Adsorption studies of molasse's wastewaters on activated carbon: modelling with a new fractal kinetic equation and evaluation of kinetic models.

Adsorption kinetic of molasses wastewaters after anaerobic digestion (MSWD) and melanoidin respectively on activated carbon was studied at different pH. The kinetic parameters could be determined using classical kinetic equations and a recently published fractal kinetic equation. A linear form of this equation can also be used to fit adsorption data. Even with lower correlation coefficients the fractal kinetic equation gives lower normalized standard deviation values than the pseudo-second order model generally used to fit adsorption kinetic data, indicating that the fractal kinetic model is much more accurate for describing the kinetic adsorption data than the pseudo-second order kinetic model.

Parameters from a new kinetic equation to evaluate activated carbons efficiency for water treatment.

The fractal dimension of some commercial activated carbon (AC) was determined in the micro-, meso- and macropore range using mercury porosimetry and N(2) adsorption data. We studied the kinetic of adsorption of phenol, tannic acid and melanoidin on those ACs. The typical concentration-time profiles obtained here could be very well fitted by a general fractal kinetics equation q(n,alpha)(t)=q(e)[1-(1+(n-1)(t/tau(n,alpha))(alpha))(-1/(n-1))] deduced from recently new methods of analysis of reaction kinetics and relaxation. The parameter n is the reaction order, alpha is a fractional time index, q(e) measures the maximal quantity of solute adsorbed, and a "half-reaction time", tau(1/2), can be calculated, which is the time necessary to reach half of the equilibrium. The adsorption process on AC is clearly a heterogeneous process, taking place at the liquid-solid boundary, and the diffusion process occurs in a complex matrix with a fractal architecture as demonstrated here. In fact, these systems belong to what has been called "complex systems" and the fractal kinetic, which has been extensively applied to biophysics, can be a useful theoretical tool for study adsorption processes.

Is fractal geometry useful in medicine and biomedical sciences?

Fractal geometry has become very useful in the understanding of many phenomena in various fields such as astrophysics, economy or agriculture and recently in medicine. After a brief intuitive introduction to the basis of fractal geometry, the clue is made about the correlation between Df and the complexity or the irregularity of a structure. However, fractal analysis must be applied with certain caution in natural objects such as bio-medical ones. The cardio-vascular system remains one of the most important fields of application of these kinds of approach. Spectral analysis of the R-R interval, morphology of the distal coronary arteries constitute two examples. Other very interesting applications are founded in bacteriology, medical imaging or ophthalmology. In our institution, we apply fractal analysis in order to quantitate angiogenesis and other vascular processes.

Fractal quantification of the microvasculature heterogeneity in cutaneous melanoma.

BACKGROUND: Recent advances in angiogenesis research have led to the introduction of new prognosis factors. Although the vessel count is effective in breast cancer, the prognosis of primary cutaneous melanoma (PCM) does not seems to be directly influenced by this parameter. However, the microscopic examination of PCM suggests variability in the repartition of the microvasculature. OBJECTIVE AND METHOD: To explore the possibility of extracting information about the vessel distribution by performing a textural analysis on the grey level of histological sections by means of fractal characterization by both Fourier spectrum and multifractal analysis. RESULTS: Three different patterns of vasculature were identified according to the vessel density and distribution. CONCLUSION: It is possible to differentiate and quantify clearly the differences in the microvessel profile organization using the fractal and multifractal methods.

Fractal Analysis of Mercury Porosimetry Data in the Framework of the Thermodynamic Method.

The thermodynamic method for fractal analysis is applied to mercury intrusion data. The results for representative commercial carbon black samples and a series of resorcinol-formaldehyde (RF) freeze-dried gels for different values of the molar ratio of resorcinol (R) to catalyst (C) are discussed in relation with the type of behavior exhibited by the samples during mercury porosimetry measurements. The obtained surface fractal dimensions are compared with those derived previously from the small-angle X ray scattering (SAXS) and the nitrogen adsorption. Copyright 1999 Academic Press.