory and convergence. The study first focuses on the combustion air flow and its delivery to the combustion zone. An isothermal computational model was developed to allow the examination of the flow characteristics as it enters the burner and progresses through the various sections prior to the discharge face in the combustion area. Important features identified include the air recuperator swirler coil, the step ring, the primary/secondary air splitting flame tube and the fuel nozzle. It was revealed that the effectiveness of the air recuperator swirler is significantly compromised by the need for a generous assembly tolerance. Also, there is a substantial circumferential flow maldistribution introduced by the swirier, but that this is effectively removed by the positioning of a ring constriction in the downstream passage. Computations using the k-ε turbulence model show good agreement with experimentally measured velocity profiles in the combustion zone and proved the use of the modelling strategy prior to the combustion study. Reasonable mesh independence was obtained with 200,000 nodes. Agreement was poorer with the RNG  k-ε and Reynolds Stress models. The study continues to address the combustion process itself and the heat transfer process internal to the RTB. A series of combustion and radiation model configurations were developed and the optimum combination of the Eddy Dissipation (ED) combustion model and the Discrete Transfer (DT) radiation model was used successfully to validate a burner experimental test. The previously cold flow validated k-ε turbulence model was used and reasonable mesh independence was obtained with 300,000 nodes. The combination showed good agreement with temperature measurements in the inner and outer walls of the burner, as well as with flue gas composition measured at the exhaust. The inner tube wall temperature predictions validated the experimental measurements in the largest portion of the thermocouple locations, highlighting a small flame bias to one side, although the model slightly over predicts the temperatures towards the downstream end of the inner tube. NOx emissions were initially over predicted, however, the use of a combustion flame temperature limiting subroutine allowed convergence to the experimental value of 451 ppmv. With the validated model, the effectiveness of certain RTB features identified previously is analysed, and an analysis of the energy transfers throughout the burner is presented, to identify the dominant mechanisms in each region. The optimum turbulence-combustion-radiation model selection was then the baseline for further model development. One of these models, an eccentrically positioned flame tube model highlights the failure mode of the RTB during long term operation. Other models were developed to address NOx reduction and improvement of the flame profile in the burner combustion zone. These included a modified fuel nozzle design, with 12 circular section fuel ports, which demonstrates a longer and more symmetric flame, although with limited success in NOx reduction. In addition, a zero bypass swirler coil model was developed that highlights the effect of the stronger swirling combustion flow. A reduced diameter and a 20 mm forward displaced flame tube model shows limited success in NOx reduction; although the latter demonstrated improvements in the discharge face heat distribution and improvements in the flame symmetry. Finally, Flue Gas Recirculation (FGR) modelling attempts indicate the difficulty of the application of this NOx reduction technique in the Wellman RTB. Recommendations for further work are made that include design mitigations for the fuel nozzle and further burner modelling is suggested to improve computational validation. The introduction of fuel staging is proposed, as well as a modification in the inner tube to enhance the effect of FGR.

CFD-modeling and Experiments of insulation debris transport phenomena in water flow

The investigation of insulation debris generation, transport and sedimentation becomes important with regard to reactor safety research for PWR and BWR, when considering the long-term behavior of emergency core cooling systems during all types of loss of coolant accidents (LOCA). The insulation debris released near the break during a LOCA incident consists of a mixture of disparate particle population that varies with size, shape, consistency and other properties. Some fractions of the released insulation debris can be transported into the reactor sump, where it may perturb/impinge on the emergency core cooling systems. Open questions of generic interest are the sedimentation of the insulation debris in a water pool, its possible re-suspension and transport in the sump water flow and the particle load on strainers and corresponding pressure drop. A joint research project on such questions is being performed in cooperation between the University of Applied Sciences Zittau/Görlitz and the Forschungszentrum Dresden-Rossendorf. The project deals with the experimental investigation of particle transport phenomena in coolant flow and the development of CFD models for its description. While the experiments are performed at the University at Zittau/Görlitz, the theoretical modeling efforts are concentrated at Forschungszentrum Dresden-Rossendorf. In the current paper the basic concepts for CFD modeling are described and feasibility studies including the conceptual design of the experiments are presented.

Flow processes in a radiant tube burner: isothermal flow

This paper presents the first part of a study of the combustion processes in an industrial radiant tube burner (RTB). The RTB is used typically in heat-treating furnaces. The work was initiated because of the need for improvements in burner lifetime and performance. The present paper is concerned with the flow of combustion air; a future paper will address the combusting flow. A detailed three-dimensional computational fluid dynamics model of the burner was developed, validated with experimental air flow velocity measurements using a split-film probe. Satisfactory agreement was achieved using the k-e turbulence model. Various features along the air inlet passage were subsequently analysed. The effectiveness of the air recuperator swirler was found to be significantly compromised by the need for a generous assembly tolerance. Also, a substantial circumferential flow maldistribution introduced by the swirler is effectively removed by the positioning of a constriction in the downstream passage.

Flow processes in a radiant tube burner:combusting flow

This paper describes a study of the combustion process in an industrial radiant tube burner (RTB), used in heat treating furnaces, as part of an attempt to improve burner performance. A detailed three-dimensional Computational Fluid Dynamics model has been used, validated with experimental test furnace temperature and flue gas composition measurements. Simulations using the Eddy Dissipation combustion model with peak temperature limitation and the Discrete Transfer radiation model showed good agreement with temperature measurements in the inner and outer walls of the burner, as well as with flue gas composition measured at the exhaust (including NO). Other combustion and radiation models were also tested but gave inferior results in various aspects. The effects of certain RTB design features are analysed, and an analysis of the heat transfer processes within the burner is presented.

The charge effect on the hindrance factors for diffusion and convection of a solute in pores II

The diffusion and convection of a solute suspended in a fluid across porous membranes are known to be reduced compared to those in a bulk solution, owing to the fluid mechanical interaction between the solute and the pore wall as well as steric restriction. If the solute and the pore wall are electrically charged, the electrostatic interaction between them could affect the hindrance to diffusion and convection. In this study, the transport of charged spherical solutes through charged circular cylindrical pores filled with an electrolyte solution containing small ions was studied numerically by using a fluid mechanical and electrostatic model. Based on a mean field theory, the electrostatic interaction energy between the solute and the pore wall was estimated from the Poisson-Boltzmann equation, and the charge effect on the solute transport was examined for the solute and pore wall of like charge. The results were compared with those obtained from the linearized form of the Poisson-Boltzmann equation, i.e.the Debye-Hückel equation. © 2012 The Japan Society of Fluid Mechanics and IOP Publishing Ltd.

Deflection of jets discharged into a reservoir with a free surface

Deflections of jets discharged into a reservoir with a free surface are investigated numerically. The jets are known to deflect towards either side of the free surface or the bottom, whose direction is not determined uniquely in some experimental conditions, i.e. there are multiple stable states realizable in the same condition. The origin of the multiple stable states is explored by utilizing homotopy transformations in which the top boundary of the reservoir is transformed from a rigid to a free boundary and also the location of the outlet throat is continuously moved from mid-height to the top. We depicted bifurcation diagrams of the flow compiling the data of numerical simulations, from which we identified the origin as an imperfect pitchfork bifurcation, and obtained an insight into the mechanism for the direction to be determined. The parameter region where such multiple stable states are possible is also delimited. © 2011 The Japan Society of Fluid Mechanics and IOP Publishing Ltd.

Charge effects on hindrance factors for diffusion and convection of solute in pores I

The transport of a spherical solute through a long circular cylindrical pore filled with an electrolyte solution is studied numerically, in the presence of constant surface charge on the solute and the pore wall. Fluid dynamic analyses were carried out to calculate the flow field around the solute in the pore to evaluate the drag coefficients exerted on the solute. Electrical potentials around the solute in the electrolyte solution were computed based on a mean-field theory to provide the interaction energy between the charged solute and the pore wall. Combining the results of the fluid dynamic and electrostatic analyses, we estimated the rate of the diffusive and convective transport of the solute across the pore. Although the present estimates of the drag coefficients on the solute suggest more than 10% difference from existing studies, depending on the radius ratio of the solute relative to the pore and the radial position of the solute center in the pore, this difference leads to a minor effect on the hindrance factors. It was found that even at rather large ion concentrations, the repulsive electrostatic interaction between the charged solute and the pore wall of like charge could significantly reduce the transport rate of the solute.

Effect of aspect ratio on thermal convection in open and closed systems

Internally heated fluids are found across the nuclear fuel cycle. In certain situations the motion of the fluid is driven by the decay heat (i.e. corium melt pools in severe accidents, the shutdown of liquid metal reactors, molten salt and the passive control of light water reactors) as well as normal operation (i.e. intermediate waste storage and generation IV reactor designs). This can in the long-term affect reactor vessel integrity or lead to localized hot spots and accumulation of solid wastes that may prompt local increases in activity. Two approaches to the modeling of internally heated convection are presented here. These are based on numerical analysis using codes developed in-house and simulations using widely available computational fluid dynamics solvers. Open and closed fluid layers at around the transition between conduction and convection of various aspect ratios are considered. We determine optimum domain aspect ratio (1:7:7 up to 1:24:24 for open systems and 5:5:1, 1:10:10 and 1:20:20 for closed systems), mesh resolutions and turbulence models required to accurately and efficiently capture the convection structures that evolve when perturbing the conductive state of the fluid layer. Note that the open and closed fluid layers we study here are bounded by a conducting surface over an insulating surface. Conclusions will be drawn on the influence of the periodic boundary conditions on the flow patterns observed. We have also examined the stability of the nonlinear solutions that we found with the aim of identifying the bifurcation sequence of these solutions en route to turbulence.

Modelling and simulation of biomass gasification in a circulating fluidized bed reactor

Computational Fluid Dynamics (CFD) has found great acceptance among the engineering community as a tool for research and design of processes that are practically difficult or expensive to study experimentally. One of these processes is the biomass gasification in a Circulating Fluidized Bed (CFB). Biomass gasification is the thermo-chemical conversion of biomass at a high temperature and a controlled oxygen amount into fuel gas, also sometime referred to as syngas. Circulating fluidized bed is a type of reactor in which it is possible to maintain a stable and continuous circulation of solids in a gas-solid system. The main objectives of this thesis are four folds: (i) Develop a three-dimensional predictive model of biomass gasification in a CFB riser using advanced Computational Fluid Dynamic (CFD) (ii) Experimentally validate the developed hydrodynamic model using conventional and advanced measuring techniques (iii) Study the complex hydrodynamics, heat transfer and reaction kinetics through modelling and simulation (iv) Study the CFB gasifier performance through parametric analysis and identify the optimum operating condition to maximize the product gas quality. Two different and complimentary experimental techniques were used to validate the hydrodynamic model, namely pressure measurement and particle tracking. The pressure measurement is a very common and widely used technique in fluidized bed studies, while, particle tracking using PEPT, which was originally developed for medical imaging, is a relatively new technique in the engineering field. It is relatively expensive and only available at few research centres around the world. This study started with a simple poly-dispersed single solid phase then moved to binary solid phases. The single solid phase was used for primary validations and eliminating unnecessary options and steps in building the hydrodynamic model. Then the outcomes from the primary validations were applied to the secondary validations of the binary mixture to avoid time consuming computations. Studies on binary solid mixture hydrodynamics is rarely reported in the literature. In this study the binary solid mixture was modelled and validated using experimental data from the both techniques mentioned above. Good agreement was achieved with the both techniques. According to the general gasification steps the developed model has been separated into three main gasification stages; drying, devolatilization and tar cracking, and partial combustion and gasification. The drying was modelled as a mass transfer from the solid phase to the gas phase. The devolatilization and tar cracking model consist of two steps; the devolatilization of the biomass which is used as a single reaction to generate the biomass gases from the volatile materials and tar cracking. The latter is also modelled as one reaction to generate gases with fixed mass fractions. The first reaction was classified as a heterogeneous reaction while the second reaction was classified as homogenous reaction. The partial combustion and gasification model consisted of carbon combustion reactions and carbon and gas phase reactions. The partial combustion considered was for C, CO, H2 and CH4. The carbon gasification reactions used in this study is the Boudouard reaction with CO2, the reaction with H2O and Methanation (Methane forming reaction) reaction to generate methane. The other gas phase reactions considered in this study are the water gas shift reaction, which is modelled as a reversible reaction and the methane steam reforming reaction. The developed gasification model was validated using different experimental data from the literature and for a wide range of operating conditions. Good agreement was observed, thus confirming the capability of the model in predicting biomass gasification in a CFB to a great accuracy. The developed model has been successfully used to carry out sensitivity and parametric analysis. The sensitivity analysis included: study of the effect of inclusion of various combustion reaction; and the effect of radiation in the gasification reaction. The developed model was also used to carry out parametric analysis by changing the following gasifier operating conditions: fuel/air ratio; biomass flow rates; sand (heat carrier) temperatures; sand flow rates; sand and biomass particle sizes; gasifying agent (pure air or pure steam); pyrolysis models used; steam/biomass ratio. Finally, based on these parametric and sensitivity analysis a final model was recommended for the simulation of biomass gasification in a CFB riser.

Modelling of wastewater treatment plants:how far shall we go with sophisticated modelling tools?

Several levels of complexity are available for modelling of wastewater treatment plants. Modelling local effects rely on computational fluid dynamics (CFD) approaches whereas activated sludge models (ASM) represent the global methodology. By applying both modelling approaches to pilot plant and full scale systems, this paper evaluates the value of each method and especially their potential combination. Model structure identification for ASM is discussed based on a full-scale closed loop oxidation ditch modelling. It is illustrated how and for what circumstances information obtained via CFD (computational fluid dynamics) analysis, residence time distribution (RTD) and other experimental means can be used. Furthermore, CFD analysis of the multiphase flow mechanisms is employed to obtain a correct description of the oxygenation capacity of the system studied, including an easy implementation of this information in the classical ASM modelling (e.g. oxygen transfer). The combination of CFD and activated sludge modelling of wastewater treatment processes is applied to three reactor configurations, a perfectly mixed reactor, a pilot scale activated sludge basin (ASB) and a real scale ASB. The application of the biological models to the CFD model is validated against experimentation for the pilot scale ASB and against a classical global ASM model response. A first step in the evaluation of the potential of the combined CFD-ASM model is performed using a full scale oxidation ditch system as testing scenario.

Influence of downstream processing on the breakage of whey protein precipitates

Whey proteins may be fractionated by isoelectric precipitation followed by centrifugal recovery of the precipitate phase. Transport and processing of protein precipitates may alter the precipitate particle properties, which may affect how they behave in subsequent processes. For example, the transport of precipitate solution through pumps, pipes and valves and into a centrifugal separator may cause changes in particle size and density, which may affect the performance of the separator. This work investigates the effect of fluid flow intensity, flow geometry and exposure time on the breakage of whey protein precipitates: Computational fluid dynamics (CFD) was used to quantify the flow intensity in different geometries. Flow geometry can have a critical impact on particle breakage. Sharp geometrical transitions induce large increases in turbulence that can result in substantial particle breakage. As protein precipitate particles break, they tend to form denser more compact structures. The reduction in particle size and increase in compaction is due to breakage. This makes the particles become more resistant to further breakage as particle compactness increases. The effect of flow intensity on particle breakage is coupled to exposure time, with greater exposure time producing more breakage. However, it is expected that the particles will attain an equilibrium particle size and density after prolonged exposure in a constant flow field where no further breakage will occur with exposure time. © 2005 Institution of Chemical Engineers.

Predicting the effect of mixing on oxygen transfer and nutrient removal in activated sludge basins

Activated sludge basins (ASBs) are a key-step in wastewater treatment processes that are used to eliminate biodegradable pollution from the water discharged to the natural environment. Bacteria found in the activated sludge consume and assimilate nutrients such as carbon, nitrogen and phosphorous under specific environmental conditions. However, applying the appropriate agitation and aeration regimes to supply the environmental conditions to promote the growth of the bacteria is not easy. The agitation and aeration regimes that are applied to activated sludge basins have a strong influence on the efficacy of wastewater treatment processes. The major aims of agitation by submersible mixers are to improve the contact between biomass and wastewater and the prevention of biomass settling. They induce a horizontal flow in the oxidation ditch, which can be quantified by the mean horizontal velocity. Mean values of 0.3-0.35 m s-1 are recommended as a design criteria to ensure best conditions for mixing and aeration (Da Silva, 1994). To give circulation velocities of this order of magnitude, the positioning and types of mixers are chosen from the plant constructors' experience and the suppliers' data for the impellers. Some case studies of existing plants have shown that measured velocities were not in the range that was specified in the plant design. This illustrates that there is still a need for design and diagnosis approach to improve process reliability by eliminating or reducing the number of short circuits, dead zones, zones of inefficient mixing and poor aeration. The objective of the aeration is to facilitate the quick degradation of pollutants by bacterial growth. To achieve these objectives a wastewater treatment plant must be adequately aerated; thus resulting in 60-80% of all energetic consummation being dedicated to the aeration alone (Juspin and Vasel, 2000). An earlier study (Gillot et al., 1997) has illustrated the influence that hydrodynamics have on the aeration performance as measure by the oxygen transfer coefficient. Therefore, optimising the agitation and aeration systems can enhance the oxygen transfer coefficient and consequently reduce the operating costs of the wastewater treatment plant. It is critically important to correctly estimate the mass transfer coefficient as any errors could result in the simulations of biological activity not being physically representative. Therefore, the transfer process was rigorously examined in several different types of process equipment to determine the impact that different hydrodynamic regimes and liquid-side film transfer coefficients have on the gas phase and the mass transfer of oxygen. To model the biological activity occurring in ASBs, several generic biochemical reaction models have been developed to characterise different biochemical reaction processes that are known as Activated Sludge Models, ASM (Henze et al., 2000). The ASM1 protocol was selected to characterise the impact of aeration on the bacteria consuming and assimilating ammonia and nitrate in the wastewater. However, one drawback of ASM protocols is that the hydrodynamics are assumed to be uniform by the use of perfectly mixed, plug flow reactors or as a number of perfectly mixed reactors in series. This makes it very difficult to identify the influence of mixing and aeration on oxygen mass transfer and biological activity. Therefore, to account for the impact of local gas-liquid mixing regime on the biochemical activity Computational Fluid Dynamics (CFD) was used by applying the individual ASM1 reaction equations as the source terms to a number of scalar equations. Thus, the application of ASM1 to CFD (FLUENT) enabled the investigation of the oxygen transfer efficiency and the carbon & nitrogen biological removal in pilot (7.5 cubic metres) and plant scale (6000 cubic metres) ASBs. Both studies have been used to validate the effect that the hydrodynamic regime has on oxygen mass transfer (the circulation velocity and mass transfer coefficient) and the effect that this had on the biological activity on pollutants such as ammonia and nitrate (Cartland Glover et al., 2005). The work presented here is one part to of an overall approach for improving the understanding of ASBs and the impact that they have in terms of the hydraulic and biological performance on the overall wastewater treatment process. References CARTLAND GLOVER G., PRINTEMPS C., ESSEMIANI K., MEINHOLD J., (2005) Modelling of wastewater treatment plants ? How far shall we go with sophisticated modelling tools? 3rd IWA Leading-Edge Conference & Exhibition on Water and Wastewater Treatment Technologies, 6-8 June 2005, Sapporo, Japan DA SILVA G. (1994). Eléments d'optimisation du transfert d'oxygène par fines bulles et agitateur séparé en chenal d'oxydation. PhD Thesis. CEMAGREF Antony ? France. GILLOT S., DERONZIER G., HEDUIT A. (1997). Oxygen transfer under process conditions in an oxidation ditch equipped with fine bubble diffusers and slow speed mixers. WEFTEC, Chicago, USA. HENZE M., GUJER W., MINO T., van LOOSDRECHT M., (2000). Activated Sludge Models ASM1, ASM2, ASM2D and ASM3, Scientific and Technical Report No. 9. IWA Publishing, London, UK. JUSPIN H., VASEL J.-L. (2000). Influence of hydrodynamics on oxygen transfer in the activated sludge process. IWA, Paris - France.

Vortex shedding from a row of square bars

Interactions of wakes in a flow past a row of square bars, which is placed across a uniform flow, are investigated by numerical simulations and experiments on the tassumption that the flow is two-dimensional and incompressible. At small Reynolds numbers the flow is steady and symmetric with respect not only to streamwise lines through the center of each square bar but also to streamwise centerlines between adjacent square bars. However, the steady symmetric flow becomes unstable at larger Reynolds numbers and make a transition to a steady asymmetric flow with respect to the centerlines between adjacent square bars in some cases or to an oscillatory flow in other cases. It is found that vortices are shed synchronously from adjacent square bars in the same phase or in anti-phase depending upon the distance between the bars when the flow is oscillatory. The origin of the transition to the steady asymmetric flow is identified as a pitchfork bifurcation, while the oscillatory flows with synchronous shedding of vortices are clarified to originate from a Hopf bifurcation. The critical Reynolds numbers of the transitions are evaluated numerically and the bifurcation diagram of the flow is obtained.

Effect of oscillatory flow on nucleation kinetics of butyl paraben

More than 165 induction times of butyl paraben-ethanol solution in a batch moving fluid oscillation baffled crystallizer with various amplitudes (1-9 mm) and frequencies (1.0-9.0 Hz) have been determined to study the effect of COBR operating conditions on nucleation. The induction time decreases with increasing amplitude and frequency at power density below about 500 W/m3; however, a further increase of the frequency and amplitude leads to an increase of the induction time. The interfacial energies and pre-exponential factors in both homogeneous and heterogeneous nucleation are determined by classical nucleation theory at oscillatory frequency 2.0 Hz and amplitudes of 3 or 5 mm both with and without net flow. To capture the shear rate conditions in oscillatory flow crystallizers, a large eddy simulation approach in a computational fluid dynamics framework is applied. Under ideal conditions the shear rate distribution shows spatial and temporal periodicity and radial symmetry. The spatial distributions of the shear rate indicate an increase of average and maximum values of the shear rate with increasing amplitude and frequency. In continuous operation, net flow enhances the shear rate at most time points, promoting nucleation. The mechanism of the shear rate influence on nucleation is discussed.