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An Exponential‐Hyperbolic Crystal Growth Rate Model
Author(s) -
Mydlarz Jerzy
Publication year - 1995
Publication title -
crystal research and technology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.377
H-Index - 64
eISSN - 1521-4079
pISSN - 0232-1300
DOI - 10.1002/crat.2170300604
Subject(s) - exponential function , crystal (programming language) , crystallization , exponential growth , hyperbolic function , cumulative distribution function , growth rate , crystal growth , mathematics , function (biology) , exponential distribution , particle size distribution , statistics , chemistry , thermodynamics , mathematical analysis , physics , probability density function , particle size , computer science , geometry , biology , evolutionary biology , programming language
Abstract A new exponential‐hyperbolic size‐dependent crystal growth rate function G (L) = G m ( e aL – b )/( e aL – c ) is proposed. The model has been examined in detail for the direct determination of size‐dependent crystal growth rates from the cumulative number oversize distribution of continuous Mixed‐Suspension Mixed‐Product Removal (MSMPR) crystallizers using both simulated and realistic data, both for systems that hold and that violate McCabe's Δ law, respectively. It is show that direct fitting of cumulative number oversize distribution data using the proposed model gives an improved estimation of effective crystal growth rates over the whole size range during MSMPR crystallization compared with previous models tested.