A multi-stage model for drop breakage in stirred vessels

Existing models for dmax predict that, in the limit of μd → ∞, dmax increases with 3/4 power of μd. Further, at low values of interfacial tension, dmax becomes independent of σ even at moderate values of μd. However, experiments contradict both the predictions show that dmax dependence on μd is much weaker, and that, even at very low values of σ,dmax does not become independent of it. A model is proposed to explain these results. The model assumes that a drop circulates in a stirred vessel along with the bulk fluid and repeatedly passes through a deformation zone followed by a relaxation zone. In the deformation zone, the turbulent inertial stress tends to deform the drop, while the viscous stress generated in the drop and the interfacial stress resist deformation. The relaxation zone is characterized by absence of turbulent stress and hence the drop tends to relax back to undeformed state. It is shown that a circulating drop, starting with some initial deformation, either reaches a steady state or breaks in one or several cycles. dmax is defined as the maximum size of a drop which, starting with an undeformed initial state for the first cycle, passes through deformation zone infinite number of times without breaking. The model predictions reduce to that of Lagisetty. (1986) for moderate values of μd and σ. The model successfully predicts the reduced dependence of dmax on μd at high values of μd as well as the dependence of dmax on σ at low values of σ. The data available in literature on dmax could be predicted to a greater accuracy by the model in comparison with existing models and correlations.

A new approach to the kinetics of size reduction in ball milling

The rate of breakage of feed in ball milling is usually represented in the form of a first-order rate equation. The equation was developed by treating a simple batch test mill as a well mixed reactor. Several case of deviation from the rule have been reported in the literature. This is attributed to the fact that accumulated fines interfere with the feed material and breaking events are masked by these fines. In the present paper, a new rate equation is proposed which takes into account the retarding effect of fines during milling. For this purpose the analogy of diffusion of ions through permeable membranes is adopted, with suitable modifications. The validity of the model is cross checked with the data obtained in batch grinding of ?850/+600 ?m size quartz. The proposed equation enables calculation of the rate of breakage of the feed at any instant of time.

A new model for the breakage frequency of drops in turbulent stirred dispersions

A model of drop breakage in turbulent stirred dispersions based on interaction of a drop with eddies of a length scale smaller than the drop diameter has been developed. It predicts that, unlike the equal breakage assumed by earlier models, a large drop reduces in size due to stripping of smaller segments off it through unequal breakage. It is only when the drop nears the value of the maximum stable drop diameter that it breaks into equal parts. This new model of drop breakage, coupled with the pattern of interaction of drops with eddies of different sizes existing in the vessel, has been used to evaluate not only the breakage frequency, but also the size distribution of the daughter droplets(which was hitherto assumed). The model has been incorporated in the population balance equation and the resulting cumulative size distributions compared with those availble in the literature.

A new model for coalescence efficiency of drops in stirred dispersions

A model for coalescence efficiency of two drops embedded in an eddy has been developed. Unlike the other models which consider only head-on collisions, the model considers the droplets to approach at an arbitrary angle. The drop pair is permitted to undergo rotation while they approach each other. For coalescence to occur, the drops are assumed to approach each other under a squeezing force acting over the life time of eddy but which can vary with time depending upon the angle of approach. The model accounts for the deformation of tip regions of the approaching drops and, describes the rupture of the intervening film, based on stability considerations while film drainage is continuing under the combined influence of the hydrodynamic and van der Waals forces. The coalescence efficiency is defined as the ratio of the range of angles resulting in coalescence to the total range of all possible approach angles. The model not only reconciles the contradictory predictions made by the earlier models based on similar framework but also brings out the important role of dispersed-phase viscosity. It further predicts that the dispersions involving pure phases can be stabilized at high rps values. Apart from explaining the hitherto unexplained experimental data of Konno et al. qualitatively, the model also offers an alternate explanation for the interesting observations of Shinnar.

Desorption from concentrated polymer solutions in good and poor solvents

The objective of the study was to investigate the effects of the nature of solvent and polymer concentration on the mass-transfer coefficients in desorption of solvents and to develop a correlation to predict them. Desorption was experimentally studied in a Lewis cell with concentrated binary solutions of polymer in good and poor solvents. The range of parameters covered are polymer weight fraction between 0.25 and 0.6, Reynolds number between 3 and 100; Schmidt number between 1.4 X lo6 and 2.5 X lo8, and Sherwood number between 3.5 X lo2 and 1.2 X lo4. Desorption from moderately concentrated solutions (polymer weight fraction -0.25) is gas-phase controlled. Studies with more concentrated solutions showed that the effects of solvent and concentration were such that corrections due to concentration-dependent diffusivity and viscosity as well as high flux had to be applied to the mass-transfer coefficients before they could be correlated.

Finite element estimation of elastic interlaminar stresses in laminates

Low interlaminar strength and the consequent possibility of interlaminar failures in composite laminates demand an examination of interlaminar stresses and/or strains to ensure their satisfactory performance. As a first approximation, these stresses can be obtained from thickness-wise integration of ply equilibrium equations using in-plane stresses from the classical laminated plate theory. Implementation of this approach in the finite element form requires evaluation of third and fourth order derivatives of the displacement functions in an element. Hence, a high precision element developed by Jayachandrabose and Kirkhope (1985) is used here and the required derivatives are obtained in two ways. (i) from direct differentiation of element shape functions; and (ii) by adapting a finite difference technique applied to the nodal strains and curvatures obtained from the finite element analysis. Numerical results obtained for a three-layered symmetric and a two-layered asymmetric laminate show that the second scheme is quite effective compared to the first scheme particularly for the case of asymmetric laminates.

Role of Gypsum in the Strength Development of Fly Ashes with Lime

The strength of fly ash mixture often needs to be enhanced for its better utilization in geotechnical and environmental applications. Many fly ashes often improve their strength with lime but may not meet the requirements. Gypsum, which reduces the lime leachability, further improves the strength. An attempt is made in this paper to study the effect of gypsum on the strength development of two Class F fly ashes with different lime contents after curing them for different periods. The sustainability of improved strength has been examined after soaking the cured specimens in water and with different leachates containing heavy-metal ions. The strength of both the fly ashes investigated improved markedly up to a particular amount of the lime content, which can be taken as optimum lime content, and thereafter the improvement is gradual. The improvement in strength at higher lime contents continues for a longer period (even up to 180 days). Gypsum accelerates the gain in strength for lime-stabilized fly ashes, particularly in the initial curing periods at about optimum lime content. At high lime contents gypsum attributes very high strength after curing for long periods mainly due to the alteration of fly ash lime reaction compounds. Gypsum not only improves the reduction in the loss of strength due to soaking even at low curing periods but also improves the durability of stabilized fly ashes due to repeated cycles of wetting and drying.

Solubility of sulfur dioxide at low partial pressures in dilute sulfuric acid solutions

Equilibrium of dissolution of sulfur dioxide at ppm levels in aqueous solutions of dilute sulfuric acid is analyzed, and a general expression is derived relating the total concentration of sulfur dioxide in the liquid phase to the partial pressure of SO2 in the gas and to the concentration of sulfuric acid in the solution. The equation is simplified for zero and high concentrations of the acid. Experiments at high concentrations of sulfuric acid have enabled the direct determination of Henry’s constant and its dependency on temperature. Heat of dissolution is -31.47 kJ/mol. Experiments in the absence of sulfuric acid and the related simplified expression have led to the determination of the equilibrium constant of the hydrolysis of aqueous sulfur dioxide and its temperature dependency.The heat of hydrolysis is 15.69 kJ/mol. The model equation with these parameters predicts the experimental data of the present work as well as the reported data very well.

Deblurring in a noncoherent optical processing system: pupil function synthesis and experimental implementation

The bipolar point spread function (PSF) corresponding to the Wiener filter tor correcting linear-motion-blurred pictures is implemented in a noncoherent optical processor. The following two approaches are taken for this implementation: (1) the PSF is modulated and biased so that the resulting function is non-negative and (2) the PSF is split into its positive and sign-reversed negative parts, and these two parts are dealt with separately. The phase problem associated with arriving at the pupil function from these modified PSFs is solved using both analytical and combined analytical-iterative techniques available in the literature. The designed pupil functions are experimentally implemented, and deblurring in a noncoherent processor is demonstrated. The postprocessing required (i.e., demodulation in the first approach to modulating the PSF and intensity subtraction in the second approach) are carried out either in a coherent processor or with the help of a PC-based vision system. The deblurred outputs are presented.

Precipitation in small systems-I. stochastic analysis

Precipitation in small droplets involving emulsions, microemulsions or vesicles is important for Producing multicomponent ceramics and nanoparticles. Because of the random nature of nucleation and the small number of particles in a droplet, the use of a deterministic population balance equation for predicting the number density of particles may lead to erroneous results even for evaluating the mean behavior of such systems. A comparison between the predictions made through stochastic simulation and deterministic population balance involving small droplets has been made for two simple systems, one involving crystallization and the other a single-component precipitation. The two approaches have been found to yield quite different results under a variety of conditions. Contrary to expectation, the smallness of the population alone does not cause these deviations. Thus, if fluctuation in supersaturation is negligible, the population balance and simulation predictions concur. However, for large fluctuations in supersaturation, the predictions differ significantly, indicating the need to take the stochastic nature of the phenomenon into account. This paper describes the stochastic treatment of populations, which involves a sequence of so-called product density equations and forms an appropriate framework for handling small systems.

The gasification of wood-char spheres in CO2---N2 mixtures: analysis and experiments

The gasification of charcoal spheres in an atmosphere of carbon-dioxide-nitrogen mixture involving diffusion and reactions in the pores is modelled and the results are compared with experiments of Standish and Tanjung and those performed in the laboratory on wood-char spheres to determine the effects of diameter, density, gas composition and flow. The results indicate that the conversion time, t(c) approximately d1.03 for large particles (> 5 mm), departing substantially from the t(c) approximately d2 law valid for diffusion limited conditions. The computational studies indicate that the kinetic limit for the particle is below 100 mum. The conversion time varies inversely as the initial char density as expected in the model. Predictions from the model show that there is no significant change in conversion time up to 60% N2 consistent with the CO2-N2 experiments. The variation of diameter and density with time are predicted. The peculiar dependence of conversion time on flow velocity in the experiments is sought to be explained by opposing free and forced convection heat transfer and the attempt is only partly successful. The studies also indicate that the dependence on the CO concentration with low CO2 is significant, indicating the need for multistep reaction mechanism against the generally accepted single-step reaction.