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A simplified mathematical study of thermochemical preparation of particle oxide under counterflow configuration for use in biomedical applications

  • Amir Tabaei
  • Sadegh Sadeghi
  • Saman Hosseinzadeh
  • Mehdi Bidabadi
  • Qingang XiongEmail author
  • Nader Karimi
Article
  • 21 Downloads

Abstract

This study mathematically presents a counterflow non-premixed thermochemical technique for preparing a particle oxide used for cancer diagnosis and treatment. For this purpose, preheating, reaction, melting, and oxidation processes were simulated considering an asymptotic concept. Mass and energy conservation equations in dimensional and non-dimensional forms were solved using MATLAB®. To preserve the continuity in the system and calculate the locations of melting and flame fronts, promising jump conditions were derived. In this research, variations in flame temperature, flame front location and mass fractions of the particle, particle oxide and oxidizer, with position, Lewis number and initial temperature of the particles were investigated. The simulation results were compared with those obtained from an earlier experimental study under the same conditions. Regarding the comparison, an appropriate compatibility was observed between the results. Based on the simulation results, flame temperature was found to be about 1310 K. Positions of flame and melting fronts were found to be − 1.8 mm and − 1.78 mm, respectively.

Keywords

Biomedical applications Cancer diagnosis and treatment Particle oxide Non-premixed mode Numerical simulation Counterflow design 

List of symbols

a

Strain rate \(\left( {\frac{1}{a}} \right)\)

C

Mixture specific heat capacity (kJ kg−1 K−1)

Ca

Heat capacity of the gas (kJ kg−1 K−1)

Cp

Heat capacity of the particle (kJ kg−1 K−1)

DC

Damkohler number

DF

Diffusion coefficient of particle (m2 s−1)

Dm

Diffusion coefficient of particle oxide in liquid phase (m2 s−1)

DO

Diffusion coefficient of oxidizer (m2 s−1)

DT

Thermal diffusion coefficient (m2 s−1)

E

Overall activation energy (kJ)

erf(x)

Error function

H

Heaviside function

Le

Lewis number

m

Mixture molecular mass (kg mol−1)

mF

Fuel molecular mass (kg mol−1)

mO

Oxidizer molecular mass (kg mol−1)

np

Local number density of particles (number of particles per unit volume)

\({\mathcal{Q}}\)

Heat of reaction (kJ kg−1)

Qmelt

Latent heat of melting (kJ kg−1)

\({\fancyscript{q}}_{\rm melt}\)

Ratio of latent heat of melting to the heat released from reaction

R

The universal gas constant (m3 Pa mol−1 K−1)

rp

Particle radius (µm)

T

Temperature (K)

Ta

Activation temperature (K)

Tad

Adiabatic temperature (K)

Tf

Flame temperature (K)

Tig

Ignition temperature of particles (K)

Tmelt

Melting temperature of particle oxide (K)

T

Ambient temperature (K)

\({\mathcal{W}}_{\text{F}}\)

Molecular weight of the particle (kg kmol−1)

x

Dimensional length (m)

xf

Dimensional flame sheet position (m)

Xf

Non-dimensional flame sheet position

xmelt

Onset position of melting in dimensional form (m)

Xmelt

Onset position of melting in non-dimensional form

Ym

Mass fraction of particle oxide in liquid phase

YO

Mass fraction of the oxidizer

YS

Mass fraction of the particle

YS−∞

Mass fraction of the particle at the distance − ∞

ym

Dimensionless form of the mass fraction of particle oxide in liquid phase

yO

Dimensionless form of the mass fraction of oxidizer

yS

Dimensionless form of the mass fraction of particle

Greek symbols

ωmelt

Melting rate of particle oxide (kg m−1 s−2)

\(\widetilde{\omega }_{\text{melt}}\)

Dimensionless form of melting

ωS

Reaction rate (kg m−1 s−2)

\(\widetilde{\omega }_{\text{S}}\)

Dimensionless form of the reaction rate

τmelt

Constant characteristic time of melting

λ

Thermal conductivity (kJ m−1 s−1 K)

ρ

Density of the mixture (kg m−3)

ρa

Density of the gas (kg m−3)

ρp

Density of the particle (kg m−3)

θ

Dimensionless form of the temperature

θf

Dimensionless form of the flame temperature

θmelt

Dimensionless form of the melting temperature

vO

Oxidizer stoichiometric coefficient

vp

Product stoichiometric coefficient

vS

Fuel stoichiometric coefficient

Subscripts

a

Gas

f

Flame

melt

Melting

P

Product

S

Particle

V

Velocity

Ambient condition

Notes

References

  1. 1.
    Shahbazi-Gahrouei D, Keshtkar M. Magnetic nanoparticles and cancer treatment. Immunopathol Persa. 2016;2(1):e03.Google Scholar
  2. 2.
    Berry CC. Progress in functionalization of magnetic nanoparticles for applications in biomedicine. J Phys D Appl Phys. 2009;42(22):224003.CrossRefGoogle Scholar
  3. 3.
    Atiq S, Ansar MZ, Riaz S, Naseem S. Synthesis and characterization of magnetic nanoparticles for cancer therapy. In: Proceedings of 2013 world congress on advances in nano, biomechanics, robotics and energy research (ANBRE), 25 Aug 2013.Google Scholar
  4. 4.
    Gupta AK, Naregalkar RR, Vaidya VD, Gupta M. Recent advances on surface engineering of magnetic iron oxide nanoparticles and their biomedical applications. Future Med. 2007;2:23–39.Google Scholar
  5. 5.
    Wu W, Wu Z, Yu T, Jiang C, Kim WS. Recent progress on magnetic iron oxide nanoparticles: synthesis, surface functional strategies and biomedical applications. Sci Technol Adv Mater. 2015;16(2):023501.CrossRefPubMedPubMedCentralGoogle Scholar
  6. 6.
    Arruebo M, Fernández-Pacheco R, Ibarra MR, Santamaría J. Magnetic nanoparticles for drug delivery. Nano Today. 2007;2(3):22–32.CrossRefGoogle Scholar
  7. 7.
    Moacă EA, Coricovac ED, Soica CM, Pinzaru IA, Păcurariu CS, Dehelean CA. Preclinical aspects on magnetic iron oxide nanoparticles and their interventions as anticancer agents: enucleation, apoptosis and other mechanism. In: Shatokha V, editor. Iron ores and iron oxide materials. London: IntechOpen; 2018. p. 229.Google Scholar
  8. 8.
    Laurent S, Forge D, Port M, Roch A, Robic C, Vander Elst L, Muller RN. Magnetic iron oxide nanoparticles: synthesis, stabilization, vectorization, physicochemical characterizations, and biological applications. Chem Rev. 2008;108(6):2064–110.CrossRefPubMedGoogle Scholar
  9. 9.
    Mata-Pérez F, Martínez JR, Guerrero AL, Ortega-Zarzosa G. New way to produce magnetite nanoparticles at low temperature. Adv Chem Eng Res. 2015;4(1):48–55.  https://doi.org/10.12783/acer.2015.0401.04.CrossRefGoogle Scholar
  10. 10.
    Guo B, Kennedy IM. Gas-phase flame synthesis and characterization of iron oxide nanoparticles for use in a health effects study. Aerosol Sci Technol. 2007;41(10):944–51.CrossRefGoogle Scholar
  11. 11.
    Ali A, Hira Zafar MZ, ul Haq I, Phull AR, Ali JS, Hussain A. Synthesis, characterization, applications, and challenges of iron oxide nanoparticles. Nanotechnol Sci Appl. 2016;9:49.CrossRefPubMedPubMedCentralGoogle Scholar
  12. 12.
    Ling D, Hyeon T. Chemical design of biocompatible iron oxide nanoparticles for medical applications. Small. 2013;9(9-10):1450–66.CrossRefPubMedGoogle Scholar
  13. 13.
    Stumm W, Lee GF. Oxygenation of ferrous iron. Ind Eng Chem. 1961;53(2):143–6.CrossRefGoogle Scholar
  14. 14.
    McAllister S, Chen JY, Fernandez-Pello AC. Fundamentals of combustion processes. New York: Springer; 2011.CrossRefGoogle Scholar
  15. 15.
    Shadloo MS. Numerical simulation of compressible flows by lattice Boltzmann method. Numer Heat Transf Part A Appl. 2019;75(3):167–82.CrossRefGoogle Scholar
  16. 16.
    Hopp-Hirschler M, Shadloo MS, Nieken U. Viscous fingering phenomena in the early stage of polymer membrane formation. J Fluid Mech. 2019;864:97–140.CrossRefGoogle Scholar
  17. 17.
    Shadloo MS, Poultangari R, Jamalabadi MA, Rashidi MM. A new and efficient mechanism for spark ignition engines. Energy Convers Manag. 2015;96:418–29.CrossRefGoogle Scholar
  18. 18.
    Hopp-Hirschler M, Shadloo MS, Nieken U. A smoothed particle hydrodynamics approach for thermo-capillary flows. Comput Fluids. 2018;176:1–19.CrossRefGoogle Scholar
  19. 19.
    Shadloo MS, Hadjadj A. Laminar-turbulent transition in supersonic boundary layers with surface heat transfer: a numerical study. Numer Heat Transf Part A Appl. 2017;72(1):40–53.CrossRefGoogle Scholar
  20. 20.
    Daoush WM. Co-precipitation and magnetic properties of magnetite nanoparticles for potential biomedical applications. J Nanomed Res. 2017;5(1):e6.Google Scholar
  21. 21.
    Andrade ÂL, Valente MA, Ferreira JM, Fabris JD. Preparation of size-controlled nanoparticles of magnetite. J Magn Magn Mater. 2012;324(10):1753–7.CrossRefGoogle Scholar
  22. 22.
    Setyawan H, Widiyastuti W. Progress in the preparation of magnetite nanoparticles through the electrochemical method. KONA Powder Particle J. 2019;36:145–55.CrossRefGoogle Scholar
  23. 23.
    Dresco PA, Zaitsev VS, Gambino RJ, Chu B. Preparation and properties of magnetite and polymer magnetite nanoparticles. Langmuir. 1999;15(6):1945–51.CrossRefGoogle Scholar
  24. 24.
    Koushika EM, Shanmugavelayutham G, Saravanan P, Balasubramanian C. Rapid synthesis of nano-magnetite by thermal plasma route and its magnetic properties. Mater Manuf Process. 2018;33(15):1701–7.CrossRefGoogle Scholar
  25. 25.
    Rashid H, Mansoor MA, Haider B, Nasir R, Abd Hamid SB, Abdulrahman A. Synthesis and characterization of magnetite nano particles with high selectivity using in situ precipitation method. Sep Sci Technol. 2019;2:1–9.CrossRefGoogle Scholar
  26. 26.
    de Almeida Silva R, Castro CD, Vigânico EM, Petter CO, Schneider IA. Selective precipitation/UV production of magnetite particles obtained from the iron recovered from acid mine drainage. Min Eng. 2012;29:22–7.CrossRefGoogle Scholar
  27. 27.
    Lei P, Girshick SL. Thermal plasma synthesis of superparamagnetic iron oxide nanoparticles for biomedical applications. Plasma Chem Plasma Process. 2012.  https://doi.org/10.1007/s11090-012-9364-1.CrossRefGoogle Scholar
  28. 28.
    Owens GI, Singh RK, Foroutan F, Alqaysi M, Han CM, Mahapatra C, Kim HW, Knowles JC. Sol–gel based materials for biomedical applications. Prog Mater Sci. 2016;77:1–79.CrossRefGoogle Scholar
  29. 29.
    Bidabadi M, Panahifar P, Sadeghi S. Analytical development of a model for counter-flow non-premixed flames with volatile biofuel particles considering drying and vaporization zones with finite thicknesses. Fuel. 2018;231:172–86.CrossRefGoogle Scholar
  30. 30.
    Nematollahi M, Rasam H, Sadeghi S, Bidabadi M. Asymptotic prediction of multi-region planar non-premixed combustion of moisty porous coal particles in counter-flow design considering pyrolysis, homogeneous and heterogeneous reactions. Combust Flame. 2019;207:281–94.CrossRefGoogle Scholar
  31. 31.
    Bidabadi M, Ramezanpour M, Poorfar AK, Monteiro E, Rouboa A. Mathematical modeling of a non-premixed organic dust flame in a counterflow configuration. Energy Fuels. 2016;30(11):9772–82.CrossRefGoogle Scholar
  32. 32.
    Sun JH, Dobashi R, Hirano T. Temperature profile across the combustion zone propagating through an iron particle cloud. J Loss Prev Process Ind. 2001;14(6):463–7.CrossRefGoogle Scholar

Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2019

Authors and Affiliations

  • Amir Tabaei
    • 1
  • Sadegh Sadeghi
    • 1
  • Saman Hosseinzadeh
    • 1
  • Mehdi Bidabadi
    • 1
  • Qingang Xiong
    • 2
    Email author
  • Nader Karimi
    • 3
  1. 1.School of Engineering, Mechanical Engineering DepartmentIran University of Science and TechnologyNarmak, TehranIran
  2. 2.IT Innovation Center, General MotorsWarrenUSA
  3. 3.School of EngineeringUniversity of GlasgowGlasgowUK

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