Analysis of bubble growth on a hot plate during decompression in microgravity

The focus of the present work is the modeling of bubble growth on a hot plate during decompression (depressurization) of a volatile liquid at temperatures close to saturation and in the presence of dissolved gas. In particular, this work presents an organized attempt to analyze data obtained from an experiment under microgravity conditions. In this respect, a bubble growth mathematical model is developed and solved at three stages, all realistic under certain conditions but of increasing physical and mathematical complexity: At the first stage, the temperature variation both in time and space is ignored leading to a new semi-analytical solution for the bubble growth problem. At the second stage, the assumption of spatial uniformity of temperature is relaxed and instead a steady linear temperature profile is assumed in the liquid surrounding the bubble from base to apex. The semi-analytical solution is extended to account for the two-dimensionality of the problem. As the predictions of the above models are not in agreement with the experimental data, at the third stage an inverse heat transfer problem is set up. The third stage model considers an arbitrary average bubble temperature time profile and it is solved numerically using a specifically designed numerical technique. The unknown bubble temperature temporal profile is estimated by matching theoretical and experimental bubble growth curves. A discussion follows on the physical mechanisms that may explain the evolution of the average bubble temperature in time

On the Adequacy of Some Low-Order Moments Method to Simulate Certain Particle Removal Processes

The population balance is an indispensable tool for studying colloidal, aerosol, and, in general, particulate systems. The need to incorporate spatial variation (imposed by flow) to it invokes the reduction of its complexity and degrees of freedom. It has been shown in the past that the method of moments and, in particular, the log-normal approximation can serve this purpose for certain phenomena and mechanisms. However, it is not adequate to treat gravitational deposition. In the present work, the ability of the particular method to treat diffusional and convective diffusional depositions relevant to colloid systems is studied in detail

ΜΕΛΕΤΗ ΦΑΙΝΟΜΕΝΩΝ ΣΥΣΣΩΜΑΤΩΣΗΣ ΚΟΛΛΟΕΙΔΩΝ ΣΩΜΑΤΙΔΙΩΝ ΣΕ ΠΟΛΙΚΟΥΣ ΔΙΑΛΥΤΕΣ

ΚΥΡΙΟΣ ΣΤΟΧΟΣ ΤΗΣ ΔΙΑΤΡΙΒΗΣ ΕΙΝΑΙ Η ΑΝΑΠΤΥΞΗ ΥΠΟΛΟΓΙΣΤΙΚΩΝ ΕΡΓΑΛΕΙΩΝ ΓΙΑ ΤΗΝ ΠΡΟΣΟΜΟΙΩΣΗ ΣΥΝΘΕΤΩΝ ΔΙΕΡΓΑΣΙΩΝ (ΠΥΡΗΝΟΓΕΝΕΣΗ, ΑΝΑΠΤΥΞΗ ΣΩΜΑΤΙΔΙΩΝ, ΣΥΣΣΩΜΑΤΩΣΗ, ΔΗΜΙΟΥΡΓΙΑ ΕΠΙΚΑΘΗΣΕΩΝ) ΠΟΥ ΛΑΜΒΑΝΟΥΝ ΧΩΡΑ ΚΑΤΑ ΤΗ ΡΟΗ ΥΠΕΡΚΟΡΕΣΜΕΝΩΝ ΔΙΑΛΥΜΑΤΩΝ. ΑΡΧΙΚΑ ΓΙΝΕΤΑΙ ΣΥΣΤΗΜΑΤΙΚΗ ΑΞΙΟΛΟΓΗΣΗ ΓΙΑ ΤΗΝ ΕΠΙΛΟΓΗ ΤΟΥ ΑΠΟΔΟΤΙΚΟΤΕΡΟΥ ΣΥΝΟΛΙΚΑ ΤΡΟΠΟΥ ΕΠΙΛΥΣΗΣ ΤΟΥ ΜΑΘΗΜΑΤΙΚΟΥ ΠΡΟΒΛΗΜΑΤΟΣ ΤΗΣ ΠΡΟΣΟΜΟΙΩΣΗΣ. ΟΙ ΕΞΙΣΩΣΕΙΣ ΣΥΣΣΩΜΑΤΩΣΗΣ ΚΑΙ ΑΥΞΗΣΗΣ ΜΕΓΕΘΟΥΣ ΣΩΜΑΤΙΔΙΩΝ ΕΞΕΤΑΖΟΝΤΑΙ ΧΩΡΙΣΤΑ ΚΑΙ ΤΑ ΑΠΟΤΕΛΕΣΜΑΤΑ ΣΥΝΔΥΑΖΟΝΤΑΙ ΓΙΑ ΤΟ ΠΛΗΡΕΣ ΠΛΗΘΥΣΜΙΑΚΟ ΙΣΟΖΥΓΙΟ. ΟΙ ΑΡΙΘΜΗΤΙΚΕΣ ΜΕΘΟΔΟΙ ΠΟΥ ΕΧΟΥΝ ΕΠΙΛΕΓΕΙ ΑΠΟ ΤΗΝ ΠΑΡΑΠΑΝΩ ΑΞΙΟΛΟΓΗΣΗ ΧΡΗΣΙΜΟΠΟΙΟΥΝΤΑΙΣΕ ΣΥΝΔΥΑΣΜΟ ΜΕ ΕΠΙΜΕΡΟΥΣ ΠΡΟΤΥΠΑ ΓΙΑ ΤΑ ΔΙΑΦΟΡΑ ΦΑΙΝΟΜΕΝΑ ΠΟΥ ΛΑΜΒΑΝΟΥΝ ΧΩΡΑ ΚΑΤΑ ΤΗ ΡΟΗ ΥΠΕΡΚΟΡΕΣΜΕΝΩΝ ΔΙΑΛΥΜΑΤΩΝ ΣΕ ΑΓΩΓΟΥΣ, ΓΙΑ ΤΗΝ ΑΝΑΠΤΥΞΗ ΕΝΟΣ ΟΛΟΚΛΗΡΩΜΕΝΟΥ ΥΠΟΛΟΓΙΣΤΙΚΟΥ ΕΡΓΑΛΕΙΟΥ. ΤΟ ΕΡΓΑΛΕΙΟ ΑΥΤΟ ΧΡΗΣΙΜΟΠΟΙΕΙΤΑΙ ΓΙΑ ΤΗΝ ΠΡΟΣΟΜΟΙΩΣΗ ΜΙΑΣ ΠΙΛΟΤΙΚΗΣ ΜΟΝΑΔΑΣ ΠΟΥ ΛΕΙΤΟΥΡΓΕΙ ΣΤΟ ΕΡΓΑΣΤΗΡΙΟ. Η ΣΥΓΚΡΙΣΗ ΜΕΤΑΞΥ ΘΕΩΡΗΤΙΚΩΝ ΚΑΙ ΠΕΙΡΑΜΑΤΙΚΩΝ ΑΠΟΤΕΛΕΣΜΑΤΩΝ ΕΙΝΑΙ ΠΟΛΥ ΕΝΘΑΡΡΥΝΤΙΚΗ. Η ΕΠΙΤΥΧΙΑ ΤΟΥ ΥΠΟΛΟΓΙΣΤΙΚΟΥ ΕΡΓΑΛΕΙΟΥ ΒΑΣΙΖΕΤΑΙ ΣΤΗΝ ΕΠΙΤΥΧΙΑ ΤΩΝ ΕΠΙΜΕΡΟΥΣ ΘΕΩΡΗΤΙΚΩΝ ΠΡΟΤΥΠΩΝ ΠΟΥ ΠΕΡΙΛΑΜΒΑΝΟΝΤΑΙ ΣΕ ΑΥΤΟ. ΕΙΝΑΙ ΓΝΩΣΤΟ ΟΤΙ Η ΚΛΑΣΙΚΗ ΘΕΩΡΙΑ ΤΗΣ ΗΛΕΚΤΡΙΚΗΣ ΔΙΠΛΟΣΤΟΙΒΑΔΑΣ ΠΡΟΒΛΕΠΕΙ ΡΥΘΜΟΥΣ ΕΠΙΚΑΘΗΣΕΩΝ ΚΑΙ ΣΥΣΣΩΜΑΤΩΣΗΣ ΔΙΑΦΟΡΕΤΙΚΟΥΣ ΑΠΟ ΤΟΥΣ ΠΕΙΡΑΜΑΤΙΚΟΥΣ. ΓΙ'ΑΥΤΟ ΓΙΝΕΤΑΙ ΜΙΑ ΠΡΟΣΠΑΘΕΙΑ ΓΙΑ ΤΗΝ ΑΝΑΙΡΕΣΗ ΤΩΝ ΚΥΡΙΟΤΕΡΩΝ ΠΑΡΑΔΟΧΩΝ ΤΗΣ ΠΟΥ ΑΦΟΡΟΥΝ ΤΗ ΔΙΑΚΡΙΤΟΤΗΤΑ ΤΩΝ ΕΠΙΦΑΝΕΙΑΚΩΝ ΦΟΡΤΙΩΝ, ΤΗΝ ΕΠΙΦΑΝΕΙΑΚΗ ΤΡΑΧΥΤΗΤΑ ΤΩΝ ΚΟΛΛΟΕΙΔΩΝ ΣΩΜΑΤΙΔΙΩΝ ΚΑΙ ΤΗΝ ΕΠΙΦΑΝΕΙΑΚΗ ΔΥΝΑΜΙΚΗ (ΠΕΡΙΚΟΠΗ ΠΕΡΙΛΗΨΗΣ)THE MAIN TARGET OF THIS DISSERTATION IS THE DEVELOPMENT OF COMPUTATIONAL TOOLS FOR THE SIMULATION OF COMPLICATED PROCESSES (NUCLEATION, CRYSTAL GROWTH, COAGULATION, DEPOSIT FORMATION), OCCURRING DURING FLOW OF SUPERSATURATED SOLUTIONS. INITIALLY A SYSTEMATIC COMPARISON IS MADE TO SELECT THE MOST EFFICIENT METHOD FOR THE SOLLUTION OF THE MATHEMATICAL PROBLEM. THE EQUATIONS OF COAGULATION AND CRYSTAL GROWTH ARE EXAMINED SEPARATELY AND THE RESULTS ARE COMBINED FOR THE SOLUTION OF THE FULL POPULATION BALANCE. THE SELECTED NUMERICAL METHODS ARE USED IN COMBINATION WITH PHYSICOCHEMICAL MODELS DESCRIBING THE PHENOMENA THAT TAKE PLACE DURING THE FLOW OF SUPERSATURATED SOLUTIONS IN PIPES, FOR THE DEVELOPMENT OF A RELIABLE COMPUTATIONAL TOOL. THE LATTER IS USED FOR THE SIMULATION OF A PILOT PLANT WHICH OPERATES IN THIS LABORATORY. THE COMPARISON BETWEEN THEORETICAL AND EXPERIMENTAL RESULTS IS VERY SATISFACTORY. THE SUCCESS OF THE COMPUTATIONAL TOOL RELIES ON THE SUCCESS OF THE INDIVIDUAL PHYSICOCHEMICAL MODELS INVOLVED. IT IS KNOWN THAT THE CLASSICAL THEORY OF THE ELECTRIC DOUBLE LAYER PREDICTS DEPOSITION AND COAGULATION RATES DIFFERENT FROM THE EXPERIMENTAL ONES. FOR THIS REASON AN EFFORT IS MADE TO RELAX THE MAIN SIMPLIFYING ASSUMPTIONS OF THE THEORY CONCERNING DISCRETENESS OF SURFACE CHARGES, SURFACE ROUGHNESS OF COLLOIDAL PARTICLES AND SURFACE DYNAMICS OF COLLOIDAL SURFACES. THE RESULTS SHOW (ABSTRACT TRUNCATED

Approximation of Any Particle Size Distribution Employing a Bidisperse One Based on Moment Matching

Dispersed phases like colloidal particles and emulsions are characterized by their particle size distribution. Narrow distributions can be represented by the monodisperse distribution. However, this is not the case for broader distributions. The so-called quadrature methods of moments assume any distribution as a bidisperse one in order to solve the corresponding population balance. The generalization of this approach (i.e., approximation of the actual particle size distribution according to a bidisperse one) is proposed in the present work. This approximation helps to compress the amount of numbers for the description of the distribution and facilitates the calculation of the properties of the dispersion (especially convenient in cases of complex calculations). In the present work, the procedure to perform the approximation is evaluated, and the best approach is found. It was shown that the approximation works well for the case of a lognormal distribution (as an example) for a moments order from 0 to 2 and for dispersivity up to 3

Why Is the Linearized Form of Pseudo-Second Order Adsorption Kinetic Model So Successful in Fitting Batch Adsorption Experimental Data?

There is a vast amount of literature devoted to experimental studies on adsorption from liquids examining the adsorption potential of various adsorbents with respect to various solutes. Most of these studies contain not only equilibrium but also kinetic experimental data. The standard procedure followed in the literature is to fit the kinetic experimental adsorption data to some models. Typically empirical models are employed for this purpose and among them, the pseudo-first and pseudo-second order kinetic models are the most extensively used. In particular, the linear form of their integrated equations is extensively employed. In most cases, it is found that the pseudo-second order model is not only better than other models but also leads to high fitting quality. This is rather strange since there is no physical justification for such a model, as it is well accepted that adsorption kinetics is dominated by a diffusion process. In the present work, it will be shown through examples and discussion that the success of the linearized pseudo-second order model in fitting the data is misleading. Specific suggestions on appropriate adsorption data treatment are given

On the Adequacy of Some Low-Order Moments Method to Simulate Certain Particle Removal Processes

The population balance is an indispensable tool for studying colloidal, aerosol, and, in general, particulate systems. The need to incorporate spatial variation (imposed by flow) to it invokes the reduction of its complexity and degrees of freedom. It has been shown in the past that the method of moments and, in particular, the log-normal approximation can serve this purpose for certain phenomena and mechanisms. However, it is not adequate to treat gravitational deposition. In the present work, the ability of the particular method to treat diffusional and convective diffusional depositions relevant to colloid systems is studied in detail

Why Is the Linearized Form of Pseudo-Second Order Adsorption Kinetic Model So Successful in Fitting Batch Adsorption Experimental Data?

There is a vast amount of literature devoted to experimental studies on adsorption from liquids examining the adsorption potential of various adsorbents with respect to various solutes. Most of these studies contain not only equilibrium but also kinetic experimental data. The standard procedure followed in the literature is to fit the kinetic experimental adsorption data to some models. Typically empirical models are employed for this purpose and among them, the pseudo-first and pseudo-second order kinetic models are the most extensively used. In particular, the linear form of their integrated equations is extensively employed. In most cases, it is found that the pseudo-second order model is not only better than other models but also leads to high fitting quality. This is rather strange since there is no physical justification for such a model, as it is well accepted that adsorption kinetics is dominated by a diffusion process. In the present work, it will be shown through examples and discussion that the success of the linearized pseudo-second order model in fitting the data is misleading. Specific suggestions on appropriate adsorption data treatment are given