The work presented in this dissertation is an investigation of-the ferric leaching of zinc from sphalerite. A further aspect of this study was an investigation of the influence of pyrite on the dissolution rate of sphalerite due to possible galvanic interactions. This study is one component of a larger study of the sub-processes involved in the bioleaching of sulphide minerals in which the ferric leaching of the sulphide mineral is assumed to be a chemical step with the bacteria oxidising ferrous iron to ferric iron and elemental sulphur, if formed, to sulphate. The literature showed that two types of model have been used to describe the ferric leaching of the sphalerite. The first type was a shrinking-particle model in which the reaction was described by first order kinetics or an electrochemical mechanism. The second type included a mass transfer resistance in terms of a shrinking-core model described by half-order kinetics or a decaying diffusion coefficient. All four of these models were tested for their ability to predict published data for the ferric leaching of sphalerite. It was found that the models fitted the data for the initial period of a leach up to conversions of about 50%. However, no one of the models was found to be successful in predicting the data for prolonged leaching to high conversions. Because of this, a new model was developed based on the assumption of deactivation of the sphalerite surface due to precipitating products. This surface area de~ctivation model for the rate of conversion has the form: where the kcR(1-xr2'3 term is based on the shrinking-particle mechanism and the surface area deactivation term is exp (k1 t). When tested against ferric leach data from the literature it was found to be satisfactory for both the initial leach period and high conversion data at prolonged leach times. In the experimental study the following factors were investigated: the effect of temperature between 30 °C and 55 °C; the size of the mineral particles in the range 106+90 μm to -45+38 μm; initial ferric iron concentration between 0.06 M to 0.5 M. Tests were run under conditions where the redox potential was controlled at fixed values ranging from 673 mVto 443 mV (vs Ag/AgCI) by the addition of 3% H202. In other tests the redox potential was not controlled but dropped during the course of the leach as the ferric iron was consumed. The Surface Area Deactivation Model was found to be a satisfactory fit for all of the leach data obtained in this study. Using Arrhenius plots, the temperature dependence of the chemical reaction rate constant was calculated to be 47 kJ.mor1 and the activation energy calculated from the surface area deactivation rate constant was 43 kJ.mor1 . In both cases, these values are in the range where the chemical reaction at the mineral surface is thought to control. The surface area specific conversion rate decreased at the same rate for each particle size. This suggests a constant chemical rate per unit surface area and a constant specific rate of surface deactivation, in both cases independent of particle size. Examination of the leach residue by scanning electron micrography showed that at long leach times there was a layer of elemental sulphur attached to the surface of the sphalerite leading to its deactivation. From the data obtained under controlled redox potential conditions, it was found that the reaction rate constants were a linear function of the redox potential. However, the gradient of the relationship changed at a redox potential of approximately 520 mV (vs Ag/AgCI). These results are consistent with the work of Crundwell (1988b) where the chemical reaction was shown to be dependent on the solution equilibrium of the iron species and the ionic species responsible for transfer of charge. From the data where the redox potential was not controlled, the reaction was limited by the amount of ferric iron available for the dissolution reaction. The effect on the leach kinetics of possible galvanic interactions between pyrite and sphaleri~e were tested in two ways: the addition of pyrite concentrate to the sphalerite concentrate, and leaching of hand-picked samples of ore containing particles of combined unliberated pyrite and sphalerite in direct contact. Where the pyrite concentrate was added to the sphalerite concentrate, no increase in the rate of zinc leaching was measured for pyrite/sphalerite mass ratios of 0.01, 0.1 and 1.0. On the other hand, in the ferric leaching of the particles of combined unliberated pyrite-sphalerite, the rate of zinc leaching was found to be greater than for sphalerite on its own under the same conditions. This suggests that for galvanic interactions to improve the rate leaching, the minerals have to be in intimate contact.

The use of Synthol High Temperature Fischer-Tropsch (HTF-T) pro"ducts as an inexpensive and alternative hydroformylation feedstock for producing Oxo alcohols has been investigated. These alcohols are precursors for biodegradable detergents. The HTF-T product targeted as a feedstock source was Synthol Light Oil (SLO}, in the Ca to C12 range. The aim of the work was to identify a suitable hydroformylation catalyst system for use with SLO feeds. Process variables such as feed composition, temperature, pressure and contact time were investigated. Emphasis was placed on the determination of feed-catalyst compatibility; the development of a "working" kinetic model on a batch micro-reactor scale; and extrapolation of the results to a continuous catalyst testing unit. An integral part of the work therefore involved characterization and quantification of these complex hydroformylation systems, as well as the development of methods to achieve this goal. Hydroformylation of various SLO fractions in the Ca to C12 range was undertaken. As a yardstick, the results were compared with those generated using pure 1-decene feed. The results obtained with pure feeds were duplicated, and in some cases improved upon when using SLO. The Ca_9 , C9 , C10 and C11 _12 single and double carbon number SLO fractions tested were prepared by distillation. This, apart from caustic washing to remove carboxylic acids, was demonstrated as the only step required to produce suitable hydroformylation feeds. Minimal cleanup of the feed was facilitated by the apparent "inertness" of non-olefinic components in SLO. These consist of various aromatics, oxygenates and paraffins. The olefins in SLO consist mainly of linear a-olefins, mono-methyl a-olefins and smaller quantities of internal olefins. Different olefin isomer distributions could be obtained by refractionation of the SLO. Feed, as well as resultant product compositions, could therefore be tailored according to the distillation procedures employed. Phosphine modified hydrocarbonyl rhodium and cobalt hydroformylation catalysts were screened. These experiments were undertaken with a view to maximizing product linearity and establishing feed - catalyst compatibility. In this regard, TriPhenylPhospine (TPP) ligand was tested with Rh and Tri-nButylPhosphine (TBP) as well as TPP ligands were tested with Co. Various so called heterogeneous catalysts based on Co were unsuccessfully evaluated. The RhffPP and CoffBP experiments were successful, but the Rh catalysts appeared more susceptible to poisoning. It was demonstrated that the unique character of the olefin composition and distribution in the HTF-T fractions could be exploited in n-alkylphosphine modified Co systems. These catalyst systems facilitate isomerization of a-olefins to internal olefins and interchange between internal and a-olefins occurs rapidly. Despite this however, the aldehydes and alcohols produced are predominantly linear because of the higher rate of hydroformylation of the a-olefins. It was shown that more internal olefins undergo hydroformylation in pure linear feeds compared with SLO feeds. This may be explained due to the methyl-branched internal olefins in SLO being thermodynamically favoured, but also being less reactive for hydroformylation compared with linear internal olefins. Because of the screening results, and the perceived difficulties in efficient recycling of Rh catalysts, further work concentrated on phosphine modified Co catalysts for the hydroformylation of SLO. This involved constant pressure "batch" experiments, and development of a system for quantifying olefins in the complex feeds. Emphasis was placed on testing and comparing results obtained with a "conventional" n'"alkylphosphine ligand and a bi-cyclic alkylphosphine ligand. The specific ligands under consideration were Tri-n-OctylPhosphine (TOP) and 9-Eicosyl-9-Phosphabicyclonane (EP). The following "standard" reaction conditions were selected based on the screening experiment results, and using reports in the literature as a guideline: Reaction temperature = 170°C; Pressure = 75 bar (g) constant; Syngas composition= 2:1 pure H2:CO; Molar ratio of phosphine: Co= 2:1; Stirrer speed · · = SOOrpm. The kinetics of olefin consumption for both pure linear and HTF-T product feed olefins of a single carbon number were shown to be approximately first order with respect to the olefin concentration. The rate was directly proportional to the . cobalt concentration. This first order relationship was relatively independent of the (methyl branched) : (linear) olefin ratio in the F-T feed. It was however demonstrated that longer olefins (for example C12 ) reacted more slowly than shorter olefins (for example C11 ). A kinetic expression describing the effect of carbon number and catalyst concentration on the rate of olefin consumption was derived for the Co/EP catalyst system. This expression was expanded to include the effect of temperature as well as syngas composition and pressure. Similar results were obtained with pure 2:1 H2:CO syngas, commercial syngas from an existing F-T facility, as well as syngas that had a 14% C02 content. On varying the H2:CO ratio in the syngas from 2:1 to 1 :2 and the total pressure from 45 to 90 bar (g), it was evident that reactions undertaken at 75 bar(g) with a H2:CO ratio of 2:1 were suitable for achieving high reaction rates coupled with satisfactory product linearity and catalyst stability. The catalyst systems were shown to be sensitive to temperature. Temperatures of around 185°C and higher resulted in Co/EP catalyst deactivation with concomitant precipitation of cobalt. This was ascribed to disintegration of the catalyst complex. The selected "standard" operating conditions therefore appeared to be in the correct regime. Based on the results in this study, coupled to the reported results of other workers, a theory on the effect of temperature in Co hydroformylation systems was proposed. The onset of catalyst deactivation was linked to the reaction rate and temperature and this was quantified. The hydroformylation activation energy (Ea) was calculated as being 99 kJ per mole for C10 , C,, and C,2 olefins in SLO with the Co/EP catalyst. This value is similar to values reported by other workers, who used different feeds and catalysts. The high value of Ea indicates that the system was free of diffusion constraints. The effect of an alkali modifier - namely potassium hydroxide (KOH) - was investigated for pure and HTF-T feeds. Contrary to reports in the literature, KOH did not appear to catalyse aldol condensation reactions with resultant heavy oxygenate formation at "standard" reaction conditions. Instead, the predominant heavier oxygenates were esters. These in turn were mostly formates formed as a result of CO incorporation into adsorbed alde~yde intermediates. The effect of KOH on Co/EP systems was more marked compared with Co/TOP. For the Co/EP systems, the KOH resulted in slower rates of reaction and appeared to have a similar effect to that of increasing the EP:Co ratio.

The high efficiency of separation of fine (typically the -150 ~m fraction) particles achievable with column flotation technology is well established. The principal aim of this thesis is to investigate whether column flotation can be used to recover saleable, particularly low-ash quality, coal from South African coal fines which are presently discarded. Samples of thickener underflow fines from the Durnacol, Kleinkopje and Greenside Collieries were used in laboratory column testwork. In addition, on-line column trials were performed at the Kleinkopje Colliery. The effects of co 1 umn operating parameters were established using both one-variable-at-a-time testing and fractional factorial design experiments. An investigation into coal slurry conditioning using oil and oil-water dispersions was also undertaken. The results of laboratory and plant column testwork showed that it was possible to recover the desired quality products from all three of the coal fines samples investigated. For all the coals tested, better grades were obtained at any given yield from column cell flotation than with conventional (batch) froth flotation. The test results also demonstrated that the column cell is best suited to recovering and upgrading the finer (< 75 ~m) size fractions. Column performance was found to be strongly affected by the petrographic composition of the coal fines feed, i.e. by coal TYPE. Coals with high vitrinite and, conversely, low inertinite contents were found to be the most easily floatable. Depending on the coal TYPE, the rate of mass transport in either the pulp or froth phase was found to be rate limiting; this in turn dictated which operating parameters affected product yields and grades. Existing methods of conditioning coal slurries were found to be inadequate. Considerable scope for improvement in coal conditioning lies in better choice of collector and "promotor" reagents as well as in designing more energetically efficient conditioning vessels.

The Air-Sparged Hydrocyclone (ASH) is a high capacity flotation device which is alleged to be more efficient for the flotation of fine particles than conventional flotation equipment. The principal aims of this thesis were to investigate the use of an ASH in the flotation of South African coal ultrafines ( -150 micron), and to determine the effect of various design and operating parameters on the performance of the process, in terms of the product yields and grades obtainable. The testwork was carried out on a typical Witbank coal, from the Kleinkopje Colliery, with an ash content of 23.7 %. The coal was characterised by means of size, ash-by-size and float-and-sink analyses. Batch flotation experiments were carried out to provide a benchmark against which the ASH could be compared. Preliminary ASH work was carried out to determine the required collector and frother dosages and the optimal slurry feed rate. A fractional factorial design, at two levels, was carried out to investigate the effects of the underflow configuration (the use of an orifice and a baffle instead of the conventional pedestal/annular opening), the ratio of the overflow to underflow openings (A*), the ASH length to diameter ratio (Lc/dc), the ratio of the air to slurry feed rates (Q*), the ratio of the vortex-finder length to the cyclone diameter (Lvtfdc) and the size of the slurry inlet (Ainlet)· The effect of pulp density was investigated separately. The results of the testwork showed that the ASH beneficiated the coal successfully at capacities of up to 300 times those possible in conventional (batch) flotation, and in the -region of 1500 times those achieved using the same coal in a column cell. The overall results, in terms of concentrate ash contents at particular yi e ids, showed that the ASH results were comparable with those of the batch cell, but not as good as those of the column cell. The nature of the material being floated resulted in collector dosages in the region of 36 kg/ton being used in the factorial design to achieve concentrate yields in the region of 50 %. However, use of the optimal ASH configuration reduced this required collector dosage to about 25 kg/ton, without loss in performance. A typical (good) ASH result achieved was a yield of 47.7% at a concentrate ash content of 8.8 %. Size analyses indicated that the ASH product is recovered by both flotation and classification with the result that, for the small diameter ASH and Kleinkopje coal sample used, the ASH could not be considered to be a more efficient device for the flotation of fine particles, but rather a less efficient device for the recovery of coarse particles. However, the ASH performance in the ultrafine size fractions (-150 micron) was comparable with that of the batch cell~ The underflow configuration, A* and Lcfdc all had a significant effect on the performance of the ASH. Q* had a minor effect, Lvfldc may have had an effect and Ainlet had no effect on the performance of the ASH. In addition, increasing the pulp density from 1.6 to 9.4% (mass/volume) had no effect on the performance of the ASH. It is recommended that future research include the investigation of preconditioning for the flotation of poorly floatable (inertinite rich) South African coals, the use of an ASH on more floatable coals, the determination of the limit to which the pulp density can be increased (without loss in flotation performance) and the determination of scale-up criteria for the ASH.

Two series of batch and fed-batch fermentations were carried out using S.cerevisiae in a semi-defined medium containing 200 gl-1 glucose as limiting substrate. Growth rates were calculated and the data used to test the applicability of eight empirical kinetic models. The form proposed by Levenspiel, combining the concept of a limiting ethanol concent~ation with a power-law form, gave the best results with these data. Glucose concentration was found to have a far smaller, though not negligible, effect on growth rate under these conditions. It was also observed that in fed-batch fermentations the total substrate uptake rate of the broth became constant soon after commencement of feeding, without cessation of growth. It is suggested that ethanol inhibits the synthesis of a rate-controlling enzyme in the glycolyti·c chain, but no previous work could be found to support or refute this explanation. A quasi-mechanistic model of growth under the condition of constant substrate consumption rate is formulated and discussed.

The objective of this study was to investigate the anaerobic biological treatment of an organic-bearing wastewater from a particular paper manufacturing process at laboratory scale. The process produces paper by re-pulping waste paper. Effluent from the process has a Chemical Oxygen Demand CCOD> concentration of approximately 4500 mg/l with a sulphate content of approximately 300 mg SQ4 2 -/l. The upflow anaerobic sludge bed CUASB> reactor was selected for the study. Important information derived from the laboratory treatability study was: Cl> the extent of COD removal possible! (2) the effluent quality! <3> the maximum COD leading rate CkgCOD/m3 reactor/day) which can be achieved while maintaining reasonable COD removal. and the influence on loading rate of temperature: (4) the nature of the sludge produced in the reactor with particular reference to the extent of pelletisation: and (5) the effect of reactor effluent recycling on alkalinity requirements. The following specific conclusions may be itemised from the results obtained: Wastewater characteristics and chemical addition: (1) The waste is amenable to anaerobic treatment in a UASB system. <2> The unbiodegradable COD content of the waste is in the region of 10 to 15 percent, and COD removals of approximately 85 percent are possible on a continuous basis. <3> The short chain volatile fatty acids acetic and propionic comprise approximately 45'percent of the COD in the influent. The remainder is made up principally of starch, carbohydrates and more complex organics. (4) The wastewater is deficient in the elements nitrogen and phosphorus. These elements must be supplemented through chemical addition in order to achieve complete anaerobic treatment. (5) The wastewater is acidic, with a pH in the range 5 to 6 generally. Alkalinity must be added to the waste prior to treatment to adjust the pH to approximately neutral. Organic loading rates: (6) Organic loading rates of approximately 25 kgCOD/m3 reactor/day were attained at both 25 and 35°C. This corresponded to a hydraulic retention time of 5 hours at an influent COO concentration of 4500 mg/1. The loading rate was not constrained by limitations in the biological treatment capacity. Rather, difficulties associated with the settleability of the sludge were encountered: blockages of the under-designed laboratory reactor settler occurred. Sludge characteristics: (7) A dense bed of biological sludge extended from the base to approximately half the height of the UASB reactors. This sludge had a granular, well-flocculated form with the floes appearing to be in the size range 1-2 mm. Very fine sludge was also present within the bed. A small number of true sludge pellets <4-5 mm) were present within the dense sludge bed1 particularly near the base. <B> The settleability of the dense granular sludge appeared reasonable, and the bed was not disturbed unduly by gas production. However.the settleability of the sludge was inferior to that of a wellpelletised sludge. (9) The absence of true sludge pellet formation appears to relate to the absence of a high hydrogen partial pressure zone in the lower region of the UASB ·reactor. With this particular wastewater two factors appear to reduce the possibility of creating a high partial pressure of hydrogen near the inlet, thus reducing the possibility of pellet formation. These are Cl> the nature of the feed, and <2> the role of sulphate reduction. Nature of feed: Approximately 45 percent of the influent COD is in the form of acetic and propionic acid. Therefore, the amount of remaining substrate available for acidogenesis1 with its associated

In South Africa, ever increasing quantities of fine (-0,5 mm) coal are being produced as a result of the increased use of mechanised mining methods. Very few mines beneficiate the fines; in most cases they are discarded. However the fine size of this material suggests that it should be well liberated, with the potential to produce a low ash product. This thesis forms part of an ongoing research program examining the use of flotation to beneficiate coal fines to produce a low ash product. Coal is a highly heterogeneous material, consisting of a number of both organic (maceral) and inorganic (mineral) components with different physical and technological properties. Therefore in order to evaluate and interpret flotation results, an understanding of the 1iberation characterist ics of both the organic and inoganic components is required. This thesis presents a 1iberation study on fine coal from the Greenside Colliery, a typical colliery in the Witbank Coalfield which is the most important source of South African low ash coal. The study was performed by mi 11 ing a run of mine coal sample to varying degrees of fineness (from 30 % finer than 150 micron to 90 % finer than 150 micron), screening, and assessing the liberation of each size fraction. These results were compared to those obtained from a sample of naturally arising fines (thickener underflow). Liberation was assessed by float and sink analysis, and for this purpose a new technique was developed that enables rapid and accurate float and sink analysis of coal down to a few micron in size. Petrographic analyses were performed to determine the 1iberation of the organic coal components.

The computer analysis of structures and solids using finite element methods has now taken on very significant proportions [1-4J. In many cases the safety of a structure may be significantly increased and its cost reduced if an appropriate finite element analysis can be and is performed. In the development and use of finite element methods, we recognize that, considering static linear analysis, already towards the end of the nineteen sixties the methods were highly developed -- thus it had taken only about one decade from the inception to the extensive practical use of finite element methods. Although difficulties were still encountered in the linear static analysis of some structures, e.g. complex shells, most of the structures could already be analysed in a routine manner. This situation in engineering analysis was, however, quite different when dynamic or nonlinear conditions had to be considered. Whereas the finite element methods could be developed relatively quickly for linear static analysis, methods for practical dynamic and nonlinear analyses are much more difficult to establish. Although much emphasis has been placed on research in nonlinear analysis, the progress in the development of valuable techniques has been quite slow [5-7J. The practical objectives in the development of finite element methods for dynamic and nonlinear analysis are, in essence, that we want to be able to analyze increasingly more complex structures which are subjected to loads that vary rapidly -- causing dynamic response -- and loads of high intensity -- causing the structure to respond beyond its linear range. In nonlinear conditions, geometric and/or material non1inearities may have to be taken into consideration. These analysis conditions are encountered already in many industries (e.g. design of nuclear power plants) and, with the current needs towards usage of new materials and more efficient structures, nonlinear analysis will undoubtedly be required to an increasing extent. Considering research in finite element analysis procedures, emphasis must be placed on the development of reZiabZe~ generaZ and cost-effective techniques. The reliability of the analysis techniques is of utmost concern in order that the analyst can employ the methods with confidence. The results of an analysis can only be interpreted with confidence if reliable methods have been employed. The generality and cost-effectiveness of the methods are important in order to produce analysis tools that, in a design office, are applicable to a relatively large number of problems. With the above aims in mind, the development of finite element procedures for dynamic and nonlinear analysis becomes a very formidable task. Not only is it necessary to propose -guided by knowledge and intuition -- improved analysis techniques and then to implement and test these methods, but it is of major importance and di ffi cul ty to "fully" veri fy and qualify these theories and their computer program implementations. Whereas the verification and qualification of a finite element method is usually quite straight-forward in linear static analysis, this process may represent the major task in the development of a method for nonlinear analysis. During the last decade I have endeavored to advance the state-of-the-art of general and reliable finite element analysis procedures for dynamic and nonlinear response calculations. The areas in which I have worked primarily are - the development of eigensolution methods for large eigenproblems that arise in dynamic and buckling analysis of structures; - the development of finite element procedures for nonlinear analysis with emphasis on - the formulation of finite elements and material models, - the methods of solution for the nonlinear equations. The finite element procedures proposed in this research have been implemented in computer programs that are now in very wide use [8-12]. In accordance with the above areas of my research activities, I am presenting in this document relevant papers in three different Parts. The contents of each Part are briefly described below. Part I Solution Methods for Large Generalized Eigenproblems The eigenproblems considered in this research are the one arising in dynamic analysis, -K I"',. = A,. -~1 I"',. and the one arising in linearized buckling analysis, -K I",'. = A,. K,. "'. ~ I, (1) (2) where ~, ~ and M are the linear stiffness, geometric stiffness and mass matrices of the finite element assemblage, and (Ai' 1i)' i=l, 2, 3 ... are the eigenpairs to be evaluated.

A knowledge of the strength of a material is an essential prerequisite to the successful design of a structure in that material. Consequently, in designing deep level mining excavations and large civil engineering structures, an understanding of the mechanics of rock fracture, particularly under compressive stress conditions, is of fundamental importance. This thesis contains details of an investigation into the applicability of Griffith's brittle fracture theory, modified to account for the effects of crack closure in compression, to the prediction of rock fracture behaviour. It is shown that this theory provides a reliable basis for the analysis of hard rock fracture under static stress conditions. The application of the Griffith's the~ry to the prediction of rock fracture initiation and propagation in a complex stre~s field is illustrated by means of a detailed analysis of the behaviour of the rock around a circular hole in a biaxial stTess field~ While this study is primarily concerned with rock fracture problems associated with deep level mining, it is believed that the general principles are ~qually useful in the analy~is of rock and concrete fracture problems encountered in civil engineering.

A critical review of the mechanisma, models arui heat-tr~~sfer correlations for nucleate boiling is presented,. The importance of nucleation is stressed.. It is pointed. out that the bulk of correlations are based on the erroneous notion that the energy transferred away from the heating surface by bubbles as such, in the form of latent heat, contribute$ insignificantly to the total flux. - A critical review of the correlations for the upper limit of the nucleate boiling regime - the peak flux is also presentede The theory of nucleation during boiling is reviewed and extended in an attempt to explain the complete absence of the nucleate regime, noted in preliminary testa conducted at low pressures. The following equation charaoteriz,ing nucleation is derived rc = <J(Tw + Ts) vV A.v(Tw - T s) J where r is the mouth radius of the smallest cavit,y for vmich nucleation can pro&eeil. under the conditions reflected in the right-hand. terms of the equation; T is the {absolute) wall temperature'; T is the (absolute.) saturltion temperature corresponding to the s§stem presaure; 0'" is the surface tension; A.v is the latent heat of vaporization; vV is the specific volume of the vapour; (all physical properties evaluated. at (Tw + Ts)/2.) j and J is the mechanical equivalent of heat. ol The nucleation mechanism embod.i.e.s in this equation is the one according to which the nucleation superheat for ap!.t'ticular surfta.c.e caYity is determined by the equilibrium (expressed by the Gibbs equation) of a vapour cap formed. over a cav:1-ty mouth, with the bubble radius of curvature. equal to the cavity mouth radius. Experimental data are reported for benzene and ethanol boiling from the same surfa{}e; at various pressures. At atmospheric ancl moderate subatmospheric pressures the usual stable boiling curves are obtained. In an intermediate region a hitherto unreported, permanently unstable, nucleate boiling regime exists, which is characterized by erratic bubble behaviour and by boiling curves of unusunl. shape. At even lower pressures the nucleate regime is altogether absent, the heat-transfer changing from natural. convection straight to film boiling as the wall superheat is raised.. Application of the nucleation equation to the stable runs andl to the point of disappearance. of the last bubble on a stable boiling curv~- (flux decreasing) allows the prediction of the size range of surface cavities available for nucleation, A method is given to determine the point where this size range becomes zero, and. where the above mechanism ceases to operate. Comparison with the experimental data shows reillmzkab~y quamtitrntively that when th:i.s mechanism ceases to operate - a, situation that can occur in the middle of a. boiling curve - nucleate boiling changes from stable to unstable and the bubble behaviour becomes, erratic:. Thus a. method of predicting the threshold of unstable nucleation which becomes operative before complete cessation of nuc~eation occurs, is presented. Photomicrographs of the heating surfac_·e employed. are shown, which illustrate the existence of cavities of such sizes as are required by the theory.