Unified mathematical model of the kinetics of nanoparticle phase condensation in magnetic fields

Autor: Maxime Raboisson-Michel, Pavel Kuzhir, Gregory Verger-Dubois, Andrey Zubarev, Jordy Queiros Campos
Přispěvatelé: Institut de Physique de Nice (INPHYNI), Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA), Axlepios Biomedical, Ural Federal University [Ekaterinburg] (UrFU), COMPLEX SYSTEMS ACADEMY
Jazyk: angličtina
Rok vydání: 2021
Předmět:
non-equilibrium phase transition
AGGREGATE SIZE DISTRIBUTIONS
ENVIRONMENTAL APPLICATIONS
General Mathematics
Kinetics
Nanoparticle
MAGNETIC FIELD
AGGREGATES
magnetic field
02 engineering and technology
ROTATING MAGNETIC FIELDS
01 natural sciences
CONDENSATION
APPLIED MAGNETIC FIELDS
Phase (matter)
0103 physical sciences
SIZE DISTRIBUTION
ARBITRARY FUNCTIONS
[MATH]Mathematics [math]
010306 general physics
METHOD OF MOMENTS
ComputingMilieux_MISCELLANEOUS
Mathematics
[PHYS]Physics [physics]
MAGNETIC NANOPARTICLES
ALTERNATING MAGNETIC FIELD
NANOPARTICLE SUSPENSION
Condensation
General Engineering
DISTRIBUTION FUNCTIONS
MAGNETIC FIELDS
021001 nanoscience & nanotechnology
Magnetic field
Chemical physics
Magnetic nanoparticles
NON-EQUILIBRIUM PHASE TRANSITION
0210 nano-technology
METHOD OF CHARACTERISTICS
Zdroj: Mathematical Methods in the Applied Sciences
Mathematical Methods in the Applied Sciences, Wiley, 2021, 44, pp.12088-12100. ⟨10.1002/mma.6739⟩
Mathematical Methods in the Applied Sciences, Wiley, 2021, 44 (16), pp.12088-12100. ⟨10.1002/mma.6739⟩
Math Methods Appl Sci
Mathematical Methods in the Applied Sciences, Wiley, 2020, ⟨10.1002/mma.6739⟩
ISSN: 0170-4214
1099-1476
DOI: 10.1002/mma.6739⟩
Popis: In this paper, we aim to present a unified mathematical modeling and description of the kinetics of magnetic nanoparticles phase condensation (conducting to the appearance of bulk elongated aggregates) under homogeneous permanent or alternating magnetic field. For such case, the aggregate growth rate usually takes the form dV/dt = G(V)∆(t), with V and t being the aggregate's volume and time, respectively, ∆(t)—the supersaturation of the nanoparticle suspension, and with the function G(V) depending on the precise configuration of the applied field. The Liouville equation for the aggregate size distribution function is solved by the method of characteristics. The solution is obtained in parametric form for an arbitrary function G(V), providing a general framework for any type of the applied magnetic field. In the particular case of low-frequency rotating magnetic field (G(V)~V2/3), an explicit expression of the distribution function is obtained, while the dimensionless average aggregate volume 〈V〉 is found by the method of moments allowing a complete decoupling of the system of equations for the statistical moments 〈Vn〉 of the distribution function. Numerical examples are provided for the cases of permanent and low- or medium-frequency rotating fields. It is shown that in all cases, the average volume 〈V〉 only slightly depends on the relative width of the initial size distribution. Nevertheless, at any times, t > 0, the size distribution shows a significant spreading around the average value 〈V〉, which increases progressively with time and achieves a final plateau at long times. This model can be helpful for several biomedical or environmental applications of magnetic nanoparticles in which the nanoparticle suspension undergoes a field-induced phase condensation. © 2020 John Wiley & Sons, Ltd. PK acknowledges the French “Agence Nationale de la Recherche,” Project Future Investments UCA JEDI, No. ANR‐15‐IDEX‐01 (projects ImmunoMag and MagFilter) and the private company Axlepios Biomedicals for financial support. JQC acknowledges the financial support of UCA JEDI and Axlepios Biomedicals through the PhD fellowship. AZ thanks the Russian Science Foundation, project 20‐12‐00031, for the financial support.
Databáze: OpenAIRE
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