Biomedical subjects

A J Karabelas

Publications and source records attributed to A J Karabelas.

3 recordsLinked to original sources

PubMed2006

A study of the collisional fragmentation problem using the Gamma distribution approximation.

The nonlinear fragmentation population balance formulation has been elevated in recent years from a prototype for studying nonlinear integro-differential equations to a vehicle for analyzing and understanding several physicochemical processes of technological interest. The so-called pure collisional fragmentation, which is the particular mode of nonlinear fragmentation induced by collisions between particles, is studied here. It is shown that the corresponding population balance equation admits large time asymptotic (self-similarity) solutions for homogeneous fragmentation and collision functions (kernels). The self-similar solutions are given in closed form for some simple kernels. Based on the shape of the self-similar solutions the method of moments with Gamma distribution approximation is employed for transient solution (from initial state to establishment of the asymptotic shape) of the collisional fragmentation equation. These solutions are presented for several sets of parameters and their behavior is discussed rather extensively. The present study is similar to the one has already been performed for the case of the much simpler linear fragmentation equation [G. Madras, B.J. McCoy, AIChE J. 44 (1998) 647].

Chemical Phenomena↗

PubMed2005

On the self-similar solution of fragmentation equation: Numerical evaluation with implications for the inverse problem.

It is well known that the fragmentation equation admits self-similar solutions for evolving particle-size distributions (PSD); i.e., if the shape of PSD is independent of time after an initial transient period. Although an analytical derivations of the self-similar PSD cases have been studied extensively, results for cases requiring numerical solutions are rare. The aim of the present work is to fill this gap for the case of homogeneous breakage functions. The known analytical and approximate solutions for the self-similar PSD are reviewed and a general algorithm for the numerical solution is proposed. Results for a broad range of breakage functions (kernel and rate) are presented. Further, the work is focused on the sensitivity of the relation between self-similar PSD and breakage kernel and its influence on the inverse breakage problem, i.e., that of estimating the breakage kernel from experimental self-similar PSDs. Useful suggestions are made for tackling the inverse problem.

Journal Article↗

PubMed2003

Incipient CdS thin film formation.

The quality of a final thin film is essentially determined by the processes taking place at incipient CdS deposition, which in turn are strongly influenced by the physicochemical properties of the substrate and liquid in contact. SEM pictures of deposits formed through steady flow of a supersaturated (with respect to CdS) solution suggest that initially nuclei are continuously generated on the substrate and grow as discrete "surface" particles. With time, these particles tend to "coalesce" with neighboring ones, while new nuclei keep forming and growing, leading to the formation of a coherent film. There is evidence that similar growth patterns prevail in CdS deposition via the chemical bath deposition (CBD) process. Based on experimental observations, a simple model is developed, which is capable of predicting macroscopically determined film characteristics such as the temporal thickness evolution including the "induction period." Two cases of the growth pattern are examined theoretically; one based on instantaneous surface nucleation (due to its simplicity) and another with a constant surface nucleation rate, which appears to be closer to experimental observations.

Journal Article↗