Please use this identifier to cite or link to this item: http://hdl.handle.net/10995/112156
Title: Unified mathematical Model of the Kinetics of Nanoparticle Phase Condensation in Magnetic Fields
Authors: Kuzhir, P.
Raboisson-Michel, M.
Queiros, Campos, J.
Verger-Dubois, G.
Zubarev, A. Y.
Issue Date: 2021
Publisher: John Wiley and Sons Ltd
Wiley
Citation: Kuzhir P. Unified mathematical Model of the Kinetics of Nanoparticle Phase Condensation in Magnetic Fields / P. Kuzhir, M. Raboisson-Michel, Campos J. Queiros // Mathematical Methods in the Applied Sciences. — 2021. — Vol. 44. — Iss. 16. — P. 12088-12100.
Abstract: 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.
Keywords: MAGNETIC FIELD
MAGNETIC NANOPARTICLES
NON-EQUILIBRIUM PHASE TRANSITION
AGGREGATES
CONDENSATION
DISTRIBUTION FUNCTIONS
MAGNETIC FIELDS
METHOD OF MOMENTS
SIZE DISTRIBUTION
AGGREGATE SIZE DISTRIBUTIONS
ALTERNATING MAGNETIC FIELD
APPLIED MAGNETIC FIELDS
ARBITRARY FUNCTIONS
ENVIRONMENTAL APPLICATIONS
METHOD OF CHARACTERISTICS
NANOPARTICLE SUSPENSION
ROTATING MAGNETIC FIELDS
MAGNETIC NANOPARTICLES
URI: http://hdl.handle.net/10995/112156
Access: info:eu-repo/semantics/openAccess
SCOPUS ID: 85089080637
PURE ID: 23818278
ISSN: 0170-4214
metadata.dc.description.sponsorship: 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.
RSCF project card: 20-12-00031
Appears in Collections:Научные публикации, проиндексированные в SCOPUS и WoS CC

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