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Aggregation study of Brownian nanoparticles in convective phenomena

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Abstract

The explanation of abnormal enhancement of transported energy in colloidal nanoparticles in a liquid has sparked much interest in recent years. The complexity comes from the inter-particle phenomenon and cluster formation. The process of nanoparticle aggregation, which is caused by convective phenomena and particle-to-particle interaction energy in a flow, is investigated in this research. Therefore, the probability of collision and cohesion among clusters is modelled, as stated in this research. ANSYS-Fluent 17 CFD tools are employed to implement a new method of nanoparticle aggregation, new essential forces, new heat law and cluster drag coefficient. The importance of the interaction forces is compared to drag force, and essential forces are considered in coupling between nanoparticles and fluid flow. An important parameter is defined for the surface energy density regarding the attractive energy between the double layer and surrounding fluid to capture the cohesion of particles. Particles’ random migration is also presented through their angular and radial displacement. The analyses for interactions show the significance of Brownian motion in both particles’ migration and coupling effects in the fluid. However, nanoparticles are pushed away from walls due to repulsive forces, and Brownian motion is found to be effective mainly on angular displacement around the tube centreline. The attractive energy is found to be dominant when two clusters are at an equal distance. Hence, the cluster formation in convective regions should be taken into account for modelling purposes. A higher concentrated region also occurs midway between the centreline and the heated wall.

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Abbreviations

\(A\) :

Hamaker constant (J)

\(A_{\text{p}}\) :

Particle surface area (m2)

\(A_{\text{pp}}\) :

Particle projected area (m2)

\(C_{\text{c}}\) :

Cunningham correction factor

\(C_{\text{D}}\) :

Drag coefficient

\(C_{\text{ML}}\) :

Rotational coefficient

\(C_{\upomega}\) :

Rotational drag coefficient

\(c_{\text{p}}\) :

Specific heat (J kg−1 K−1)

\(d_{\text{p}}\) :

Particle diameter (m)

\(D_{\text{T}}\) :

Thermophoresis coefficient

\(f_{{{\text{B}}_{\text{i}} }}\) :

Brownian force (N kg−1)

\(f_{\text{s}}\) :

Interaction forces (N m−3)

\(f_{\text{d}}\) :

Drag function

\(G_{\text{w}}\) :

Gaussian weight function

h :

Particle–particle distance (m)

\(I_{\text{p}}\) :

Moment of inertia (kg m−2)

\(k\) :

Thermal conductivity (W m−1 K−1)

\(K_{\text{B}}\) :

Boltzmann constant (m2 kg K−1 s−2)

\(m_{\text{p}}^{{}}\) :

Particle mass (kg)

\(\dot{m}_{\text{p}}^{{}}\) :

Particle mass flow rate (kg s−1)

\(N_{\text{particle}}\) :

Number of particles in the parcel

\(n\) :

Possible number of collision

P :

Poisson distribution

\(Re_{\text{p}}\) :

Particle Reynolds number

\(S_{\text{h}}\) :

Thermal interaction between particles and fluid (W m−3)

\(\Delta t_{\text{p}}\) :

Particle time step (s)

U 1, U 2 :

Uniform random number

\(u_{\text{p}}\) :

Particle velocity (m s−1)

\(u_{\text{s}}\) :

Particle–fluid relative velocity (m s−1)

V EDL :

Electric double-layer energy (J)

V vdw :

van der Waals energy (J)

x :

Location (m)

\(\Delta x\) :

Characteristic length of the cell

\(We\) :

Webber number

\(\varepsilon_{0}\) :

Vacuum permittivity (CV−1 m−1)

\(\varepsilon {}_{\text{r}}\) :

Relative permittivity

\(\kappa\) :

Debye–Huckel parameter (m−1)

\(\gamma\) :

Surface energy density (J m−2)

\(\dot{\gamma }\) :

Shear rate (1/s)

\({\varvec{\upomega}}_{\text{p}}\) :

Particle angular velocity (1/s)

\({\varvec{\Omega}}\) :

Relative particle–liquid angular velocity (1/s)

\(\psi\) :

Potential on the surface of particle (V)

\(\theta_{\text{particle}}\) :

Particle variable in the node

\(\bar{\theta }_{\text{parcel}}\) :

Particle variables affected by nodes in the neighbourhood

\(\tau\) :

Particle relaxation time (s)

\(\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\rightharpoonup}$}} {\zeta }\) :

Random function

\(\chi\) :

Random number between 0 and 1

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Authors and Affiliations

  1. Department of Mechanical and Aeronautical Engineering, University of Pretoria, Pretoria, 0028, South Africa

    Mostafa Mahdavi, Mohsen Sharifpur & Josua P. Meyer

  2. Faculty of Mechanical Engineering, Shahrood University of Technology, Shahrood, Iran

    Mohammad H. Ahmadi

Authors
  1. Mostafa Mahdavi
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  2. Mohsen Sharifpur
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  3. Mohammad H. Ahmadi
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  4. Josua P. Meyer
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Correspondence to Mohsen Sharifpur or Mohammad H. Ahmadi.

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Mahdavi, M., Sharifpur, M., Ahmadi, M.H. et al. Aggregation study of Brownian nanoparticles in convective phenomena. J Therm Anal Calorim 135, 111–121 (2019). https://doi.org/10.1007/s10973-018-7283-y

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