New mathematical models and CFD numerical tools for the investigation of macromolecular crystal growth at macroscopic and microscopic length scales

Research output: Contribution to journalArticle

Abstract

This analysis deals with advances in computational methods for the investigation of macromolecular crystal growth. The modelling of these processes leads to the introduction of a group of equations, strictly related, from a mathematical point of view, to the ‘kinetic conditions’ used to model mass transfer at the crystal surface as well as to the level of detail required by the analysis ('local' or 'global'); i.e. diversification of the model occurs according to the desired scale length. If the "local" evolution of the crystal surface is the subject of the investigation (distribution of the local growth rate along crystal face, shape instabilities, onset of surface depressions due to diffusive and/or convective effects, etc, i.e. all those factors dealing with the "local" history of the shape) the method must provide "microscopic" and "morphological" details. For this case a ‘kinetic-coefficient-based’ Volume of Fluid Method is specifically and carefully developed taking into account the possibility of anisotropic (faceted) surface-orientation-dependent growth. On the contrary, if the size of the crystals is negligible with respect to the size of the reactor (i.e. if they are small and undergo only small dimensional changes with respect to the overall dimensions of the cell containing the feeding solution), the shape of the crystals is ignored and the proposed approach relies directly on an algebraic formulation of the nucleation events and on the application of an integral form of the mass balance kinetics for each protein crystal. The applicability and the suitability of the different models are discussed according to some worked examples dealing with microgravity conditions.
LanguageEnglish
Pages11-22
Number of pages11
JournalMicrogravity & Space Station Utilization (MSSU)
Volume3
Issue number3
Publication statusPublished - 2002

Fingerprint

charge flow devices
Crystallization
crystal growth
mathematical models
Theoretical Models
crystal surfaces
crystals
Weightlessness
kinetics
Growth
mass balance
microgravity
mass transfer
reactors
histories
nucleation
proteins
formulations
fluids
Proteins

Keywords

  • macromolecular crystal growth
  • mathematical modeling
  • volume of fluid method
  • microgravity

Cite this

@article{1777f8a008614ec592ea0f365fd2c903,
title = "New mathematical models and CFD numerical tools for the investigation of macromolecular crystal growth at macroscopic and microscopic length scales",
abstract = "This analysis deals with advances in computational methods for the investigation of macromolecular crystal growth. The modelling of these processes leads to the introduction of a group of equations, strictly related, from a mathematical point of view, to the ‘kinetic conditions’ used to model mass transfer at the crystal surface as well as to the level of detail required by the analysis ('local' or 'global'); i.e. diversification of the model occurs according to the desired scale length. If the {"}local{"} evolution of the crystal surface is the subject of the investigation (distribution of the local growth rate along crystal face, shape instabilities, onset of surface depressions due to diffusive and/or convective effects, etc, i.e. all those factors dealing with the {"}local{"} history of the shape) the method must provide {"}microscopic{"} and {"}morphological{"} details. For this case a ‘kinetic-coefficient-based’ Volume of Fluid Method is specifically and carefully developed taking into account the possibility of anisotropic (faceted) surface-orientation-dependent growth. On the contrary, if the size of the crystals is negligible with respect to the size of the reactor (i.e. if they are small and undergo only small dimensional changes with respect to the overall dimensions of the cell containing the feeding solution), the shape of the crystals is ignored and the proposed approach relies directly on an algebraic formulation of the nucleation events and on the application of an integral form of the mass balance kinetics for each protein crystal. The applicability and the suitability of the different models are discussed according to some worked examples dealing with microgravity conditions.",
keywords = "macromolecular crystal growth, mathematical modeling, volume of fluid method, microgravity",
author = "Marcello Lappa",
year = "2002",
language = "English",
volume = "3",
pages = "11--22",
journal = "Microgravity & Space Station Utilization (MSSU)",
issn = "0958-5036",
publisher = "Pergamon Press Ltd.",
number = "3",

}

TY - JOUR

T1 - New mathematical models and CFD numerical tools for the investigation of macromolecular crystal growth at macroscopic and microscopic length scales

AU - Lappa, Marcello

PY - 2002

Y1 - 2002

N2 - This analysis deals with advances in computational methods for the investigation of macromolecular crystal growth. The modelling of these processes leads to the introduction of a group of equations, strictly related, from a mathematical point of view, to the ‘kinetic conditions’ used to model mass transfer at the crystal surface as well as to the level of detail required by the analysis ('local' or 'global'); i.e. diversification of the model occurs according to the desired scale length. If the "local" evolution of the crystal surface is the subject of the investigation (distribution of the local growth rate along crystal face, shape instabilities, onset of surface depressions due to diffusive and/or convective effects, etc, i.e. all those factors dealing with the "local" history of the shape) the method must provide "microscopic" and "morphological" details. For this case a ‘kinetic-coefficient-based’ Volume of Fluid Method is specifically and carefully developed taking into account the possibility of anisotropic (faceted) surface-orientation-dependent growth. On the contrary, if the size of the crystals is negligible with respect to the size of the reactor (i.e. if they are small and undergo only small dimensional changes with respect to the overall dimensions of the cell containing the feeding solution), the shape of the crystals is ignored and the proposed approach relies directly on an algebraic formulation of the nucleation events and on the application of an integral form of the mass balance kinetics for each protein crystal. The applicability and the suitability of the different models are discussed according to some worked examples dealing with microgravity conditions.

AB - This analysis deals with advances in computational methods for the investigation of macromolecular crystal growth. The modelling of these processes leads to the introduction of a group of equations, strictly related, from a mathematical point of view, to the ‘kinetic conditions’ used to model mass transfer at the crystal surface as well as to the level of detail required by the analysis ('local' or 'global'); i.e. diversification of the model occurs according to the desired scale length. If the "local" evolution of the crystal surface is the subject of the investigation (distribution of the local growth rate along crystal face, shape instabilities, onset of surface depressions due to diffusive and/or convective effects, etc, i.e. all those factors dealing with the "local" history of the shape) the method must provide "microscopic" and "morphological" details. For this case a ‘kinetic-coefficient-based’ Volume of Fluid Method is specifically and carefully developed taking into account the possibility of anisotropic (faceted) surface-orientation-dependent growth. On the contrary, if the size of the crystals is negligible with respect to the size of the reactor (i.e. if they are small and undergo only small dimensional changes with respect to the overall dimensions of the cell containing the feeding solution), the shape of the crystals is ignored and the proposed approach relies directly on an algebraic formulation of the nucleation events and on the application of an integral form of the mass balance kinetics for each protein crystal. The applicability and the suitability of the different models are discussed according to some worked examples dealing with microgravity conditions.

KW - macromolecular crystal growth

KW - mathematical modeling

KW - volume of fluid method

KW - microgravity

M3 - Article

VL - 3

SP - 11

EP - 22

JO - Microgravity & Space Station Utilization (MSSU)

T2 - Microgravity & Space Station Utilization (MSSU)

JF - Microgravity & Space Station Utilization (MSSU)

SN - 0958-5036

IS - 3

ER -