Tibor Blickle

The hyperbolic tangent distribution family

A general description and analysis of the hyperbolic tangent distribution family are presented. Analytical formulae are given for both the cumulative and frequency functions of the distribution, as well as for the ordinary moments of whole order. A linear transformation of the size coordinate axis is applied by means of which the distribution function can be located appropriately over the interval between the observed smallest and largest sizes of particles during the fitting procedure. Including the parameters of this transformation, the distribution family possesses four parameters, which allows for effective fitting to experimental size distribution data. A two-level fitting procedure has been developed which was tested by using simulated noisy data. A number of distribution functions (log-normal, Rosin-Rammler, and beta distributions) may also be described well by hyperbolic tangent distribution functions, so that it provides a convenient method for comparing measurement data described quantitatively in different ways.

A simulation model for analysis and design of continuous grinding mills

Abstract A computer model and simulation program were elaborated for studying the stationary state processes of grinding mills. The computer model was developed on the basis of the axial dispersion model taking into consideration also the effects of mixing of the ground material. The final form of the model was expressed as a set of recursive equations, the successive solution of which converges to the stationary state of the mill. By means of the newly developed simulation program, the effects of parameters of a continuous grinding mill on the size distribution of the particulate product were studied for selection and breakage distribution functions of the form S(L) = KsLα and B(L, l) = (L/l)β, respectively. The program, however, can be utilized in the simulation-based analysis and design of both continuous and batch grinding devices by selecting the respective input—output as well as the mixing conditions of the computer model.

Enhancement of gas absorption rate as a function of the particle size in slurry reactors

Abstract Exact relationships are given for the enhancement of gas absorption rate as a function of particle size in a three-phase slurry reactor. The solid-liquid mass transfer in the liquid film at the gas-liquid interface is considered as a transfer through spherical surface. The solid phase is the catalyst or reactant. The enhancement of the gas absorption rate calculated by the given equations are in very good agreement with the experimental data as a function of particle size and solid phase concentration.

Nonlinear dynamics of isothermal CMSMPR crystallizers: a simulation study

Abstract Complex dynamic phenomena of isothermal CMSMPR crystallizers were studied by means of computer simulation, based on the moment equations model. Applying external and internal periodic forcing to the system, resonance horns, quasi periodic oscillations, period doubling cascades to chaos and noise driven oscillations were observed.

Determination of size-dependent crystal growth characteristics from batch experiments

Abstract An experimental technique and a calculation method have been developed for the evaluation of size-dependent crystal growth. The experimental data were taken from batch-wide cooling crystallization of potash alum. The calculation is based on the population balance method, with the assumption that the overall linear growth rate can be written as the product of a size-dependent and a concentration-dependent function. A computer program has been developed for the calculation. Results are compared with literature data.

Mathematical model for the calculation of internal granule porosity

Abstract A mathematical model was derived for the calculation of the average internal porosity value of granules produced in a fluidised bed granulator. The model allows the description of the variation of granule porosity as a function of the granule size. Granules were formed in a batch-wise operated granulator from lactose, sodium nitrate, sodium chloride, sand, polyethylene, two pharmaceutical products — Halidor® and Chloricide® powders — and glass beads, and their measured internal porosity values were compared with the calculated data. The measured and calculated data agreed within ±20%.

Computer-aided analysis and design of complex batch solid-fluid disperse systems

Abstract A model-based computerized system has been developed for computer-aided engineering Einalysis and design of complex batch solid-fluid disperse systems involving such solid processing operations as crystallization, grinding and granulation, as well as their technological environments.

Computer-aided generation of mathematical models of steady-state heat and mass transfer processes

Abstract This paper describes a study of joint heat and mass transfer processes taking place between two heterogeneous phases in steady-state operational units, such as sorption processes, or heat exchangers. The basis of the program system is the unified mathematical description of various reactor models. The various models of the operational units are generated with the help of a dialog system. The model generalization is carried out using information gained from a practical expert when communicating with the computer. The generated equation set describing the operational units was solved numerically, and tested on various sorption processes.