Application of Gaussian cubature to model two-dimensional population balances

Journal title

Chemical and Process Engineering




vol. 38


No 3



crystallization ; drop breakage ; extraction ; Gaussian cubature ; population balance ; QMOM

Divisions of PAS

Nauki Techniczne




Polish Academy of Sciences Committee of Chemical and Process Engineering




Artykuły / Articles


DOI: 10.1515/cpe-2017-0030 ; ISSN 0208-6425


Chemical and Process Engineering; 2017; vol. 38; No 3; 393-409


Golub (1969), Calculation of quadrature rules, Math Comput, 23, 221, ; Gunawan (2004), High resolution algorithms for multidimensional population balance equations, AIChE J, 2738, ; Marchisio (2005), Solution of population balance equations using direct quadrature method of moments, Aerosol Sci, 36, ; Sack (1972), An algorithm for Gaussian quadrature given modified moments, Math, 18, 465, ; Bałdyga (1993), Drop breakup intermittent turbulence, Chem Eng Jpn, 26, 738, ; Hill (1995), New discretization procedure for the breakage equation, AIChE J, 1204, ; Hulburt (1964), Some problems in particle technology statistical mechanical formulation, Chem Eng Sci, 19, 555, ; Bałdyga (1998), Drop break - up in intermittent turbulence : maximum stable and transient sizes of drops, Can J Chem Eng, 456, ; Borchert (2009), On the prediction of crystal shape distributions in a steady - state continuous crystallizer, Chem Eng Sci, 686, ; Brändström (1966), On the existence of acid salts of monocarboxylic acids in water solutions, Acta Chem Scand, 20, 1335, ; McGraw (1997), Description of aerosol dynamics by the quadrature method of moments, Aerosol Sci Technol, 27, 255, ; Bałdyga (1995), Interpretation of turbulent mixing using fractals multifractals, Chem Eng Sci, 381, ; Gordon (1968), Error bounds in equilibrium statistical mechanics, Math Phys, 9, 655, ; Wright (2001), Bivariate extension of the quadrature method of moments for modeling simultaneous coagulation and sintering of particle populations, Interface Sci, 236, ; Silva (2007), Crystallization from solution InTrends in Hazardous Materials Research Publishers New York, Science. ; Sorgato (1983), Statistical approach to kinetics Degli Studi di Padova - Istituto di Impianti, null. ; Batchelor (1980), Mass transfer from small particles suspended in turbulent fluid, Fluid Mech, 609, ; DeVuyst (2007), Gaussian cubature practitioner guide, Math Comput Modell, 787, ; Sen (2014), Two - dimensional population balance model development and validation of a pharmaceutical crystallization process, Am Mod Chem Eng, 1. ; Okamoto (1981), dissipation rate distribution in mixing vessels and its effects on liquid - liquid dispersion and solid - liquid mass transfer, Energy International Chemical Engineering, 21, 88.

Editorial Board

Editorial Board

Ali Mesbach, UC Berkeley, USA

Anna Gancarczyk, Institute of Chemical Engineering, Polish Academy of Sciences, Poland

Anna Trusek, Wrocław University of Science and Technology, Poland

Bettina Muster-Slawitsch, AAE Intec, Austria

Daria Camilla Boffito, Polytechnique Montreal, Canada

Donata Konopacka-Łyskawa, Gdańsk University of Technology, Poland

Dorota Antos, Rzeszów University of Technology, Poland

Evgeny Rebrov, University of Warwick, UK

Georgios Stefanidis, National Technical University of Athens, Greece

Ireneusz Grubecki, Bydgoszcz Univeristy of Science and Technology, Poland

Johan Tinge, Fibrant B.V., The Netherlands

Katarzyna Bizon, Cracow University of Technology, Poland

Katarzyna Szymańska, Silesian University of Technology, Poland

Marcin Bizukojć, Łódź University of Technology, Poland

Marek Ochowiak, Poznań University of Technology, Poland

Mirko Skiborowski, Hamburg University of Technology, Germany

Nikola Nikacevic, University of Belgrade, Serbia

Rafał Rakoczy, West Pomeranian University of Technology, Poland

Richard Lakerveld, Hong Kong University of Science and Technology, Hong Kong

Tom van Gerven, KU Leuven, Belgium

Tomasz Sosnowski, Warsaw University of Technology, Poland