Powstawanie i rozpad agregatów ciała stałego zawieszonych w cieczy

Gierczycki, A.

Artykuł - szczegóły

Tytuł artykułu

Powstawanie i rozpad agregatów ciała stałego zawieszonych w cieczy

Autorzy

Gierczycki A.

Identyfikatory

Warianty tytułu

Formation and breakage of solid aggregates suspended in liquid

Języki publikacji

Abstrakty

W pracy podjęto teoretyczno - doświadczalną analizę zachodzących równocześnie procesów powstawania i rozpadu agregatów ciała stałego zawieszonych w mieszanej cieczy. Dokonano przeglądu prac dotyczących powstawania i rozpadu agregatów. Przeprowadzono badania doświadczalne związane z tymi procesami dla dwóch rodzajów pyłu kredowego i czterech rodzajów monodyspersyjnych kulek z lateksu zawieszonych w wodzie destylowanej w obecności wielkocząsteczkowego, polimerowego związku powierzchniowo czynnego o nazwie handlowej Zetag 63. Doświadczenia wykonano na dwóch instalacjach laboratoryjnych wyposażonych w mieszadła: turbinowe (dwa rodzaje) wibracyjne, (trzy rodzaje) i śmigłowe. Badania dotyczyły warunków, w których ruch cieczy w mieszalnku miał charakter burzliwy. Pomiary dla pojedynczej serii prowadzono początkowo dla niższych wartości średniej globalnej szybkości dyssypacji energii epsilon, uzyskując agregację, a po osiągnięciu stanu ustalonego wprowadzono skokową zmianę epsilon, powodując rozpad dopiero co powstałych agregatów. Dla kulek z lateksu ograniczono się do etapu z przeważającą agregacją. Próbki zawiesiny pobierane w ściśle określonych interwałach czasowych analizowano pod kątem składu ziarnowego i średnich rozmiarów Sautera populacji agregatów d32 w laserowych analizatorach cząstek (Malvern 3600Ec i Analysette 22 firmy Fritsch). Na podstawie uzyskanych wyników stwierdzono, że zachodzące w mieszalnikach procesy agregacji i rozpadu dążą w swym przebiegu do osiągnięcia stanu dynamicznej równowagi, a wartość epsilon decyduje o tym, czy przeważa agregacja lub rozpad. Agregacja zachodziła zgodnie z mechanizmem ortokinetycznym, a rozmiary cząstek pierwotnych i agregatów przemawiały za dominującym wpływem procesów zachodzących w lepkościowym podzakresie dyssypacji energii kinetycznej turbulencji. Rozpad miał charakter kawałkowy, potwierdzony przez uzyskane wyniki rozkładów ziarnowych oraz zdjęcia mikroskopowe próbek agregatów (mikroskopy typu Vickers i Olympus CH30). Oba procesy miały charakter częściowo odwracalny. Do opisu ewolucji agregatów wykorzystano model matematyczny (w dwóch wersjach) oparty na metodzie skupionej równań bilansu populacji (RBP) i połączony z odpowiednimi założeniami dotyczącymi kinetyki procesu i struktury agregatów. W wersji niefraktalnej modelu założono stałą porowatość agregatów, a w wersji fraktalnej przyjęto, że agregaty są fraktalami masowymi opisanymi jednym wymiarem fraktalnym dr w całym zakresie rozmiarów. W modelowaniu kinetyki, w celach upraszczających, nie brano pod uwagę lokalnych warunków przepływu w mieszalniku, natury sił odpowiedzialnych za agregację i rozpad, a także kompozycji zawiesiny, uzależniając parametry kinetyczne agregacji i rozpadu beta a,0 i beta r,0, wyłącznie od rozmiarów agregatów i ich struktury. W rozwiązaniu układu RBP zastosowano specjalnie opracowaną procedurę w języku Turbo Pascal, którą wyznaczono optymalne wartości beta a,0 i beta r,0 w taki sposób, aby uzyskać najlepsze dopasowanie rozkładów ziarnowych obliczonych za pomocą modelu i otrzymanych w doświadczeniach. Uzyskano zadowalającą zgodność rozkładów ziarnowych dla obu wariantów modelu. Na podstawie otrzymanych wyników dobrano postać funkcji rozpadu (parametr a=1/3) oraz przeanalizowano wpływ średniej globalnej szybkości dyssypacji energii epsilon na beta a,0 i b e,0. Stwierdzono, że główną przyczyną zróżnicowania wyników otrzymanych dla mieszadeł różnego typu są różne wartości współczynnika prawdopodobieństwa zderzeń i inna odporność agregatów na rozpad. Badania eksperymentalne pozwoliły na identyfikację mechanizmów agregacji i rozpadu w złożonym przypadku, gdy procesy te występują równocześnie. Zaproponowany model matematyczny (pomimo pewnych założeń upraszczających) wraz z opracowaną procedura obliczeń numerycznych, pozwalający na wyznaczenie optymalnych wartości parametrów kinetycznych beta a,0 i beta r,0 może być z powodzeniem stosowany do opisu podobnych układów fizykalnych. Nie otrzymano jednoznacznej odpowiedzi dotyczącej wyboru wariantu niefraktalnego lub fraktalnego modelu. Można natomiast sądzić, że skomplikowanie modelu przez założenie innego charakteru funkcji rozpadu, przyjęcie multifraktalnej struktury agregatów, jak również uwzględnienie wpływu rozkładu chwilowych wartości szybkości dyssypacji energii w zawiesinie na kinetykę procesu powinno poprawić dokładność otrzymanych wyników.

A theoretically experimental analysis dealing with simultaneously occurring aggregation and breakage processes of solid particles suspended in liquid has been presented. A survey of literature concerning processes mentioned has been performed. The experimental tests for two types of chalk particles, four monodispersed latex spheres suspended in water in the presence of high-molecular, polymer surfactant called Zetag 63 have been carried out. The experiments were performed in two laboratory set-ups equipped with: the turbine (two types), vibrating (three types) and propeller impellers. Suspension in a tank was stirred turbulently in all cases. A typical measuring run started at a lower value of bulk-averaged energy dissipation rate in the tank epsilon, for which aggregation was obtained. Then, when steady state was achieved, a step change in epsilon was introduced and breakage of just formed aggregates took place. For latex spheres tests were restricted to the period with prevailing aggregation. Samples of suspensions were taken in appropriate time intervals and analysed in the laser particle analysers for PSD and the Sauter mean diameter of aggregates, d32 (Malvern 3600Ec and Analysette 22 of Fritsch). It has been stated that aggregation and breakage processes have a tendency to obtain a state of dynamic equilibrium, and their course a value of epsilon decided which of them (i. e. aggregation of breakage) prevailed. The mechanism of aggregation exhibited the orthokinetic characteristic while a size of initial particles and aggregates proved the viscosity subrange of turbulence. Breakage showed the lump characteristics confirmed by a shape of PSDs and microscopic photographs of aggregates (microscopes: Vickers and Olympus (CH30). In description of the aggregate evolution, a mathematical model (in two versions) based on lumped discrete population balance equations solving method and appropriate assumptions dealing with the process kinetics and aggregate structure was employed. In the non-fractal version, it was assumed that aggregates showed a constant porosity, whereas in the fractal version it was assumed that aggregates represented mass fractal objects described by one fractal dimension, df, in the whole size range. In kinetics modeling, due to simplifying approach, local flow conditions in the tank, characteristic of aggregation and breakage forces and also composition of suspension have not been taken into account. Process kinetic parameters beta a,o and beta r,0 depended only on aggregate size and structure. The population balance equations were solved using specially written procedure in Turbo Pascal language. The procedure enabled one to calculate optimum values of beta a,0 and beta r,0 in such a way that the best fit of experimental and measured PSDs was obtained. An acceptable compatibility between PSDs was achieved for both variants of the model. Based on the calculation results, the best shape of breakage function was selected (parameter a=1/3) and an influence of the bulk-averaged energy dissipation rate, epsilon, on beta a,0 and beta r,0 was determined. The main reason of differentitation of the results for different impeller types lies possibly in different values of aggregation probability coefficients and different aggregates' resistance against beakage. The researches carried out enabled one to identify correctly aggregation and breakage mechanisms in such a compound case where both of them occurred simultaneously. The mathematical model proposed (despite a number of simplified assumptions), together with the numerical procedure for calculation of the values of kinetic parameters, beta a,0 and beta r,0, can be successfully used in a description of physically similar systems. However, an unequivocal answer concerning the selection between the non-fractal and fractal model variant has not been obtained. Introduction of a more compound breakage function, mulitfractal character of aggregates or an influence of energy dissipation rate distribution in the tank should improve the model.

Słowa kluczowe

agregat agregat ciała stałego powstawanie agregatów rozpad agregatów

agregat formation aggregates dissolution aggregates

Wydawca

Wydawnictwo Politechniki Śląskiej

Czasopismo

Zeszyty Naukowe. Chemia / Politechnika Śląska

Rocznik

2005

Tom

z. 149

Strony

5--133

Opis fizyczny

bibliogr. 253 poz.

Twórcy

autor

Gierczycki A.

Katedra Inżynierii Chemicznej i Procesowej Politechnika Śląska, 44-100 Gliwice, ul.Strzody 7 tel. (032) 237-27-70, andrzej.gierczycki@polsl.pl

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