Mathematical Modelling of Nanocrystal Growth

  • Claudia FanelliEmail author
  • Timothy G. Myers
  • Vincent Cregan
Conference paper
Part of the Mathematics in Industry book series (MATHINDUSTRY, volume 30)


We will describe a model for the process of synthesizing nanoparticles of a specific size from a liquid solution. Initially, we will consider a single particle model that accounts for monomer diffusion in solution around the particle and kinetic reactions at the particle surface. For the far-field bulk concentration, a mass conservation expression is used. Based on a small dimensionless parameter, we propose a pseudo-steady state approximation to the model. The model is then extended to a system of N particles. Numerical solutions for the time-dependent average particle radius compared against experimental data are shown to have excellent agreement.


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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Claudia Fanelli
    • 1
    • 2
    Email author
  • Timothy G. Myers
    • 1
    • 2
  • Vincent Cregan
    • 3
  1. 1.Centre de Recerca Matemàtica/BGSMathBarcelonaSpain
  2. 2.Universitat Politècnica de CatalunyaBarcelonaSpain
  3. 3.MACSI/PMTCUniversity of LimerickLimerickIreland

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